[EM] Ordering defeats in Minimax

[Andrew Myers]

Hi all,

I recently added Minimax to the algorithms supported by CIVS, because it
has some nice properties, especially regarding stability of the
ordering. However, there's a bit of a challenge lurking. Minimax as
classically defined assumes that all ballots are totally ordered. CIVS
allows ties, however. So for any pair of alternatives there is a (W, L)
pair where W is the number of people who prefer the first alternative
and L is the number who prefer the second.

Recall that Minimax chooses the alternative whose strongest defeat is
the weakest. What is the right way to define the ordering on defeats?

1. WV: (W1, L1) > (W2, L2) if W1 > W2 or (W1=W2 and L2 > L1)
[currently implemented]
2. Margins: (W1, L1) > (W2, L2) if W1 - L1 > W2 - L2
3. LV: (W1, L1) > (W2, L2) if L1 < L2 or (L1 = L2 and W1 > W2)

I'm sure this has been discussed already at great length. Your advice is
appreciated.

Best,

-- Andrew
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[Kristofer Munsterhjelm]

Post by Andrew Myers
Hi all,
I recently added Minimax to the algorithms supported by CIVS, because it
has some nice properties, especially regarding stability of the
ordering. However, there's a bit of a challenge lurking. Minimax as
classically defined assumes that all ballots are totally ordered. CIVS
allows ties, however. So for any pair of alternatives there is a (W, L)
pair where W is the number of people who prefer the first alternative
and L is the number who prefer the second.
Recall that Minimax chooses the alternative whose strongest defeat is
the weakest. What is the right way to define the ordering on defeats?
1. WV: (W1, L1) > (W2, L2) if W1 > W2 or (W1=W2 and L2 > L1)
[currently implemented]
2. Margins: (W1, L1) > (W2, L2) if W1 - L1 > W2 - L2
3. LV: (W1, L1) > (W2, L2) if L1 < L2 or (L1 = L2 and W1 > W2)
I'm sure this has been discussed already at great length. Your advice is
appreciated.

It depends on what properties you want. The most obvious difference that
comes to mind: Minmax(wv) passes the Plurality criterion (if I recall
correctly) whereas Minmax(margins) passes Mono-add-top; but wv doesn't
pass MAT and margins doesn't pass Plurality.

I'm usually a wv person, but I think Minmax is more classically
associated with margins. Or perhaps I think that because Juho is here
and he prefers margins :-)

On a side note, Minmax can produce a lot of ties if there are few voters
involved, so sometimes I prefer to break ties by second strongest defeat
(and then third strongest, fourth strongest, etc). That isn't
*classical* Minmax, but it shouldn't break any of Minmax's criteria.
----
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[Kevin Venzke]

Yes, WV satisfies Plurality. In fact margins methods are among the only serious proposals that don't satisfy it. This propertysays that e.g. A can't win in this scenario:
7 A>B5 B8 C
Methods that have added Smith compliance to MinMax usually call for WV. Schulze's paper describing the Schulze methodused to say that there had been discussion concluding that margins wasn't recommended due to strategic reasons, though Ican't find that language there anymore. That being said, I would be a bit surprised to learn that anyone using Schulze has chosen a margins version of it.
The issue is pretty controversial and becomes complicated when you get into the strategic implications. Arguments that margins just "makes more sense" than WV are common, but I find them rather abstract in comparison to what I think voterswould expect from a method.
As an example of the latter, suppose there is only one pairwise contest A>B in which all of the voters expressed a strictpreference. Say it was very close, 51%-49%. The margins logic is that this contest is fair game to be discarded because ofhow close a race it was. But I would say that this contest is probably the one that the voters view as the most important one,everyone having voted on it, and they would not expect its loser to be elected. They (at least the 51%) will likely view thisas a spoiler situation, as whatever other candidates were in the race (to cause this outcome) did not themselves win; theysimply threw the race to the candidate who (without their presence) would have lost.
The desire to say that a 35-0 win is stronger than a 51-49 win could make sense if a strong win in itself was of some value.But all that realistically matters is who wins the entire race. If the 35-0 winner is not in a position to get elected, there is nothing to be gained in letting that contest affect the outcome. It doesn't aid him or his supporters, it is pure noise. It couldas well be treated as zero strength.
Kevin

De : Kristofer Munsterhjelm <***@t-online.de>
À : Andrew Myers <***@cs.cornell.edu>; Election Methods <election-***@lists.electorama.com>
Envoyé le : Mardi 25 avril 2017 3h08
Objet : Re: [EM] Ordering defeats in Minimax

Post by Andrew Myers
Hi all,
I recently added Minimax to the algorithms supported by CIVS, because it
has some nice properties, especially regarding stability of the
ordering. However, there's a bit of a challenge lurking. Minimax as
classically defined assumes that all ballots are totally ordered. CIVS
allows ties, however. So for any pair of alternatives there is a (W, L)
pair where W is the number of people who prefer the first alternative
and L is the number who prefer the second.
Recall that Minimax chooses the alternative whose strongest defeat is
the weakest. What is the right way to define the ordering on defeats?
1. WV: (W1, L1) > (W2, L2) if W1 > W2 or (W1=W2 and L2 > L1) 
[currently implemented]
2. Margins: (W1, L1) > (W2, L2) if W1 - L1 > W2 - L2
3. LV: (W1, L1) > (W2, L2) if L1 < L2 or (L1 = L2 and W1 > W2)
I'm sure this has been discussed already at great length. Your advice is
appreciated.

It depends on what properties you want. The most obvious difference that
comes to mind: Minmax(wv) passes the Plurality criterion (if I recall
correctly) whereas Minmax(margins) passes Mono-add-top; but wv doesn't
pass MAT and margins doesn't pass Plurality.

I'm usually a wv person, but I think Minmax is more classically
associated with margins. Or perhaps I think that because Juho is here
and he prefers margins :-)

On a side note, Minmax can produce a lot of ties if there are few voters
involved, so sometimes I prefer to break ties by second strongest defeat
(and then third strongest, fourth strongest, etc). That isn't
*classical* Minmax, but it shouldn't break any of Minmax's criteria.
----
Election-Methods mailing list - see http://electorama.com/em for list info

[Kristofer Munsterhjelm]

Post by Kevin Venzke
Yes, WV satisfies Plurality. In fact margins methods are among the only
serious proposals that don't satisfy it. This property
7 A>B
5 B
8 C
Methods that have added Smith compliance to MinMax usually call for
WV. Schulze's paper describing the Schulze method
used to say that there had been discussion concluding that margins
wasn't recommended due to strategic reasons, though I
can't find that language there anymore. That being said, I would be a
bit surprised to learn that anyone using Schulze has
chosen a margins version of it.

From a criterion perspective, that makes sense. Smith,Minmax doesn't
pass mono-add-top anyway, so you might as well pick up Plurality on your
way by going wv.

Post by Kevin Venzke
The issue is pretty controversial and becomes complicated when you get
into the strategic implications. Arguments that
margins just "makes more sense" than WV are common, but I find them
rather abstract in comparison to what I think voters
would expect from a method.

Warren wrote about wv versus margins here:
http://rangevoting.org/WinningVotes.html and seems to have reached
roughly the same conclusion. That is, that margins can in some ways be
more "natural", but wv is more strategy resistant. (He then says that it
doesn't much matter because both wv and margins are vulnerable to DH3. A
method like Smith,IRV is more robust to DH3, but wv vs margins doesn't
matter to that method.)

Post by Kevin Venzke
As an example of the latter, suppose there is only one pairwise contest
A>B in which all of the voters expressed a strict
preference. Say it was very close, 51%-49%. The margins logic is that
this contest is fair game to be discarded because of
how close a race it was. But I would say that this contest is probably
the one that the voters view as the most important one,
everyone having voted on it, and they would not expect its loser to be
elected. They (at least the 51%) will likely view this
as a spoiler situation, as whatever other candidates were in the race
(to cause this outcome) did not themselves win; they
simply threw the race to the candidate who (without their presence)
would have lost.
The desire to say that a 35-0 win is stronger than a 51-49 win could
make sense if a strong win in itself was of some value.
But all that realistically matters is who wins the entire race. If the
35-0 winner is not in a position to get elected, there is
nothing to be gained in letting that contest affect the outcome. It
doesn't aid him or his supporters, it is pure noise. It could
as well be treated as zero strength.
Kevin

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Election-Methods mailing list - see http://electorama.com/em for list info

[Juho Laatu]

1. WV: (W1, L1) > (W2, L2) if W1 > W2 or (W1=W2 and L2 > L1) [currently implemented]
2. Margins: (W1, L1) > (W2, L2) if W1 - L1 > W2 - L2
3. LV: (W1, L1) > (W2, L2) if L1 < L2 or (L1 = L2 and W1 > W2)

Those functions make sense to me. I would maybe separate the basic WV, margins and LV definitions from the additional tie breaker definitions ("W1=W2 and L2 > L1" and "L1 = L2 and W1 > W2").

I'm usually a wv person, but I think Minmax is more classically
associated with margins. Or perhaps I think that because Juho is here
and he prefers margins :-)

The strongest argument in favour of margins must be that it is a relatively natural preference function. WV and LV are discontinuous functions and therefore can not really be called natural. Interest in using them comes mainly form strategic defence reasons, not from studying what would be a natural way of measuring strengths of preference. In addition the results that you get close to those discontinuities may appear strange (one additional vote may change the outcome radically).

Preference function between two candidates (A, B) can be given as a function of x and y, where x is the proportion of votes (0..1) ranking A over B, and y is the proportion of votes (0..1) ranking B over A. The values of the function range from 1 (100% of voters rank A over B) to -1 (100% of voters rank B over A). Value 0 refers to a tie.

Margins preference function is x-y
WV preference function is 0 if x=y, x if x>y, -y if y>x
LV preference function is 0 if x=y, 1-y if x>y, x-1 if y>x

WV and LV are not continuous around the x=y line. It is for example strange that in WV result 51-49 is considered a strong victory to A (0.51), while 50-50 gives 0 and 49-51 gives -0.51.

There are also other possible preference functions. One could measure for example the proportion of A>B preferences against all given preferences (A>B or B>A). This one is close to margins in the sense that it can be seen as one natural preference function. It is also smooth and continuous, except that at point 0-0 it is not even defined. The value of result 1-0 is 1, and the value of result 0-1 is -1, which is a quite radical approach.

Margins and proportions have different philosophy with respect to votes that have not given any preference between A and B (indifferent voters). Margins thinks that indifferent voters gave half a vote to support A>B and half a vote to support B>A. Preferences thinks that indifferent voters want to vote in favour of A vs B in same proportion as those voters did that gave a preference. Both approaches can thus be explained as natural approaches to explaining how the indifferent votes should be read.

The desire to say that a 35-0 win is stronger than a 51-49 win could
make sense if a strong win in itself was of some value.

This (comparison of different results) is a good approach to evaluating how the indifferent votes should be handled. I already wrote above on how proportions could be considered bad around the 0-0 result. In margins it is a good question if 2-0 should be considered to have equal preference strength to 51-49.

I'll define some additional preference strength functions (P). I start from the assumption that margins philosophy can be taken as the starting point for results where all voters have expressed preference (= no indifferent votes). As a result preference value for 100-0 is 1 (for all preference functions of this group of P functions), i.e. P(100,0)=1, and P(50,50)=0, and P(75,25)=0.5. The preference function is thus linear at that line (y = 1-x). Preference value should also always be 0 at line x=y. More formally, P(x,x)=0 and P(x,1-x)=2x-1. We should require also symmetry, P(x,y)=-P(y,x).

One family of preference functions that meets these criteria is (x-y)*(x+y)^k. We get margins when k=0. We get proportion when k=-1. The next interesting possibility is to use value k=1. This one is interesting because it has some WV like properties without introducing the weird discontinuities of WV. I'll study this function (k=1) a bit more.

(Note that when k=1 the function becomes quite simple, (x-y)*(x+y)^1 = x^2 - y^2.)

First few words about sincere votes. In margins the preference values of 50-0 and 75-25 are equal. Pm(50,0) = Pm(75,25). If one doesn't think this is ideal, one can adjust this relation by adjusting the value of k. When k=1 (P1) we have P1(75,25) = 0.5 (by definition). P1(50,0) = 0.25, Pm(50,0) = 0.5 and Pp(50,0) = 1 (p = proportion). The point of this paragraph is to demonstrate that if you want to have a P that gives best possible results with sincere votes, one can adjust k to reach best performance (within this family of preference functions). One parameter may be enough to address the most typical concerns (?).

What about defence against strategic voting then. In many large public elections such defences may be unnecessary. But for for people that like the WV properties P1 may be of interest also for strategy defence related reasons. It for example gives P1(10,0) = 0.01 while P1(55,45) = 0.1. I will not go further into details although it could be interesting to study the impact of parameters to strategic defence capabilities. The point here is that there are also continuous "natural" preference functions that can reach some of the targets of discontinuous functions like WV.

If one uses parameterized preference functions like the one described above, one can also adjust the parameters (k) so that the function reaches the required strategy resistance, but at the same time deviates from the preferred sincere preference function only as little as possible.

On a side note, Minmax can produce a lot of ties if there are few voters
involved, so sometimes I prefer to break ties by second strongest defeat
(and then third strongest, fourth strongest, etc). That isn't
*classical* Minmax, but it shouldn't break any of Minmax's criteria.

I just note that the parameterized versions may also reduce the probability of ties (e.g. if one uses value k=0.00001 instead of k=0).

Juho



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[Juho Laatu]

At least one correction / improvement already detected.

Post by Juho Laatu
LV preference function is 0 if x=y, 1-y if x>y, x-1 if y>x

I should have written "0 if x=y, 1-2y if x>y, 2x-1 if y>x". That does not change the results, but gives more logical values to the preference function. P_LV(x,y) is now close to 0 when x and y are close to 0.5.

Juho


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[robert bristow-johnson]

---------------------------- Original Message ----------------------------

Subject: [EM] Fwd: Ordering defeats in Minimax

From: "Juho Laatu" <***@gmail.com>

Date: Wed, April 26, 2017 2:09 pm

To: "Election Methods" <election-***@lists.electorama.com>

--------------------------------------------------------------------------

Post by Juho Laatu

1. WV: (W1, L1) > (W2, L2) if W1 > W2 or (W1=W2 and L2 > L1) [currently implemented]
2. Margins: (W1, L1) > (W2, L2) if W1 - L1 > W2 - L2
3. LV: (W1, L1) > (W2, L2) if L1 < L2 or (L1 = L2 and W1 > W2)

Those functions make sense to me. I would maybe separate the basic WV, margins and LV definitions from the additional tie breaker definitions ("W1=W2 and L2 > L1" and "L1 = L2 and W1 > W2").

I'm usually a wv person, but I think Minmax is more classically
associated with margins. Or perhaps I think that because Juho is here
and he prefers margins :-)

The strongest argument in favour of margins must be that it is a relatively natural preference function. WV and LV are discontinuous functions and therefore can not really be called natural. Interest in using them comes mainly form strategic defence reasons, not from studying what would be a

natural way of measuring strengths of preference. In addition the results that you get close to those discontinuities may appear strange (one additional vote may change the outcome radically).
Another "natural" reason to favor margins over winning votes to compare one pairwise outcome over another is that the net margin, in votes, is the product of two other indicators of salience. it is the product of the margin in percent and the number of voters participating.
 Or "How loud did the voters speak in this pairwise election?" times "How many voters were there?"
I mean, which more important?  That 1025 voters prefer Tom to 975 voters who prefer Harry?  Or that 525 voters that prefer Dick to 475 prefer Tom?   Or
 2024 voters prefer Harry over 1976 voters who prefer Dick?
The second pair has the most decisive defeat from a percentage POV.  A 5% win for Dick.
The third pair has the most winning votes, Harry gets a wopping 2024 votes but Dick gets nearly as much, and despite just killing
Tom, percentwise, Dick is eliminated.  and for Harry to win when Tom defeats him by more votes than Harry defeats Dick seems odd.
--
r b-j                  ***@audioimagination.com
"Imagination is more important than
knowledge.

[Juho Laatu]

Post by robert bristow-johnson
---------------------------- Original Message ----------------------------
Subject: [EM] Fwd: Ordering defeats in Minimax
Date: Wed, April 26, 2017 2:09 pm
--------------------------------------------------------------------------

Post by Juho Laatu

1. WV: (W1, L1) > (W2, L2) if W1 > W2 or (W1=W2 and L2 > L1) [currently implemented]
2. Margins: (W1, L1) > (W2, L2) if W1 - L1 > W2 - L2
3. LV: (W1, L1) > (W2, L2) if L1 < L2 or (L1 = L2 and W1 > W2)

Those functions make sense to me. I would maybe separate the basic WV, margins and LV definitions from the additional tie breaker definitions ("W1=W2 and L2 > L1" and "L1 = L2 and W1 > W2").

I'm usually a wv person, but I think Minmax is more classically
associated with margins. Or perhaps I think that because Juho is here
and he prefers margins :-)

The strongest argument in favour of margins must be that it is a relatively natural preference function. WV and LV are discontinuous functions and therefore can not really be called natural. Interest in using them comes mainly form strategic defence reasons, not from studying what would be a natural way of measuring strengths of preference. In addition the results that you get close to those discontinuities may appear strange (one additional vote may change the outcome radically).

Another "natural" reason to favor margins over winning votes to compare one pairwise outcome over another is that the net margin, in votes, is the product of two other indicators of salience. it is the product of the margin in percent and the number of voters participating. Or "How loud did the voters speak in this pairwise election?" times "How many voters were there?"
I mean, which more important? That 1025 voters prefer Tom to 975 voters who prefer Harry? Or that 525 voters that prefer Dick to 475 prefer Tom? Or 2024 voters prefer Harry over 1976 voters who prefer Dick?
The second pair has the most decisive defeat from a percentage POV. A 5% win for Dick.
The third pair has the most winning votes, Harry gets a wopping 2024 votes but Dick gets nearly as much, and despite just killing Tom, percentwise, Dick is eliminated. and for Harry to win when Tom defeats him by more votes than Harry defeats Dick seems odd.
--
"Imagination is more important than knowledge.
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I agree that it is important to understand how strong different pairwise preference results should be considered. In the generic preference function that I gave I to some extent tried to answer your question "How many voters were there?", and find a parameter (k) that could be adjusted to set the balance right (between high number and low number of voters that indicated their preference). In the function ( (x-y)*(x+y)^k ) the "x-y" part sets the margins approach as a starting point. The "(x+y)^k" part can be seen as an adjustment factor that takes into account the number of votes that had an opinion "x+y". Constant k tells us how much we should weaken (k>0) or strengthen (k<0) the pairwise comparison result in the case that not all voters gave their preference.

Juho

[robert bristow-johnson]

---------------------------- Original Message ----------------------------

Subject: Re: [EM] Ordering defeats in Minimax

From: "Juho Laatu" <***@gmail.com>

Date: Thu, April 27, 2017 6:15 pm

To: "Election Methods" <election-***@lists.electorama.com>

--------------------------------------------------------------------------

Post by Juho Laatu
I agree that it is important to understand how strong different pairwise preference results should be considered. In the generic preference function that I gave I to some extent tried to answer your question "How many voters were there?", and find a parameter (k) that could be

adjusted to set the balance right (between high number and low number of voters that indicated their preference). In the function ( (x-y)*(x+y)^k ) the "x-y" part sets the margins approach as a starting point. The "(x+y)^k" part can be seen as an adjustment factor that takes into
account the number of votes that had an opinion "x+y". Constant k tells us how much we should weaken (k>0) or strengthen (k<0) the pairwise comparison result in the case that not all voters gave their preference.
okay, i wanna restate this with the Wn and Ln symbols.
 
  (W1, L1) > (W2, L2)   means
 
   (W1-L1)*(W1+L1)^k   >   (W2-L2)*(W2+L2)^k 
 
now, if k=0, this is the same as what i am coining as
"Arithmetic Margins" (for lack of a better term).  if k = -1, then it's the same as the percentage margin, where a larger race has no more weight than a smaller race if the percent margins are the same.  this is, i believe, going to have equivalent outcome as Markus's margins of
logarithms (what i coined "Geometric Margins").
If someone has better terminology for naming these different forms of margins, please correct my neologism before it takes root.



--
r b-j                  ***@audioimagination.com
"Imagination is more important than knowledge."

[Juho Laatu]

Also this mail is a late rely. This time I had some additional problems since I didn't receive this mail in my unbox at all. I found it in the electorama mail archives. The mail traffic between electorama and me doesn't always work perfectly.

Post by Andrew Myers
Hi all,
Kristofer wrote:>Do you consider Plurality a strategic criterion? It seems to me to be>more of a "natural behavior" criterion
FWIW I don't consider Plurality a strategy criterion.

I already answered Kristofer's question once, but I was maybe not as clear as I should have been. I agree that Plurality can be classified as a criterion that is intended to be a "natural behaviour" criterion. I used term "heuristic", that os close to "intended to be a natural behaviour". Plurality is however often linked with winning votes, that I consider to be a very "strategic behaviour" related comparison method.

Post by Andrew Myers
We can bring up strategy criteriaif we wanted to, but they are more obscure than the Woodall criteria. The best knownone worth bringing up is favorite betrayal, but WV methods don't completely satisfy it,so I would be stuck talking about simulations instead of firm guarantees.
(You may ask why does favorite betrayal come into it? Because the same incentives thatare supposed to discourage margins voters from truncating at the bottom, also discouragethem from equal-ranking a set of favorites at the top. And there isn't a mechanism ensuringthat ideal strategy is to simply rank them sincerely.)
I would say margins' largest issues are strategy-related, but its most obvious issuesaren't, so I prefer to talk about "natural behavior" when I have a choice.
You feel criteria are "too far from practical election method considerations to be applieddirectly on them as viability criteria"; that is actually very close to how I view yourcriteria (even if you don't use the term "criteria"). You say the "strongest argument" formargins is that it is a relatively natural and continuous preference function.
I guess that you don't say that this involves "practical considerations," and it's justan aesthetic preference.

I often talk about performance with sincere votes when I'm not talking about performance against strategies. That is practical (although also aesthetic, like many things in formal systems :-) ).

Post by Andrew Myers
I give you credit for consistency in not even mentioning mono-add-top, which could easily be argued to be a practical consideration. On the otherhand you seem to believe WV has effective strategy incentives that result in things you don't like, so you don't seem to completely dismiss practical considerations either.

My thinking is often based on the assumption that in typical large public elections with independent voters strategic risks are not very high. I'd expect almost all Condorcet elections to be quite strategy free in practice. In most countries people would vote for the best candidates, not in some other way, trusting that giving false rankings or omitting preferences would help them in the election.

For this reason my practical considerations often tend to focus on the above mentioned performance with sincere votes. I tend to "like" margins more than winning votes not because of differences in their behaviour in the presence of strategic voting, but because of their differences in performance with sincere votes. For example with votes 51: A, 40 B>C I like more the margins thinking that C is 48 (sincere) votes away from winning the election than the winning vote thinking that C is 3 (sincere) votes away from winning the election. If we can afford to use a natural pairwise comparison method, why not use it.

Post by Andrew Myers
I find it more accurate when you complain that WV seems like an approval hybrid thanwhen you suggest that interest in WV stems from strategic defense concerns. When peopleinvent random new methods on EM they frequently behave like WV (or IRV); it's very hard toemulate margins' results without actually being margins. Methods that show approval-likebehavior stem from a relatively common expectation that expressed votes are a goodindication of viability/merit.

Yes, I'm looking forward to such use of Condorcet methods where voters rank multiple candidates, to rank all the potential winners, in the hope of allowing the fair algorithm to pick the best winner. I hope people will understand that most likely their best strategy is to do just that.

Post by Andrew Myers
There may be good historical reasons to portray WV as ahorrified reaction to margins... And I can imagine the FPP supporter who says interest inIRV "comes mainly from strategic defense reasons."

One reason behind the popularity of IRV, when compared to Condorcet, could be its tendency to favour large incumbent parties. (Another one is its interesting dramatic elimination process that appears more natural than it is.)

Post by Andrew Myers
But that seems like a limited way oflooking at it.
You write:>I think Plurality is a bit strange. Actually it is not even a criterion >of ranked methods. It is a criterion for ranked methods with implicit>approval cutoff. It makes the assumption that a voter that casts a short>vote has somehow approved those candidates that he marked, and not approved>the others. In different elections the behaviour of voters with respect>to which candidates will be marked on the ballot may vary a lot, and that>may have nothing to do with how much the voters support or approve those >candidates. In order to make any sense of the Plurality criterion we are >thus tied to having an assumption of implicit approval in the ballots, >where marking a candidate means approving that candidate at some level.
I think voters expect this behavior, and that's why it's important, for example, forthe long-term viability of the method's adoption. Now, you may say that we could convince voters not to expect this.

Yes, they should be educated if they ever get that kind of ideas somewhere.

Post by Andrew Myers
You might even (though I'm still not 100% sure)manage to do this by forbidding voters from truncating at all. In that case, I woulddrop all my objections dealing with naturalness and what voters expect. My remainingcomplaints at that point would be the strategy-related ones.

I don't want to forbid truncation because I want voting to be easy and pleasant, and I want to have a reasonably high number of candidates. If insincere truncation turns out to be a problem that threatens the soundness of the results in some elections, maybe one could try other tricks first, like e.g. completing the vote with random candidates or using some party preference list to complete the vote. I'm however living in the hope that in most cases none of these tricks are needed.

Post by Andrew Myers
One reason why I don't like implicit approval in general (as a fact that>is known by the voters) is that it encourages voters not to rank candidates>that they don't like.
Sure, I would rather criticize how margins addresses this than the fact that it triesto address it. IRV does this, for instance: You can rank the worse frontrunner in asincere way and you know that it won't hurt you. In margins we "want" you to rank theworse frontrunner, but it's not expected to be of any use to you, and it can hurt thebetter frontrunner by making "worse" look like your compromise choice.

Yes, but what is the probability of hurting one's targets by ranking numerous candidates in a Condorcet election with a bunch of potential winners and few additional candidates that are unlikely to win? And what are the benefits of ranking all the potential winners?

Post by Andrew Myers
I'm not well prepared to comment how margins can handle Plurality>criterion but I'll address one basic (but theoretical and extreme,>i.e. unlikely to happen in typical elections) example. 35:A, 34:B>C,>31:C. A has more first preferences than B has ballots where B is>marked. B's worst defeat margin is however smallest (1), so it will>win in typical margins based methods. Plurality criterion says that B>should not win. B is however two votes short of being a Condorcet>winner, so it can't be the worst of the worst. What if A would win?>Plurality criterion pays special attention to A's high number of first>preferences. But on the other hand voters would like to elect C>instead of A with large majority (C>A voters would not be happy with>the result). How about C then? Plurality criterion accepts C too, but>using the high number of first preference votes of A as an argument >that supports C does not make much sense. My conclusion is that this>is a typical mess that we can get with circular preferences. Our>voters were quite stupid when they didn't sufficiently rank the >potential winners. There are many different possible scenarios on what>the truncated opinions might have been, and different results emerging>from that. In this example my recommendation would be to tell to the>voters that they should rank all potential winners (except maybe the>worst one). I don't see any need to start blaming (or praising) margins>on what happened. Maybe you have some realistic examples in your mind,>that would give better justification to the Plurality criterion.
1. I just note that "fewest votes short of being a Condorcet winner" need notstrike one as a particularly less arbitrary standard than Plurality. I do not knowwhat stops one from dismissing yours as a criterion whose "message somehow soundsgood to people that do not regularly deal with election methods." It does "soundgood," I agree with that.

Democracies typically work via majorities, and majorities are generated by voters. To me the required number of additional voters to reach majority is a very natural measure of the popularity of some idea. I'm having hard time trying to invent something that would be a more natural measure.

Post by Andrew Myers
2. I'm not sure what is your basis for calling these voters "stupid." Are you(rhetorically) employing Plurality's assumption that voters didn't like theoutcome? I get the sense that you don't like the outcome yourself.

I referred to truncation of votes that obviously made it impossible for the election method to decide who the ideal winner is. The voters maybe failed to tell whom they would like to elect.

It is also possible that all truncations were sincere (opinions where all the remaining candidates were equally good). In that case any method with good/desired performance with sincere votes would do the job fine. It is however typical that people have clear opinions about the three potential winners, and therefore it is probable that many of the voter that truncated had some opinions that they didn't express. Giving fuller rankings would probably be in their interest (in typical elections).

Post by Andrew Myers
3. I do understand feeling that Plurality is strange. I don't love it. My view isthat Plurality is an easily articulated subset of a larger principle. Essentially,if the voters were instead legislators selecting an outcome, could B ever prevail?It seems quite unlikely, because at the moment that C is the status quo and the Bvoters wish to assert their win over C, they can't because they are outnumbered bythe A voters. The pairwise contest doesn't occur in a vacuum. In this case Pluralityconveys what I would want.

Voting about things vs. persons is about the same. Condorcet is a good method if one wants to elect a good compromise winner. In a small community where people think that they know beforehand how others will vote, and where the party leaders and strategists possibly can force the voters to vote as told, strategic problems are more likely to occur than in large public elections with independent voters. Condorcet could however work well also in such small and strategy prone environments. The problems of cyclic group opinions are incurable. If opinions have a top cycle, there will be a majority that would like to change the outcome to something else. In small political circles the solution could often be to make an agreement with some other party, I will get this and you will get that, and then vote accordingly. This is more probable than leaving uncertain decisions and expected circular opinions to be solved by a rather random outcome of a vote, or even more random outcome of a vote with strategic moves by multiple parties.

Post by Andrew Myers
A more thorough version of Plurality (in my opinion, to my taste) wouldn't talkabout first preferences or votes in total. I doubt this language is necessary toexpress the idea. (The criterion we do have is easy to apply, though.)

Yes, Plurality's reference to first preferences is not good. If one wants to say something more generic that is not tied to first preference votes, one should reformulate the criterion. The criterion would not be as sexy that way. Also the use of implicit approval should be made clearer, if the intention is to say something about voters that assume it, or a method that makes some use of it.

Juho

Post by Andrew Myers
Kevin

[Kevin Venzke]

Hi Juho,

De : Juho Laatu <***@gmail.com>
À : Election Methods <election-***@lists.electorama.com> 
Envoyé le : Jeudi 4 mai 2017 17h02
Objet : Re: [EM] Ordering defeats in Minimax

Also this mail is a late rely. This time I had some additional problems since >I didn't receive this mail in my unbox at all. I found it in the electorama >mail archives. The mail traffic between electorama and me doesn't always work>perfectly.

Ok, I will be sure to copy you. I don't receive all the traffic either.

I already answered Kristofer's question once, but I was maybe not as clear as>I should have been. I agree that Plurality can be classified as a criterion>that is intended to be a "natural behaviour" criterion. I used term>"heuristic", that os close to "intended to be a natural behaviour". Plurality>is however often linked with winning votes, that I consider to be a very>"strategic behaviour" related comparison method.

Well, Plurality is "linked" to WV only because it creates a contrast with margins. If you were comparing margins to IRV or to Bucklin one would stillbring up Plurality.

Sure, I would rather criticize how margins addresses this than the fact>>that it tries to address it. IRV does this, for instance: You can rank the>>worse frontrunner in a sincere way and you know that it won't hurt you. In>>margins we "want" you to rank the worse frontrunner, but it's not expected>>to be of any use to you, and it can hurt the better frontrunner by making>>"worse" look like your compromise choice.>>Yes, but what is the probability of hurting one's targets by ranking>numerous candidates in a Condorcet election with a bunch of potential winners>and few additional candidates that are unlikely to win? And what are the>benefits of ranking all the potential winners?

It's not whether they are ranked (margins will essentially force me to rankthem, I think), it's whether I decide to rank them sincerely. I think thespecific questions the voter might ask themselves are fairly clear.
Margins gives me the most heartburn when I consider how to rank the worstof the potential winners relative to the "additional" candidates who are"unlikely" to win and who may well be unqualified to hold the office. As Iwrote above, there is no realistic gain for me to indicate that the worstfrontrunner is better than anybody, and there could be a cost. The odds ofthe latter? I don't know, but I'm comparing "something" to a 0% chance, and that could certainly allow me to make a decision.
(It's possible that people like me raise that 0% to something higher.You should hope that doesn't happen. But yes, it would force me to think further about my strategy.)

Voting about things vs. persons is about the same. Condorcet is a good>method if one wants to elect a good compromise winner. In a small>community where people think that they know beforehand how others will>vote, and where the party leaders and strategists possibly can force the>voters to vote as told, strategic problems are more likely to occur than>in large public elections with independent voters.

We have elections because we can't just invite all the voters to aconference. The voters fill out a ballot and hope that the method will bea good steward of their interests. Legislators usually don't use electionmethods. I would say essentially they figure out among themselves whatthe outcome likely must be and then "elect" it, typically by a majorityvote. If voters could do that directly I think that would be the idealsituation, as far as minimizing the need for strategy.
I'm not sure if you thought I was talking about a legislature usingCondorcet. What I was saying is that I don't think the behavior of alegislature would be emulated well by, for example, picking any arbitraryoption from the top cycle. Some of those options may not be plausibleoutcomes, despite what the pairwise matrix says.

Yes, Plurality's reference to first preferences is not good. If one >wants to say something more generic that is not tied to first>preference votes, one should reformulate the criterion. The criterion>would not be as sexy that way. Also the use of implicit approval should>be made clearer, if the intention is to say something about voters that>assume it, or a method that makes some use of it.

One idea is that Plurality approximately says that if candidate X winsthen there should be some way to place approval cutoffs within therankings such that X is the approval winner. (First preferences comeinto play because it's assumed no one would disapprove those.)
Kevin

[Juho Laatu]

Post by Kevin Venzke
It's not whether they are ranked (margins will essentially force me to rank
them, I think), it's whether I decide to rank them sincerely.

I think all Condorcet methods have a severe incentive to apply one particular strategy. That is the strategy of sincerity, or the strategy if voting / casting one's vote. There is an incentive to rank all the potential winners (one can rank them all by listing all except one of them in the ballot).

All potential members of a top loop are included in the definition of potential winners. Both sincere and strategic potential winners are included in the definition.

Let's assume that in some group of voters all prefer A to B but they don't rank candidates A and B. B wins the election, and A is not too far behind. It is obvious that those voters would have had a better strategy, the strategy of expressing their opinion on whether A or B should win. This is not a rare incident if it is common among the voters not to rank many of the potential winners. This could thus be the most common mistake that a voter might make in an election. It is about as severe as staying home in a Plurality election, and then wondering afterwards, why the favourite of our group did not win.

Wouldn't you call this a strong strategic incentive? :-) The impact of many other strategies could be much weaker and more improbable. Any strategy that includes truncation would force you not to follow this strategy. And strategies that include changing the order of some of the candidates could be even more catastrophic. These effects are particularly strong in large public elections where nobody has accurate prior knowledge on how people are going to vote, or how much and what strategies they might apply.

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in some parliaments. Although negotiations and Plurality can be used to solve many cases, also Condorcet and the idea of having multiple candidates could have some benefits. The first one in my mind is openness. Even when the "big boys" have agreed something behind the screens, and then bring that decision into a majority vote, some smaller groupings could add some alternatives in the election that they consider better. This would open up the available alternatives to the world (media, public), and all voters would have to take position on the presented alternatives. Small parties or groupings could thus make sensible compromise proposals that might even win, if they are good enough.

Post by Kevin Venzke
I'm not sure if you thought I was talking about a legislature using
Condorcet. What I was saying is that I don't think the behavior of a
legislature would be emulated well by, for example, picking any arbitrary
option from the top cycle. Some of those options may not be plausible
outcomes, despite what the pairwise matrix says.

I think what I was thinking wast only that in small closed circles where everyone knows everyone's opinions strategic tricks are easier (but not easy) to apply than in typical large public elections.

I think Condorcet does pretty good job also when there are non-plausible alternatives in the election. If some option is really bad, it would not end up in the top cycle. Or do you expect strategic voting to be so rampant that legislators would use their most disliked options in their strategies and eventually elect them? A sensible voter should rank the non-plausible non-wanted options last.

Post by Kevin Venzke

Post by Juho Laatu
Yes, Plurality's reference to first preferences is not good. If one
wants to say something more generic that is not tied to first
preference votes, one should reformulate the criterion. The criterion
would not be as sexy that way. Also the use of implicit approval should
be made clearer, if the intention is to say something about voters that
assume it, or a method that makes some use of it.

One idea is that Plurality approximately says that if candidate X wins
then there should be some way to place approval cutoffs within the
rankings such that X is the approval winner. (First preferences come
into play because it's assumed no one would disapprove those.)

That's a good approach. Ability to win an Approval election (without changing the rankings) says pretty much everything that the traditional Plurality definition should say. Maybe it should be called and Approval criterion or something like that instead (word "Plurality" is quite confusing even with the original definition).

First preferences have an impact since they are the extreme top position in the rankings. A good definition should however not include any references to them. One viewpoint to this is that we can always add to an election n new candidates where n = number of voters. Each voter has now his own private candidate that is ranked first in one vote and last in all other votes. The results should still be the same, although all the old candidates now have zero first preference votes.

Juho

[Kristofer Munsterhjelm]

Post by Juho Laatu

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

I think some parliaments use the following procedure for multiple
proposals or amendments:

Some group decides the agenda (I'm not sure who; it probably depends on
the parliament in question).

Then the parliament discusses the first two options, and does a majority
vote between the two. It then does a majority vote between the winner so
far and the next option, and so on until all options have been
considered. The winner at the end of the procedure is the option that is
accepted.

This method is Condorcet (because the CW beats everybody pairwise, and
so whenever it becomes the winner so far, it'll stay the winner so far;
and whenever it's the challenger, it will win against the winner so far
and become the next winner so far). Furthermore, it's Smith. How cycles
are broken depends on the agenda.
----
Election-Methods mailing list - see http://electorama.com/em for list info

[Juho Laatu]

Post by Juho Laatu

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

Some group decides the agenda (I'm not sure who; it probably depends on the parliament in question).
Then the parliament discusses the first two options, and does a majority vote between the two. It then does a majority vote between the winner so far and the next option, and so on until all options have been considered. The winner at the end of the procedure is the option that is accepted.
This method is Condorcet (because the CW beats everybody pairwise, and so whenever it becomes the winner so far, it'll stay the winner so far; and whenever it's the challenger, it will win against the winner so far and become the next winner so far). Furthermore, it's Smith. How cycles are broken depends on the agenda.

Yes, this is some sort of "serial Condorcet". The biggest problem of this approach is probably the agenda based cycle breaking that you mentioned.

If there is a Condorcet winner, it will win. But if there is any chance of having a cycle, then the chairman (if he decides the agenda) may arrange the agenda so that his favourite option is the last one in the queue of options. With three candidates this already determines the order of all pairwise votes.

With three candidates the cycle could be either A>B>C>A or A>C>B>A. The chairman wants A to win. The first vote will therefore be between B and C. If we have cycle A>B>C>A, B will win the first round, and A will win the second round (against B). If we have cycle A>C>B>A, C will win the first round, and A will win the second round (against C). The chairman could thus pick the preferred winner in the case that there is no Condorcet winner.

The voters could also try to use some strategies. This gives us some quite interesting strategy patterns, since after the agenda has been set, the method is no more symmetric with respect to the different options. A and B supporters could also join forces and vote against A at the last round, if they don't like the chairmans idea of constructing a strategic agenda.

Juho


----
Election-Methods mailing list - see http://electorama.com/em for list info

[Juho Laatu]

Sorry, I should have written: "B and C supporters could also join forces and vote against A at the last round, if they don't like the chairmans idea of constructing a strategic agenda."

Juho

Post by Juho Laatu

Post by Juho Laatu

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

Some group decides the agenda (I'm not sure who; it probably depends on the parliament in question).
Then the parliament discusses the first two options, and does a majority vote between the two. It then does a majority vote between the winner so far and the next option, and so on until all options have been considered. The winner at the end of the procedure is the option that is accepted.
This method is Condorcet (because the CW beats everybody pairwise, and so whenever it becomes the winner so far, it'll stay the winner so far; and whenever it's the challenger, it will win against the winner so far and become the next winner so far). Furthermore, it's Smith. How cycles are broken depends on the agenda.

Yes, this is some sort of "serial Condorcet". The biggest problem of this approach is probably the agenda based cycle breaking that you mentioned.
If there is a Condorcet winner, it will win. But if there is any chance of having a cycle, then the chairman (if he decides the agenda) may arrange the agenda so that his favourite option is the last one in the queue of options. With three candidates this already determines the order of all pairwise votes.
With three candidates the cycle could be either A>B>C>A or A>C>B>A. The chairman wants A to win. The first vote will therefore be between B and C. If we have cycle A>B>C>A, B will win the first round, and A will win the second round (against B). If we have cycle A>C>B>A, C will win the first round, and A will win the second round (against C). The chairman could thus pick the preferred winner in the case that there is no Condorcet winner.
The voters could also try to use some strategies. This gives us some quite interesting strategy patterns, since after the agenda has been set, the method is no more symmetric with respect to the different options. A and B supporters could also join forces and vote against A at the last round, if they don't like the chairmans idea of constructing a strategic agenda.
Juho
----
Election-Methods mailing list - see http://electorama.com/em for list info

----
Election-Methods mailing list - see http://electorama.com/em for list info

[Kevin Venzke]

(I was seemingly unable to send this to lists.electorama.com so trying a slightly different address...)



----- Mail transféré -----
De : Kevin Venzke <***@yahoo.fr>
À : Juho Laatu <***@gmail.com>; Election Methods <election-***@lists.electorama.com>; Kristofer Munsterhjelm <***@t-online.de>
Envoyé le : Jeudi 11 mai 2017 18h48
Objet : Re: [EM] Voting without ballots (was: Minimax)

I think this is an interesting topic... Basically how to make a decision in a meeting when you don't have ballots and people aren't inclined to talk to each other. There's probably a whole field on this topic and I'm just not aware of it...
My idea here would be one I've mentioned before (but as an election method), that somehow a default option is initially selected, and then this option wins unless a full majority thinks another option is better. The largest such majority would immediately win in that situation; we would not chase around any cycles. So, there is both an advantage and disadvantage to being the default option. The advantage is obvious. The disadvantage is that the default option could lose when, had it not been the default, it could have won.
To rephrase a bit, I'm saying that for candidates A...Z where A is the default option, you only collect the votes for B...Z against A. Nobody's voting A over anything.
By not collecting the other pairwise information you might hopefully reduce the potential to make arguments against the winner's legitimacy. (A bit like the difficulty of undermining the winner under FPP or Approval, when the only sure data available is the counts that produced the winner.)
You could pick the default option using an election method (and even have an instant-win criterion if one is sensible). The mechanism does not enforce Plurality, only minimal defense.
Sorry for lack of other responses. I can't find enough time to write.
Kevin

De : Juho Laatu <***@gmail.com>
À : Election Methods <election-***@lists.electorama.com>
Cc : Kevin Venzke <***@yahoo.fr>
Envoyé le : Dimanche 7 mai 2017 5h32
Objet : Re: [EM] Ordering defeats in Minimax

Post by Juho Laatu

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

Some group decides the agenda (I'm not sure who; it probably depends on the parliament in question).
Then the parliament discusses the first two options, and does a majority vote between the two. It then does a majority vote between the winner so far and the next option, and so on until all options have been considered. The winner at the end of the procedure is the option that is accepted.
This method is Condorcet (because the CW beats everybody pairwise, and so whenever it becomes the winner so far, it'll stay the winner so far; and whenever it's the challenger, it will win against the winner so far and become the next winner so far). Furthermore, it's Smith. How cycles are broken depends on the agenda.

Yes, this is some sort of "serial Condorcet".  The biggest problem of this approach is probably the agenda based cycle breaking that you mentioned.

If there is a Condorcet winner, it will win. But if there is any chance of having a cycle, then the chairman (if he decides the agenda) may arrange the agenda so that his favourite option is the last one in the queue of options. With three candidates this already determines the order of all pairwise votes.

With three candidates the cycle could be either A>B>C>A or A>C>B>A. The chairman wants A to win. The first vote will therefore be between B and C. If we have cycle A>B>C>A, B will win the first round, and A will win the second round (against B).  If we have cycle A>C>B>A, C will win the first round, and A will win the second round (against C). The chairman could thus pick the preferred winner in the case that there is no Condorcet winner.

The voters could also try to use some strategies. This gives us some quite interesting strategy patterns, since after the agenda has been set, the method is no more symmetric with respect to the different options. A and B supporters could also join forces and vote against A at the last round, if they don't like the chairmans idea of constructing a strategic agenda.

Juho


----
Election-Methods mailing list - see http://electorama.com/em for list info

[Juho Laatu]

That method could be said to be problematic since it is not symmetric. But on the other hand it could be an excellent method for many elections where we the asymmetry has some explanation.

If we have an incumbent president that we might or might not change, that president could be the default option. In addition to voting on who is the best candidate, we would be voting also on whether to change the president or not. If the current president is no longer a candidate, he could nominate a proposed successor who would be the default option. Or in a two-party system one could pick the (first) candidate of the opposition party as the default option, since that's the way things tend to go anyway (at least after the current president has run out of allowed terms). Or maybe a parliament or other central but wider group would pick the default option. The default option should not be a weak option but one that is a plausible winner (the current president should thus nominate a candidate of some other party as the default option if it is obvious that he is currently popular).

This method would allow also having a threshold that would be required to not elect the incumbent or default option.

This method is a nice way to solve the problem of cyclic group preferences if one can use time to distribute the victory to multiple candidates. If there is a permanent top cycle A>B>C>A, C would win A, B would win C in the next election after maybe a year etc. No need to "break" the cycle since time will (maybe) allow all the cyclic candidates to participate. They just need to wait for their turn. (Not allowing the Minmax winner outside of the top cycle to win could be considered a disadvantage of this method.)

The ballot could be simply an approval ballot, asking "which options do you prefer to the default option". This method could thus be seen also as an improved Approval method. Adding a (strong) default option to Approval makes it more sensible than it is without that default option.

This approach could offer also a smooth path away from Plurality.

Juho

Post by Kevin Venzke
I think this is an interesting topic... Basically how to make a decision in a meeting when you don't have ballots and people aren't inclined to talk to each other. There's probably a whole field on this topic and I'm just not aware of it...
My idea here would be one I've mentioned before (but as an election method), that somehow a default option is initially selected, and then this option wins unless a full majority thinks another option is better. The largest such majority would immediately win in that situation; we would not chase around any cycles. So, there is both an advantage and disadvantage to being the default option. The advantage is obvious. The disadvantage is that the default option could lose when, had it not been the default, it could have won.
To rephrase a bit, I'm saying that for candidates A...Z where A is the default option, you only collect the votes for B...Z against A. Nobody's voting A over anything.
By not collecting the other pairwise information you might hopefully reduce the potential to make arguments against the winner's legitimacy. (A bit like the difficulty of undermining the winner under FPP or Approval, when the only sure data available is the counts that produced the winner.)
You could pick the default option using an election method (and even have an instant-win criterion if one is sensible). The mechanism does not enforce Plurality, only minimal defense.
Sorry for lack of other responses. I can't find enough time to write.
Kevin
Envoyé le : Dimanche 7 mai 2017 5h32
Objet : Re: [EM] Ordering defeats in Minimax

Post by Juho Laatu

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

Some group decides the agenda (I'm not sure who; it probably depends on the parliament in question).
Then the parliament discusses the first two options, and does a majority vote between the two. It then does a majority vote between the winner so far and the next option, and so on until all options have been considered. The winner at the end of the procedure is the option that is accepted.
This method is Condorcet (because the CW beats everybody pairwise, and so whenever it becomes the winner so far, it'll stay the winner so far; and whenever it's the challenger, it will win against the winner so far and become the next winner so far). Furthermore, it's Smith. How cycles are broken depends on the agenda.

Yes, this is some sort of "serial Condorcet". The biggest problem of this approach is probably the agenda based cycle breaking that you mentioned.
If there is a Condorcet winner, it will win. But if there is any chance of having a cycle, then the chairman (if he decides the agenda) may arrange the agenda so that his favourite option is the last one in the queue of options. With three candidates this already determines the order of all pairwise votes.
With three candidates the cycle could be either A>B>C>A or A>C>B>A. The chairman wants A to win. The first vote will therefore be between B and C. If we have cycle A>B>C>A, B will win the first round, and A will win the second round (against B). If we have cycle A>C>B>A, C will win the first round, and A will win the second round (against C). The chairman could thus pick the preferred winner in the case that there is no Condorcet winner.
The voters could also try to use some strategies. This gives us some quite interesting strategy patterns, since after the agenda has been set, the method is no more symmetric with respect to the different options. A and B supporters could also join forces and vote against A at the last round, if they don't like the chairmans idea of constructing a strategic agenda.
Juho
----
Election-Methods mailing list - see http://electorama.com/em <http://electorama.com/em>for list info

[Andy Jennings]

I like this idea, Juho. If there is an incumbent, put all the challengers
on one approval ballot and ask "Which ones do you like better than the
incumbent?" It is a nice solution to the what-does-approval-mean problem.

Like you said, the threshold doesn't have to be 50%, either. It could go
down, in a gradual sort-of term limit. After one term, the mayor will
remain if no challenger gets over 60%. After two terms, it's 50%. After
three terms, it's 40%. After four terms, it's 30%.

In the past, I haven't been sure what to do if there is no incumbent.
Letting the incumbent pick a successor is an interesting solution. As is
letting the largest opposition party choose someone (if the election is
partisan).

Andy

Post by Juho Laatu
That method could be said to be problematic since it is not symmetric. But
on the other hand it could be an excellent method for many elections where
we the asymmetry has some explanation.
If we have an incumbent president that we might or might not change, that
president could be the default option. In addition to voting on who is the
best candidate, we would be voting also on whether to change the president
or not. If the current president is no longer a candidate, he could
nominate a proposed successor who would be the default option. Or in a
two-party system one could pick the (first) candidate of the opposition
party as the default option, since that's the way things tend to go anyway
(at least after the current president has run out of allowed terms). Or
maybe a parliament or other central but wider group would pick the default
option. The default option should not be a weak option but one that is a
plausible winner (the current president should thus nominate a candidate of
some other party as the default option if it is obvious that he is
currently popular).
This method would allow also having a threshold that would be required to
not elect the incumbent or default option.
This method is a nice way to solve the problem of cyclic group preferences
if one can use time to distribute the victory to multiple candidates. If
there is a permanent top cycle A>B>C>A, C would win A, B would win C in the
next election after maybe a year etc. No need to "break" the cycle since
time will (maybe) allow all the cyclic candidates to participate. They just
need to wait for their turn. (Not allowing the Minmax winner outside of the
top cycle to win could be considered a disadvantage of this method.)
The ballot could be simply an approval ballot, asking "which options do
you prefer to the default option". This method could thus be seen also as
an improved Approval method. Adding a (strong) default option to Approval
makes it more sensible than it is without that default option.
This approach could offer also a smooth path away from Plurality.
Juho
I think this is an interesting topic... Basically how to make a decision
in a meeting when you don't have ballots and people aren't inclined to talk
to each other. There's probably a whole field on this topic and I'm just
not aware of it...
My idea here would be one I've mentioned before (but as an election
method), that somehow a default option is initially selected, and then this
option wins unless a full majority thinks another option is better. The
largest such majority would immediately win in that situation; we would not
chase around any cycles. So, there is both an advantage and disadvantage to
being the default option. The advantage is obvious. The disadvantage is
that the default option could lose when, had it not been the default, it
could have won.
To rephrase a bit, I'm saying that for candidates A...Z where A is the
default option, you only collect the votes for B...Z against A. Nobody's
voting A over anything.
By not collecting the other pairwise information you might hopefully
reduce the potential to make arguments against the winner's legitimacy. (A
bit like the difficulty of undermining the winner under FPP or Approval,
when the only sure data available is the counts that produced the winner.)
You could pick the default option using an election method (and even have
an instant-win criterion if one is sensible). The mechanism does not
enforce Plurality, only minimal defense.
Sorry for lack of other responses. I can't find enough time to write.
Kevin
------------------------------
*Envoyé le :* Dimanche 7 mai 2017 5h32
*Objet :* Re: [EM] Ordering defeats in Minimax

Post by Kristofer Munsterhjelm

Post by Juho Laatu

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good

enough.

Post by Kristofer Munsterhjelm
I think some parliaments use the following procedure for multiple
Some group decides the agenda (I'm not sure who; it probably depends on

the parliament in question).

Post by Kristofer Munsterhjelm
Then the parliament discusses the first two options, and does a majority

vote between the two. It then does a majority vote between the winner so
far and the next option, and so on until all options have been considered.
The winner at the end of the procedure is the option that is accepted.

Post by Kristofer Munsterhjelm
This method is Condorcet (because the CW beats everybody pairwise, and

so whenever it becomes the winner so far, it'll stay the winner so far; and
whenever it's the challenger, it will win against the winner so far and
become the next winner so far). Furthermore, it's Smith. How cycles are
broken depends on the agenda.
Yes, this is some sort of "serial Condorcet". The biggest problem of this
approach is probably the agenda based cycle breaking that you mentioned.
If there is a Condorcet winner, it will win. But if there is any chance of
having a cycle, then the chairman (if he decides the agenda) may arrange
the agenda so that his favourite option is the last one in the queue of
options. With three candidates this already determines the order of all
pairwise votes.
With three candidates the cycle could be either A>B>C>A or A>C>B>A. The
chairman wants A to win. The first vote will therefore be between B and C.
If we have cycle A>B>C>A, B will win the first round, and A will win the
second round (against B). If we have cycle A>C>B>A, C will win the first
round, and A will win the second round (against C). The chairman could thus
pick the preferred winner in the case that there is no Condorcet winner.
The voters could also try to use some strategies. This gives us some quite
interesting strategy patterns, since after the agenda has been set, the
method is no more symmetric with respect to the different options. A and B
supporters could also join forces and vote against A at the last round, if
they don't like the chairmans idea of constructing a strategic agenda.
Juho
----
Election-Methods mailing list - see http://electorama.com/em for list info
----
Election-Methods mailing list - see http://electorama.com/em for list info

[Kevin Venzke]

I have concerns about dropping the threshold below 50%, even if the incumbent has been in power so long that we want a bias in favor of getting rid of him. Strategically the method starts to turn into Approval, with people voting with that mindset rather than voting as though it is a pairwise comparison. (Even at 50% this could be an issue; imagine for instance the situation that the default option is so terrible that voters expect that many candidates will hit the 50% threshold.)
One of my main ideas is to address the area where Approval makes me nervous: The situation that the winner doesn't have a majority, but it looks like there could have been a majority among a divided opposition, if one posed the question right. I hope that clarifying the stakes would reduce the chicken dilemma potential.
Another motivation is to try to keep more options available for the last step of the election. It's easy to imagine this as a revision of the top-two runoff or jungle primary, where we take note of just the single frontrunner of the first round, and avoid eliminating the losing options for the second round.
I certainly think the contests against the default should use an approval ballot, but I think there should probably be an additional checkbox for those who don't want to vote for anybody as superior to the default. I just think you would want some distinction between a pro-default ballot and a blank ballot.
Kevin

De : Andy Jennings <***@jenningsstory.com>
À : Juho Laatu <***@gmail.com>
Cc : Kevin Venzke <***@yahoo.fr>; Election Methods <election-***@lists.electorama.com>
Envoyé le : Vendredi 12 mai 2017 7h32
Objet : Re: [EM] Voting without ballots (was: Minimax)

I like this idea, Juho.  If there is an incumbent, put all the challengers on one approval ballot and ask "Which ones do you like better than the incumbent?"  It is a nice solution to the what-does-approval-mean problem.

Like you said, the threshold doesn't have to be 50%, either.  It could go down, in a gradual sort-of term limit.  After one term, the mayor will remain if no challenger gets over 60%.  After two terms, it's 50%.  After three terms, it's 40%.  After four terms, it's 30%.

In the past, I haven't been sure what to do if there is no incumbent.  Letting the incumbent pick a successor is an interesting solution.  As is letting the largest opposition party choose someone (if the election is partisan).

Andy

On Thu, May 11, 2017 at 11:30 PM, Juho Laatu <***@gmail.com> wrote:

That method could be said to be problematic since it is not symmetric. But on the other hand it could be an excellent method for many elections where we the asymmetry has some explanation.
If we have an incumbent president that we might or might not change, that president could be the default option. In addition to voting on who is the best candidate, we would be voting also on whether to change the president or not. If the current president is no longer a candidate, he could nominate a proposed successor who would be the default option. Or in a two-party system one could pick the (first) candidate of the opposition party as the default option, since that's the way things tend to go anyway (at least after the current president has run out of allowed terms). Or maybe a parliament or other central but wider group would pick the default option. The default option should not be a weak option but one that is a plausible winner (the current president should thus nominate a candidate of some other party as the default option if it is obvious that he is currently popular).
This method would allow also having a threshold that would be required to not elect the incumbent or default option.
This method is a nice way to solve the problem of cyclic group preferences if one can use time to distribute the victory to multiple candidates. If there is a permanent top cycle A>B>C>A, C would win A, B would win C in the next election after maybe a year etc. No need to "break" the cycle since time will (maybe) allow all the cyclic candidates to participate. They just need to wait for their turn. (Not allowing the Minmax winner outside of the top cycle to win could be considered a disadvantage of this method.)
The ballot could be simply an approval ballot, asking "which options do you prefer to the default option". This method could thus be seen also as an improved Approval method. Adding a (strong) default option to Approval makes it more sensible than it is without that default option.
This approach could offer also a smooth path away from Plurality.
Juho


On 12 May 2017, at 02:48, Kevin Venzke <***@yahoo.fr> wrote:
I think this is an interesting topic... Basically how to make a decision in a meeting when you don't have ballots and people aren't inclined to talk to each other. There's probably a whole field on this topic and I'm just not aware of it...
My idea here would be one I've mentioned before (but as an election method), that somehow a default option is initially selected, and then this option wins unless a full majority thinks another option is better. The largest such majority would immediately win in that situation; we would not chase around any cycles. So, there is both an advantage and disadvantage to being the default option. The advantage is obvious. The disadvantage is that the default option could lose when, had it not been the default, it could have won.
To rephrase a bit, I'm saying that for candidates A...Z where A is the default option, you only collect the votes for B...Z against A. Nobody's voting A over anything.
By not collecting the other pairwise information you might hopefully reduce the potential to make arguments against the winner's legitimacy. (A bit like the difficulty of undermining the winner under FPP or Approval, when the only sure data available is the counts that produced the winner.)
You could pick the default option using an election method (and even have an instant-win criterion if one is sensible). The mechanism does not enforce Plurality, only minimal defense.
Sorry for lack of other responses. I can't find enough time to write.
Kevin

De : Juho Laatu <***@gmail.com>
À : Election Methods <election-***@lists. electorama.com>
Cc : Kevin Venzke <***@yahoo.fr>
Envoyé le : Dimanche 7 mai 2017 5h32
Objet : Re: [EM] Ordering defeats in Minimax

Post by Juho Laatu

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

Some group decides the agenda (I'm not sure who; it probably depends on the parliament in question).
Then the parliament discusses the first two options, and does a majority vote between the two. It then does a majority vote between the winner so far and the next option, and so on until all options have been considered. The winner at the end of the procedure is the option that is accepted.
This method is Condorcet (because the CW beats everybody pairwise, and so whenever it becomes the winner so far, it'll stay the winner so far; and whenever it's the challenger, it will win against the winner so far and become the next winner so far). Furthermore, it's Smith. How cycles are broken depends on the agenda.

Yes, this is some sort of "serial Condorcet".  The biggest problem of this approach is probably the agenda based cycle breaking that you mentioned.

If there is a Condorcet winner, it will win. But if there is any chance of having a cycle, then the chairman (if he decides the agenda) may arrange the agenda so that his favourite option is the last one in the queue of options. With three candidates this already determines the order of all pairwise votes.

With three candidates the cycle could be either A>B>C>A or A>C>B>A. The chairman wants A to win. The first vote will therefore be between B and C. If we have cycle A>B>C>A, B will win the first round, and A will win the second round (against B).  If we have cycle A>C>B>A, C will win the first round, and A will win the second round (against C). The chairman could thus pick the preferred winner in the case that there is no Condorcet winner.

The voters could also try to use some strategies. This gives us some quite interesting strategy patterns, since after the agenda has been set, the method is no more symmetric with respect to the different options. A and B supporters could also join forces and vote against A at the last round, if they don't like the chairmans idea of constructing a strategic agenda.

Juho


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Election-Methods mailing list - see http://electorama.com/em for list info





----
Election-Methods mailing list - see http://electorama.com/em for list info



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[Juho Laatu]

Post by Kevin Venzke
I have concerns about dropping the threshold below 50%, even if the incumbent has been in power so long that we want a bias in favor of getting rid of him. Strategically the method starts to turn into Approval, with people voting with that mindset rather than voting as though it is a pairwise comparison. (Even at 50% this could be an issue; imagine for instance the situation that the default option is so terrible that voters expect that many candidates will hit the 50% threshold.)

Yes, the default option should be strong (one of the potential winners, or stronger). Otherwise we will have all the problems of basic Approval.

Post by Kevin Venzke
One of my main ideas is to address the area where Approval makes me nervous: The situation that the winner doesn't have a majority, but it looks like there could have been a majority among a divided opposition, if one posed the question right. I hope that clarifying the stakes would reduce the chicken dilemma potential.
Another motivation is to try to keep more options available for the last step of the election. It's easy to imagine this as a revision of the top-two runoff or jungle primary, where we take note of just the single frontrunner of the first round, and avoid eliminating the losing options for the second round.

Yes. One could use the first round just to define the default option. Approval could be good enough for the first round. The first round and the combined two round method should be simple, since if it gets complex, we might as well be use some basic Condorcet method.

Post by Kevin Venzke
I certainly think the contests against the default should use an approval ballot, but I think there should probably be an additional checkbox for those who don't want to vote for anybody as superior to the default. I just think you would want some distinction between a pro-default ballot and a blank ballot.

I guess that would be for the statistics, i.e. that difference would not influence the outcome. One (not necessarily good) approach would be to allow all options to be ticked either as "worse" or "better" than the default option.

Juho

Post by Kevin Venzke
Kevin
Envoyé le : Vendredi 12 mai 2017 7h32
Objet : Re: [EM] Voting without ballots (was: Minimax)
I like this idea, Juho. If there is an incumbent, put all the challengers on one approval ballot and ask "Which ones do you like better than the incumbent?" It is a nice solution to the what-does-approval-mean problem.
Like you said, the threshold doesn't have to be 50%, either. It could go down, in a gradual sort-of term limit. After one term, the mayor will remain if no challenger gets over 60%. After two terms, it's 50%. After three terms, it's 40%. After four terms, it's 30%.
In the past, I haven't been sure what to do if there is no incumbent. Letting the incumbent pick a successor is an interesting solution. As is letting the largest opposition party choose someone (if the election is partisan).
Andy
That method could be said to be problematic since it is not symmetric. But on the other hand it could be an excellent method for many elections where we the asymmetry has some explanation.
If we have an incumbent president that we might or might not change, that president could be the default option. In addition to voting on who is the best candidate, we would be voting also on whether to change the president or not. If the current president is no longer a candidate, he could nominate a proposed successor who would be the default option. Or in a two-party system one could pick the (first) candidate of the opposition party as the default option, since that's the way things tend to go anyway (at least after the current president has run out of allowed terms). Or maybe a parliament or other central but wider group would pick the default option. The default option should not be a weak option but one that is a plausible winner (the current president should thus nominate a candidate of some other party as the default option if it is obvious that he is currently popular).
This method would allow also having a threshold that would be required to not elect the incumbent or default option.
This method is a nice way to solve the problem of cyclic group preferences if one can use time to distribute the victory to multiple candidates. If there is a permanent top cycle A>B>C>A, C would win A, B would win C in the next election after maybe a year etc. No need to "break" the cycle since time will (maybe) allow all the cyclic candidates to participate. They just need to wait for their turn. (Not allowing the Minmax winner outside of the top cycle to win could be considered a disadvantage of this method.)
The ballot could be simply an approval ballot, asking "which options do you prefer to the default option". This method could thus be seen also as an improved Approval method. Adding a (strong) default option to Approval makes it more sensible than it is without that default option.
This approach could offer also a smooth path away from Plurality.
Juho

Post by Kevin Venzke
I think this is an interesting topic... Basically how to make a decision in a meeting when you don't have ballots and people aren't inclined to talk to each other. There's probably a whole field on this topic and I'm just not aware of it...
My idea here would be one I've mentioned before (but as an election method), that somehow a default option is initially selected, and then this option wins unless a full majority thinks another option is better. The largest such majority would immediately win in that situation; we would not chase around any cycles. So, there is both an advantage and disadvantage to being the default option. The advantage is obvious. The disadvantage is that the default option could lose when, had it not been the default, it could have won.
To rephrase a bit, I'm saying that for candidates A...Z where A is the default option, you only collect the votes for B...Z against A. Nobody's voting A over anything.
By not collecting the other pairwise information you might hopefully reduce the potential to make arguments against the winner's legitimacy. (A bit like the difficulty of undermining the winner under FPP or Approval, when the only sure data available is the counts that produced the winner.)
You could pick the default option using an election method (and even have an instant-win criterion if one is sensible). The mechanism does not enforce Plurality, only minimal defense.
Sorry for lack of other responses. I can't find enough time to write.
Kevin
Envoyé le : Dimanche 7 mai 2017 5h32
Objet : Re: [EM] Ordering defeats in Minimax

Post by Juho Laatu

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

Some group decides the agenda (I'm not sure who; it probably depends on the parliament in question).
Then the parliament discusses the first two options, and does a majority vote between the two. It then does a majority vote between the winner so far and the next option, and so on until all options have been considered. The winner at the end of the procedure is the option that is accepted.
This method is Condorcet (because the CW beats everybody pairwise, and so whenever it becomes the winner so far, it'll stay the winner so far; and whenever it's the challenger, it will win against the winner so far and become the next winner so far). Furthermore, it's Smith. How cycles are broken depends on the agenda.

Yes, this is some sort of "serial Condorcet". The biggest problem of this approach is probably the agenda based cycle breaking that you mentioned.
If there is a Condorcet winner, it will win. But if there is any chance of having a cycle, then the chairman (if he decides the agenda) may arrange the agenda so that his favourite option is the last one in the queue of options. With three candidates this already determines the order of all pairwise votes.
With three candidates the cycle could be either A>B>C>A or A>C>B>A. The chairman wants A to win. The first vote will therefore be between B and C. If we have cycle A>B>C>A, B will win the first round, and A will win the second round (against B). If we have cycle A>C>B>A, C will win the first round, and A will win the second round (against C). The chairman could thus pick the preferred winner in the case that there is no Condorcet winner.
The voters could also try to use some strategies. This gives us some quite interesting strategy patterns, since after the agenda has been set, the method is no more symmetric with respect to the different options. A and B supporters could also join forces and vote against A at the last round, if they don't like the chairmans idea of constructing a strategic agenda.
Juho
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[Kevin Venzke]

I agree Approval would be good enough for the first round. But I suggest that majority approval on the first round should be an instant win. I agree in advance that that suggestion seems far from ideal. However, I'm concerned about the possibility that the second round may appear to ask a question that seemingly has already been resolved in the first round.
Example: In the first round, one candidate on the Left gets majority approval and so we take him as the default for the second round. But in the second round it could happen that candidates on the Right secure majorities against the Left candidate. (Maybe the first round result motivated the opposition to participate in greater numbers.) One could argue at the very least that the first round seems to have been pointless in that case. I wouldn't want candidates to feel there is little reason to contest the first round.
Regarding ballot format: You're right that I didn't mean it should make a difference. It's partly that I wonder what the default candidate tells his supporters to do? "Support me on election day by submitting a blank ballot"? That seems odd.
I don't have a nice name for the general mechanism. "Oppositional approval" sounds like a contradiction and "approval vs. a default option" is bulky. "Contrastive approval" produces an overused acronym... Arguably it isn't approval at all and should be named for being a "single-column" pairwise method.
Kevin


De : Juho Laatu <***@gmail.com>
À : EM list <election-***@electorama.com>
Cc : Kevin Venzke <***@yahoo.fr>
Envoyé le : Vendredi 12 mai 2017 19h02
Objet : Re: [EM] Voting without ballots (was: Minimax)


On 13 May 2017, at 01:07, Kevin Venzke <***@yahoo.fr> wrote:
I have concerns about dropping the threshold below 50%, even if the incumbent has been in power so long that we want a bias in favor of getting rid of him. Strategically the method starts to turn into Approval, with people voting with that mindset rather than voting as though it is a pairwise comparison. (Even at 50% this could be an issue; imagine for instance the situation that the default option is so terrible that voters expect that many candidates will hit the 50% threshold.)

Yes, the default option should be strong (one of the potential winners, or stronger). Otherwise we will have all the problems of basic Approval.


One of my main ideas is to address the area where Approval makes me nervous: The situation that the winner doesn't have a majority, but it looks like there could have been a majority among a divided opposition, if one posed the question right. I hope that clarifying the stakes would reduce the chicken dilemma potential.
Another motivation is to try to keep more options available for the last step of the election. It's easy to imagine this as a revision of the top-two runoff or jungle primary, where we take note of just the single frontrunner of the first round, and avoid eliminating the losing options for the second round.

Yes. One could use the first round just to define the default option. Approval could be good enough for the first round. The first round and the combined two round method should be simple, since if it gets complex, we might as well be use some basic Condorcet method.


I certainly think the contests against the default should use an approval ballot, but I think there should probably be an additional checkbox for those who don't want to vote for anybody as superior to the default. I just think you would want some distinction between a pro-default ballot and a blank ballot.

I guess that would be for the statistics, i.e. that difference would not influence the outcome. One (not necessarily good) approach would be to allow all options to be ticked either as "worse" or "better" than the default option.
Juho


Kevin

De : Andy Jennings <***@jenningsstory.com>
À : Juho Laatu <***@gmail.com>
Cc : Kevin Venzke <***@yahoo.fr>; Election Methods <election-***@lists.electorama.com>
Envoyé le : Vendredi 12 mai 2017 7h32
Objet : Re: [EM] Voting without ballots (was: Minimax)

I like this idea, Juho.  If there is an incumbent, put all the challengers on one approval ballot and ask "Which ones do you like better than the incumbent?"  It is a nice solution to the what-does-approval-mean problem.

Like you said, the threshold doesn't have to be 50%, either.  It could go down, in a gradual sort-of term limit.  After one term, the mayor will remain if no challenger gets over 60%.  After two terms, it's 50%.  After three terms, it's 40%.  After four terms, it's 30%.

In the past, I haven't been sure what to do if there is no incumbent.  Letting the incumbent pick a successor is an interesting solution.  As is letting the largest opposition party choose someone (if the election is partisan).

Andy

On Thu, May 11, 2017 at 11:30 PM, Juho Laatu <***@gmail.com> wrote:

That method could be said to be problematic since it is not symmetric. But on the other hand it could be an excellent method for many elections where we the asymmetry has some explanation.
If we have an incumbent president that we might or might not change, that president could be the default option. In addition to voting on who is the best candidate, we would be voting also on whether to change the president or not. If the current president is no longer a candidate, he could nominate a proposed successor who would be the default option. Or in a two-party system one could pick the (first) candidate of the opposition party as the default option, since that's the way things tend to go anyway (at least after the current president has run out of allowed terms). Or maybe a parliament or other central but wider group would pick the default option. The default option should not be a weak option but one that is a plausible winner (the current president should thus nominate a candidate of some other party as the default option if it is obvious that he is currently popular).
This method would allow also having a threshold that would be required to not elect the incumbent or default option.
This method is a nice way to solve the problem of cyclic group preferences if one can use time to distribute the victory to multiple candidates. If there is a permanent top cycle A>B>C>A, C would win A, B would win C in the next election after maybe a year etc. No need to "break" the cycle since time will (maybe) allow all the cyclic candidates to participate. They just need to wait for their turn. (Not allowing the Minmax winner outside of the top cycle to win could be considered a disadvantage of this method.)
The ballot could be simply an approval ballot, asking "which options do you prefer to the default option". This method could thus be seen also as an improved Approval method. Adding a (strong) default option to Approval makes it more sensible than it is without that default option.
This approach could offer also a smooth path away from Plurality.
Juho


On 12 May 2017, at 02:48, Kevin Venzke <***@yahoo.fr> wrote:
I think this is an interesting topic... Basically how to make a decision in a meeting when you don't have ballots and people aren't inclined to talk to each other. There's probably a whole field on this topic and I'm just not aware of it...
My idea here would be one I've mentioned before (but as an election method), that somehow a default option is initially selected, and then this option wins unless a full majority thinks another option is better. The largest such majority would immediately win in that situation; we would not chase around any cycles. So, there is both an advantage and disadvantage to being the default option. The advantage is obvious. The disadvantage is that the default option could lose when, had it not been the default, it could have won.
To rephrase a bit, I'm saying that for candidates A...Z where A is the default option, you only collect the votes for B...Z against A. Nobody's voting A over anything.
By not collecting the other pairwise information you might hopefully reduce the potential to make arguments against the winner's legitimacy. (A bit like the difficulty of undermining the winner under FPP or Approval, when the only sure data available is the counts that produced the winner.)
You could pick the default option using an election method (and even have an instant-win criterion if one is sensible). The mechanism does not enforce Plurality, only minimal defense.
Sorry for lack of other responses. I can't find enough time to write.
Kevin

De : Juho Laatu <***@gmail.com>
À : Election Methods <election-***@lists. electorama.com>
Cc : Kevin Venzke <***@yahoo.fr>
Envoyé le : Dimanche 7 mai 2017 5h32
Objet : Re: [EM] Ordering defeats in Minimax

Post by Juho Laatu

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

Some group decides the agenda (I'm not sure who; it probably depends on the parliament in question).
Then the parliament discusses the first two options, and does a majority vote between the two. It then does a majority vote between the winner so far and the next option, and so on until all options have been considered. The winner at the end of the procedure is the option that is accepted.
This method is Condorcet (because the CW beats everybody pairwise, and so whenever it becomes the winner so far, it'll stay the winner so far; and whenever it's the challenger, it will win against the winner so far and become the next winner so far). Furthermore, it's Smith. How cycles are broken depends on the agenda.

Yes, this is some sort of "serial Condorcet".  The biggest problem of this approach is probably the agenda based cycle breaking that you mentioned.

If there is a Condorcet winner, it will win. But if there is any chance of having a cycle, then the chairman (if he decides the agenda) may arrange the agenda so that his favourite option is the last one in the queue of options. With three candidates this already determines the order of all pairwise votes.

With three candidates the cycle could be either A>B>C>A or A>C>B>A. The chairman wants A to win. The first vote will therefore be between B and C. If we have cycle A>B>C>A, B will win the first round, and A will win the second round (against B).  If we have cycle A>C>B>A, C will win the first round, and A will win the second round (against C). The chairman could thus pick the preferred winner in the case that there is no Condorcet winner.

The voters could also try to use some strategies. This gives us some quite interesting strategy patterns, since after the agenda has been set, the method is no more symmetric with respect to the different options. A and B supporters could also join forces and vote against A at the last round, if they don't like the chairmans idea of constructing a strategic agenda.

Juho


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[Juho Laatu]

Post by Kevin Venzke
I agree Approval would be good enough for the first round. But I suggest that majority approval on the first round should be an instant win. I agree in advance that that suggestion seems far from ideal. However, I'm concerned about the possibility that the second round may appear to ask a question that seemingly has already been resolved in the first round.

In that situation we could have only one round and a separate system (e.g. a parliament) for picking the default option. One benefit of the method is that the default option need not be the absolute favourite of the second round voters, so using some other (but reasonably similar) voter group to determine the default option is not a problem.

Post by Kevin Venzke
Example: In the first round, one candidate on the Left gets majority approval and so we take him as the default for the second round. But in the second round it could happen that candidates on the Right secure majorities against the Left candidate. (Maybe the first round result motivated the opposition to participate in greater numbers.) One could argue at the very least that the first round seems to have been pointless in that case. I wouldn't want candidates to feel there is little reason to contest the first round.
Regarding ballot format: You're right that I didn't mean it should make a difference. It's partly that I wonder what the default candidate tells his supporters to do? "Support me on election day by submitting a blank ballot"? That seems odd.

Yes, it makes sense to allow all voters to use the pen. It is also ok to collect additional statistical data in the ballots (if that doesn't add too much complexity to the ballots). One could ask e.g. how good the default candidate is in numerical scale, or why not have a numerical scale (range) for indicating how much better or worse the other candidates are. I don't expect any serious conflicts like winner having only very little support in the numeric votes.

Post by Kevin Venzke
I don't have a nice name for the general mechanism. "Oppositional approval" sounds like a contradiction and "approval vs. a default option" is bulky. "Contrastive approval" produces an overused acronym... Arguably it isn't approval at all and should be named for being a "single-column" pairwise method.

Maybe one could use words "comparison", "change", "proposal", "improve". Approval doesn't sound quite right since we are not asking for approval but comparison with respect to the default option.

Juho

Post by Kevin Venzke
Kevin
Envoyé le : Vendredi 12 mai 2017 19h02
Objet : Re: [EM] Voting without ballots (was: Minimax)

Post by Kevin Venzke
I have concerns about dropping the threshold below 50%, even if the incumbent has been in power so long that we want a bias in favor of getting rid of him. Strategically the method starts to turn into Approval, with people voting with that mindset rather than voting as though it is a pairwise comparison. (Even at 50% this could be an issue; imagine for instance the situation that the default option is so terrible that voters expect that many candidates will hit the 50% threshold.)

Yes, the default option should be strong (one of the potential winners, or stronger). Otherwise we will have all the problems of basic Approval.

Post by Kevin Venzke
One of my main ideas is to address the area where Approval makes me nervous: The situation that the winner doesn't have a majority, but it looks like there could have been a majority among a divided opposition, if one posed the question right. I hope that clarifying the stakes would reduce the chicken dilemma potential.
Another motivation is to try to keep more options available for the last step of the election. It's easy to imagine this as a revision of the top-two runoff or jungle primary, where we take note of just the single frontrunner of the first round, and avoid eliminating the losing options for the second round.

Yes. One could use the first round just to define the default option. Approval could be good enough for the first round. The first round and the combined two round method should be simple, since if it gets complex, we might as well be use some basic Condorcet method.

Post by Kevin Venzke
I certainly think the contests against the default should use an approval ballot, but I think there should probably be an additional checkbox for those who don't want to vote for anybody as superior to the default. I just think you would want some distinction between a pro-default ballot and a blank ballot.

I guess that would be for the statistics, i.e. that difference would not influence the outcome. One (not necessarily good) approach would be to allow all options to be ticked either as "worse" or "better" than the default option.
Juho

Post by Kevin Venzke
Kevin
Envoyé le : Vendredi 12 mai 2017 7h32
Objet : Re: [EM] Voting without ballots (was: Minimax)
I like this idea, Juho. If there is an incumbent, put all the challengers on one approval ballot and ask "Which ones do you like better than the incumbent?" It is a nice solution to the what-does-approval-mean problem.
Like you said, the threshold doesn't have to be 50%, either. It could go down, in a gradual sort-of term limit. After one term, the mayor will remain if no challenger gets over 60%. After two terms, it's 50%. After three terms, it's 40%. After four terms, it's 30%.
In the past, I haven't been sure what to do if there is no incumbent. Letting the incumbent pick a successor is an interesting solution. As is letting the largest opposition party choose someone (if the election is partisan).
Andy
That method could be said to be problematic since it is not symmetric. But on the other hand it could be an excellent method for many elections where we the asymmetry has some explanation.
If we have an incumbent president that we might or might not change, that president could be the default option. In addition to voting on who is the best candidate, we would be voting also on whether to change the president or not. If the current president is no longer a candidate, he could nominate a proposed successor who would be the default option. Or in a two-party system one could pick the (first) candidate of the opposition party as the default option, since that's the way things tend to go anyway (at least after the current president has run out of allowed terms). Or maybe a parliament or other central but wider group would pick the default option. The default option should not be a weak option but one that is a plausible winner (the current president should thus nominate a candidate of some other party as the default option if it is obvious that he is currently popular).
This method would allow also having a threshold that would be required to not elect the incumbent or default option.
This method is a nice way to solve the problem of cyclic group preferences if one can use time to distribute the victory to multiple candidates. If there is a permanent top cycle A>B>C>A, C would win A, B would win C in the next election after maybe a year etc. No need to "break" the cycle since time will (maybe) allow all the cyclic candidates to participate. They just need to wait for their turn. (Not allowing the Minmax winner outside of the top cycle to win could be considered a disadvantage of this method.)
The ballot could be simply an approval ballot, asking "which options do you prefer to the default option". This method could thus be seen also as an improved Approval method. Adding a (strong) default option to Approval makes it more sensible than it is without that default option.
This approach could offer also a smooth path away from Plurality.
Juho

Post by Kevin Venzke
I think this is an interesting topic... Basically how to make a decision in a meeting when you don't have ballots and people aren't inclined to talk to each other. There's probably a whole field on this topic and I'm just not aware of it...
My idea here would be one I've mentioned before (but as an election method), that somehow a default option is initially selected, and then this option wins unless a full majority thinks another option is better. The largest such majority would immediately win in that situation; we would not chase around any cycles. So, there is both an advantage and disadvantage to being the default option. The advantage is obvious. The disadvantage is that the default option could lose when, had it not been the default, it could have won.
To rephrase a bit, I'm saying that for candidates A...Z where A is the default option, you only collect the votes for B...Z against A. Nobody's voting A over anything.
By not collecting the other pairwise information you might hopefully reduce the potential to make arguments against the winner's legitimacy. (A bit like the difficulty of undermining the winner under FPP or Approval, when the only sure data available is the counts that produced the winner.)
You could pick the default option using an election method (and even have an instant-win criterion if one is sensible). The mechanism does not enforce Plurality, only minimal defense.
Sorry for lack of other responses. I can't find enough time to write.
Kevin
Envoyé le : Dimanche 7 mai 2017 5h32
Objet : Re: [EM] Ordering defeats in Minimax

Post by Juho Laatu

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

Some group decides the agenda (I'm not sure who; it probably depends on the parliament in question).
Then the parliament discusses the first two options, and does a majority vote between the two. It then does a majority vote between the winner so far and the next option, and so on until all options have been considered. The winner at the end of the procedure is the option that is accepted.
This method is Condorcet (because the CW beats everybody pairwise, and so whenever it becomes the winner so far, it'll stay the winner so far; and whenever it's the challenger, it will win against the winner so far and become the next winner so far). Furthermore, it's Smith. How cycles are broken depends on the agenda.

Yes, this is some sort of "serial Condorcet". The biggest problem of this approach is probably the agenda based cycle breaking that you mentioned.
If there is a Condorcet winner, it will win. But if there is any chance of having a cycle, then the chairman (if he decides the agenda) may arrange the agenda so that his favourite option is the last one in the queue of options. With three candidates this already determines the order of all pairwise votes.
With three candidates the cycle could be either A>B>C>A or A>C>B>A. The chairman wants A to win. The first vote will therefore be between B and C. If we have cycle A>B>C>A, B will win the first round, and A will win the second round (against B). If we have cycle A>C>B>A, C will win the first round, and A will win the second round (against C). The chairman could thus pick the preferred winner in the case that there is no Condorcet winner.
The voters could also try to use some strategies. This gives us some quite interesting strategy patterns, since after the agenda has been set, the method is no more symmetric with respect to the different options. A and B supporters could also join forces and vote against A at the last round, if they don't like the chairmans idea of constructing a strategic agenda.
Juho
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Post by Juho Laatu
...
I think all Condorcet methods have a severe incentive to apply one
particular strategy. ...
...
Let's assume that in some group of voters all prefer A to B but they
don't rank candidates A and B. B wins the election, and A is not too far
behind. It is obvious that those voters would have had a better
strategy, the strategy of expressing their opinion on whether A or B
should win. This is not a rare incident if it is common among the voters
not to rank many of the potential winners. ...

In real-world situations that involve more than about 10 voters,
strategies do not work when Condorcet methods are used.

Based on my experience with the VoteFair American Idol poll, initially
voters started out using approval-like voting, or
single-mark-ballot-like voting. But over time -- when they saw that the
results revealed a full ranking and not just a single "winner" -- they
learned to more fully rank the choices. At that point the voters ranked
choices at the same level only when they didn't have much of an opinion
about which were better or worse than the others at that ranking level.

So far I have not seen any strategy that works with Condorcet methods --
which I call "pairwise counting" when I'm talking to non-math folks.
Yes, IF there is a cycle, or something close to a
rock-paper-scissors-like cycle, then yes there are strategies that
become relevant.

In the VoteFair American Idol polls the only times I saw a cycle were
when just a few people -- say less than 20 -- had cast their vote, and
by the time there were around 50 votes there was never a cycle.

Plus, the ranking at around 50 votes typically was very close to the
final ranking when a thousand or more ballots had been cast.

Richard Fobes

Post by Juho Laatu

Post by Kevin Venzke
It's not whether they are ranked (margins will essentially force me to rank
them, I think), it's whether I decide to rank them sincerely.

I think all Condorcet methods have a severe incentive to apply one
particular strategy. That is the strategy of sincerity, or the strategy
if voting / casting one's vote. There is an incentive to rank all the
potential winners (one can rank them all by listing all except one of
them in the ballot).
All potential members of a top loop are included in the definition of
potential winners. Both sincere and strategic potential winners are
included in the definition.
Let's assume that in some group of voters all prefer A to B but they
don't rank candidates A and B. B wins the election, and A is not too far
behind. It is obvious that those voters would have had a better
strategy, the strategy of expressing their opinion on whether A or B
should win. This is not a rare incident if it is common among the voters
not to rank many of the potential winners. This could thus be the most
common mistake that a voter might make in an election. It is about as
severe as staying home in a Plurality election, and then wondering
afterwards, why the favourite of our group did not win.
Wouldn't you call this a strong strategic incentive? :-) The impact of
many other strategies could be much weaker and more improbable. Any
strategy that includes truncation would force you not to follow this
strategy. And strategies that include changing the order of some of the
candidates could be even more catastrophic. These effects are
particularly strong in large public elections where nobody has accurate
prior knowledge on how people are going to vote, or how much and what
strategies they might apply.

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

Post by Kevin Venzke
I'm not sure if you thought I was talking about a legislature using
Condorcet. What I was saying is that I don't think the behavior of a
legislature would be emulated well by, for example, picking any arbitrary
option from the top cycle. Some of those options may not be plausible
outcomes, despite what the pairwise matrix says.

I think what I was thinking wast only that in small closed circles where
everyone knows everyone's opinions strategic tricks are easier (but not
easy) to apply than in typical large public elections.
I think Condorcet does pretty good job also when there are non-plausible
alternatives in the election. If some option is really bad, it would not
end up in the top cycle. Or do you expect strategic voting to be so
rampant that legislators would use their most disliked options in their
strategies and eventually elect them? A sensible voter should rank the
non-plausible non-wanted options last.

Post by Kevin Venzke

Post by Juho Laatu
Yes, Plurality's reference to first preferences is not good. If one
wants to say something more generic that is not tied to first
preference votes, one should reformulate the criterion. The criterion
would not be as sexy that way. Also the use of implicit approval should
be made clearer, if the intention is to say something about voters that
assume it, or a method that makes some use of it.

One idea is that Plurality approximately says that if candidate X wins
then there should be some way to place approval cutoffs within the
rankings such that X is the approval winner. (First preferences come
into play because it's assumed no one would disapprove those.)

That's a good approach. Ability to win an Approval election (without
changing the rankings) says pretty much everything that the traditional
Plurality definition should say. Maybe it should be called and Approval
criterion or something like that instead (word "Plurality" is quite
confusing even with the original definition).
First preferences have an impact since they are the extreme top position
in the rankings. A good definition should however not include any
references to them. One viewpoint to this is that we can always add to
an election n new candidates where n = number of voters. Each voter has
now his own private candidate that is ranked first in one vote and last
in all other votes. The results should still be the same, although all
the old candidates now have zero first preference votes.
Juho
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[Juho Laatu]

Post by Juho Laatu
...
I think all Condorcet methods have a severe incentive to apply one
particular strategy. ...
...
Let's assume that in some group of voters all prefer A to B but they
don't rank candidates A and B. B wins the election, and A is not too far
behind. It is obvious that those voters would have had a better
strategy, the strategy of expressing their opinion on whether A or B
should win. This is not a rare incident if it is common among the voters
not to rank many of the potential winners. ...

In real-world situations that involve more than about 10 voters, strategies do not work when Condorcet methods are used.

Yes, most strategic scenarios are difficult to apply and they may backfire. Or sometimes easy to apply but inefficient or harmless (e.g. incentive to rank all candidates). I note that if voters follow the advice to rank all potential winners, that makes strategy related questions somewhat simpler since we can expect to get lots of full rankings of all the potential winners. Just as you say, small elections with voters that know the opinions of each others are more problematic than large public elections with independent voters. Some societies might be more strategy oriented than others, but I hope people would soon learn that putting more effort on sincere campaigns works better than attempts to apply some strategy.

Based on my experience with the VoteFair American Idol poll, initially voters started out using approval-like voting, or single-mark-ballot-like voting. But over time -- when they saw that the results revealed a full ranking and not just a single "winner" -- they learned to more fully rank the choices. At that point the voters ranked choices at the same level only when they didn't have much of an opinion about which were better or worse than the others at that ranking level.

That sounds good. People may need some experiences or training to stat trusting new and better methods. Political elections are of course somewhat more competitive than polls, but I'd expect the same rules to apply also there.

So far I have not seen any strategy that works with Condorcet methods -- which I call "pairwise counting" when I'm talking to non-math folks. Yes, IF there is a cycle, or something close to a rock-paper-scissors-like cycle, then yes there are strategies that become relevant.

Yes, I have many times asked people to write generic guides (for Condorcet elections) that would tell the voters (or party strategists) when and how one should vote strategically. I have not seen any such working guidance yet. There are however some technically quite risk free strategies, like the idea to rank all the candidates in the hope of generating a loop that might have an effect, or strategy to give systematic guidance on how to loop the candidates of the opposing party, but also these are so far away from working strategies that they can not be considered an obvious vulnerability. Condorcet methods of course have the problem that always when there is a sincere loop, there is a majority that would like to change the winner. But making strategic decisions based on that before the election is far from easy. Considerations like "what if this particular group would have voted otherwise" are interesting to study after we know how people voted, but they are of no use before
the election when we don't know who people are planning to vote, and what other strategies some other groupings might apply.

In the VoteFair American Idol polls the only times I saw a cycle were when just a few people -- say less than 20 -- had cast their vote, and by the time there were around 50 votes there was never a cycle.

Some polls may be more prone to having cycles than political elections. If we take 100 random candidates/options that voters do not know very well, and ask the voters to rank them, we might get loops because opinions of the voters would be quite random. In typical political elections there are strong voting patterns (e.g. left wing voters vote for the left wing candidates) that make such random loops less likely.

Plus, the ranking at around 50 votes typically was very close to the final ranking when a thousand or more ballots had been cast.

This is also a good sign, indicating that the results are stable.

Juho

Richard Fobes

Post by Juho Laatu

Post by Kevin Venzke
It's not whether they are ranked (margins will essentially force me to rank
them, I think), it's whether I decide to rank them sincerely.

I think all Condorcet methods have a severe incentive to apply one
particular strategy. That is the strategy of sincerity, or the strategy
if voting / casting one's vote. There is an incentive to rank all the
potential winners (one can rank them all by listing all except one of
them in the ballot).
All potential members of a top loop are included in the definition of
potential winners. Both sincere and strategic potential winners are
included in the definition.
Let's assume that in some group of voters all prefer A to B but they
don't rank candidates A and B. B wins the election, and A is not too far
behind. It is obvious that those voters would have had a better
strategy, the strategy of expressing their opinion on whether A or B
should win. This is not a rare incident if it is common among the voters
not to rank many of the potential winners. This could thus be the most
common mistake that a voter might make in an election. It is about as
severe as staying home in a Plurality election, and then wondering
afterwards, why the favourite of our group did not win.
Wouldn't you call this a strong strategic incentive? :-) The impact of
many other strategies could be much weaker and more improbable. Any
strategy that includes truncation would force you not to follow this
strategy. And strategies that include changing the order of some of the
candidates could be even more catastrophic. These effects are
particularly strong in large public elections where nobody has accurate
prior knowledge on how people are going to vote, or how much and what
strategies they might apply.

Post by Kevin Venzke
Legislators usually don't use election
methods. I would say essentially they figure out among themselves what
the outcome likely must be and then "elect" it, typically by a majority
vote. If voters could do that directly I think that would be the ideal
situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in
some parliaments. Although negotiations and Plurality can be used to
solve many cases, also Condorcet and the idea of having multiple
candidates could have some benefits. The first one in my mind is
openness. Even when the "big boys" have agreed something behind the
screens, and then bring that decision into a majority vote, some smaller
groupings could add some alternatives in the election that they consider
better. This would open up the available alternatives to the world
(media, public), and all voters would have to take position on the
presented alternatives. Small parties or groupings could thus make
sensible compromise proposals that might even win, if they are good enough.

Post by Kevin Venzke
I'm not sure if you thought I was talking about a legislature using
Condorcet. What I was saying is that I don't think the behavior of a
legislature would be emulated well by, for example, picking any arbitrary
option from the top cycle. Some of those options may not be plausible
outcomes, despite what the pairwise matrix says.

I think what I was thinking wast only that in small closed circles where
everyone knows everyone's opinions strategic tricks are easier (but not
easy) to apply than in typical large public elections.
I think Condorcet does pretty good job also when there are non-plausible
alternatives in the election. If some option is really bad, it would not
end up in the top cycle. Or do you expect strategic voting to be so
rampant that legislators would use their most disliked options in their
strategies and eventually elect them? A sensible voter should rank the
non-plausible non-wanted options last.

Post by Kevin Venzke

Post by Juho Laatu
Yes, Plurality's reference to first preferences is not good. If one
wants to say something more generic that is not tied to first
preference votes, one should reformulate the criterion. The criterion
would not be as sexy that way. Also the use of implicit approval should
be made clearer, if the intention is to say something about voters that
assume it, or a method that makes some use of it.

One idea is that Plurality approximately says that if candidate X wins
then there should be some way to place approval cutoffs within the
rankings such that X is the approval winner. (First preferences come
into play because it's assumed no one would disapprove those.)

That's a good approach. Ability to win an Approval election (without
changing the rankings) says pretty much everything that the traditional
Plurality definition should say. Maybe it should be called and Approval
criterion or something like that instead (word "Plurality" is quite
confusing even with the original definition).
First preferences have an impact since they are the extreme top position
in the rankings. A good definition should however not include any
references to them. One viewpoint to this is that we can always add to
an election n new candidates where n = number of voters. Each voter has
now his own private candidate that is ranked first in one vote and last
in all other votes. The results should still be the same, although all
the old candidates now have zero first preference votes.
Juho
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[Kristofer Munsterhjelm]

Post by Juho Laatu

Post by Andrew Myers
1. WV: (W1, L1) > (W2, L2) if W1 > W2 or (W1=W2 and L2 > L1)
[currently implemented] 2. Margins: (W1, L1) > (W2, L2) if W1 - L1

W2 - L2 3. LV: (W1, L1) > (W2, L2) if L1 < L2 or (L1 = L2 and W1
W2)

Those functions make sense to me. I would maybe separate the basic
WV, margins and LV definitions from the additional tie breaker
definitions ("W1=W2 and L2 > L1" and "L1 = L2 and W1 > W2").

Post by Andrew Myers
On 25 Apr 2017, at 11:06, Kristofer Munsterhjelm
I'm usually a wv person, but I think Minmax is more classically
associated with margins. Or perhaps I think that because Juho is
here and he prefers margins :-)

The strongest argument in favour of margins must be that it is a
relatively natural preference function. WV and LV are discontinuous
functions and therefore can not really be called natural. Interest in
using them comes mainly form strategic defence reasons, not from
studying what would be a natural way of measuring strengths of
preference. In addition the results that you get close to those
discontinuities may appear strange (one additional vote may change
the outcome radically).

Do you consider Plurality a strategic criterion? It seems to me to be
more of a "natural behavior" criterion: if A gets more first preferences
than B gets any preferences, then B shouldn't win. This seems reasonable
from a natural behavior perspective because A dominates B in some
Approval-ish sense.

If that's a "natural behavior" criterion, then you could say that
margins is more natural from a descriptive point of view (no
discontinuities) while wv is more natural from a criterion point of
view. Though, if we're to go by the apparent popularity of IRV, it seems
that descriptive clarity weighs heavier than criterion clarity.
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[Juho Laatu]

Post by Kristofer Munsterhjelm
Do you consider Plurality a strategic criterion? It seems to me to be
more of a "natural behavior" criterion: if A gets more first preferences
than B gets any preferences, then B shouldn't win. This seems reasonable
from a natural behavior perspective because A dominates B in some
Approval-ish sense.
If that's a "natural behavior" criterion, then you could say that
margins is more natural from a descriptive point of view (no
discontinuities) while wv is more natural from a criterion point of
view. Though, if we're to go by the apparent popularity of IRV, it seems
that descriptive clarity weighs heavier than criterion clarity.

First of all, my thinking when it comes to practical election methods is not very criterion oriented. I tend to see criteria and criterion compatibility as important theoretical results that are mostly too far from practical election method considerations to be applied directly on them as viability criteria. The relevance of different criteria to practical election methods is almost as low as the relevance of latest mathematical inventions to practical everyday economic calculations (well, not quite, but something in that direction). I'm about at the level of accepting Condorcet criterion if we seriously want to have a neutral majority based method for consensus oriented single winner elections. One has to take also into account the fact that all election methods are bound to break some potentially useful criteria. All this means that I classify Plurality and most other criteria as an interesting discussion points but not something to be followed categorically. There are many
criteria that are useful in the sense that most elections should have strong orientation in the described direction, but no need, or possibly with strong reasons to deviate from some criteria in some special (usually marginal) situations.

I think Plurality is a bit strange. Actually it is not even a criterion of of ranked methods. It is a criterion for ranked methods with implicit approval cutoff. It makes the assumption that a voter that casts a short vote has somehow approved those candidates that he marked, and not approved the others. In different elections the behaviour of voters with respect to which candidates will be marked on the ballot may vary a lot, and that may have nothing to do with how much the voters support or approve those candidates. In order to make any sense of the Plurality criterion we are thus tied to having an assumption of implicit approval in the ballots, where marking a candidate means approving that candidate at some level.

One reason why I don't like implicit approval in general (as a fact that is known by the voters) is that it encourages voters not to rank candidates that they don't like. Ranked methods work well only if most voters do rank explicitly at least all the potential winners (or all of them except one). If there is an approval cutoff, it would be better if it was an explicit one (this comment is not Plurality criterion specific but a general one).

Plurality criterion is a "heuristic" criterion in the sense that its message somehow sounds good (e.g. to people that do not regularly deal with election methods and their peculiarities). People would like also criterion "if voters would prefer A to B, then B should not win". But EM experts know that this criterion would not be a very good one, although it states something that we all would like to be true in all elections. What I'm trying to say here is only that we should be careful with cyclic group opinions. They will contain some nasty features. Instead of trying to pick a set of criteria that should be met 100%, my preferred approach is to see what kind of problems each method would be likely to face in real elections (typically but not necessarily large public elections with many different kind of voters that the strategists can not control), and evaluate them based on their performance in such real life situations.

I'm not well prepared to comment how margins can handle Plurality criterion but I'll address one basic (but theoretical and extreme, i.e. unlikely to happen in typical elections) example. 35:A, 34:B>C, 31:C. A has more first preferences than B has ballots where B is marked. B's worst defeat margin is however smallest (1), so it will win in typical margins based methods. Plurality criterion says that B should not win. B is however two votes short of being a Condorcet winner, so it can't be the worst of the worst. What if A would win? Plurality criterion pays special attention to A's high number of first preferences. But on the other hand voters would like to elect C instead of A with large majority (C>A voters would not be happy with the result). How about C then? Plurality criterion accepts C too, but using the high number of first preference votes of A as an argument that supports C does not make much sense. My conclusion is that this is a typical mess that we can get with c
ircular preferences. Our voters were quite stupid when they didn't sufficiently rank the potential winners. There are many different possible scenarios on what the truncated opinions might have been, and different results emerging from that. In this example my recommendation would be to tell to the voters that they should rank all potential winners (except maybe the worst one). I don't see any need to start blaming (or praising) margins on what happened. Maybe you have some realistic examples in your mind, that would give better justification to the Plurality criterion.

Juho


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[Toby Pereira]

I think I basically agree with Juho on this. The plurality criterion sounds like a reasonable criterion on the surface, but think about it more and it's arguably less so. To summarise, in a pairwise method, first place on a ballot doesn't hold any special status, nor does indeed last place (or joint last place or "unranked"). And a criterion shouldn't be used to impose an approval cut-off on a method that doesn't have one in its definition.
So while it sounds like a good criterion, removing the special status of these positions means that we are left with just saying that a candidate who pairwise beats another candidate should finish ahead in the overall ranking. Which is what all Condorcet methods do - except when there's a cycle.
Toby

From: Juho Laatu <***@gmail.com>
To: Election Methods <election-***@lists.electorama.com>
Sent: Thursday, 27 April 2017, 22:57
Subject: Re: [EM] Fwd: Ordering defeats in Minimax

Post by Kristofer Munsterhjelm
Do you consider Plurality a strategic criterion? It seems to me to be
more of a "natural behavior" criterion: if A gets more first preferences
than B gets any preferences, then B shouldn't win. This seems reasonable
from a natural behavior perspective because A dominates B in some
Approval-ish sense.
If that's a "natural behavior" criterion, then you could say that
margins is more natural from a descriptive point of view (no
discontinuities) while wv is more natural from a criterion point of
view. Though, if we're to go by the apparent popularity of IRV, it seems
that descriptive clarity weighs heavier than criterion clarity.

First of all, my thinking when it comes to practical election methods is not very criterion oriented. I tend to see criteria and criterion compatibility as important theoretical results that are mostly too far from practical election method considerations to be applied directly on them as viability criteria. The relevance of different criteria to practical election methods is almost as low as the relevance of latest mathematical inventions to practical everyday economic calculations (well, not quite, but something in that direction). I'm about at the level of accepting Condorcet criterion if we seriously want to have a neutral majority based method for consensus oriented single winner elections. One has to take also into account the fact that all election methods are bound to break some potentially useful criteria. All this means that I classify Plurality and most other criteria as an interesting discussion points but not something to be followed categorically. There are many
  criteria that are useful in the sense that most elections should have strong orientation in the described direction, but no need, or possibly with strong reasons to deviate from some criteria in some special (usually marginal) situations.

I think Plurality is a bit strange. Actually it is not even a criterion of of ranked methods. It is a criterion for ranked methods with implicit approval cutoff. It makes the assumption that a voter that casts a short vote has somehow approved those candidates that he marked, and not approved the others. In different elections the behaviour of voters with respect to which candidates will be marked on the ballot may vary a lot, and that may have nothing to do with how much the voters support or approve those candidates. In order to make any sense of the Plurality criterion we are thus tied to having an assumption of implicit approval in the ballots, where marking a candidate means approving that candidate at some level.

One reason why I don't like implicit approval in general (as a fact that is known by the voters) is that it encourages voters not to rank candidates that they don't like. Ranked methods work well only if most voters do rank explicitly at least all the potential winners (or all of them except one). If there is an approval cutoff, it would be better if it was an explicit one (this comment is not Plurality criterion specific but a general one).

Plurality criterion is a "heuristic" criterion in the sense that its message somehow sounds good (e.g. to people that do not regularly deal with election methods and their peculiarities). People would like also criterion "if voters would prefer A to B, then B should not win". But EM experts know that this criterion would not be a very good one, although it states something that we all would like to be true in all elections. What I'm trying to say here is only that we should be careful with cyclic group opinions. They will contain some nasty features. Instead of trying to pick a set of criteria that should be met 100%, my preferred approach is to see what kind of problems each method would be likely to face in real elections (typically but not necessarily large public elections with many different kind of voters that the strategists can not control), and evaluate them based on their performance in such real life situations.

I'm not well prepared to comment how margins can handle Plurality criterion but I'll address one basic (but theoretical and extreme, i.e. unlikely to happen in typical elections) example. 35:A, 34:B>C, 31:C. A has more first preferences than B has ballots where B is marked. B's worst defeat margin is however smallest (1), so it will win in typical margins based methods. Plurality criterion says that B should not win. B is however two votes short of being a Condorcet winner, so it can't be the worst of the worst. What if A would win? Plurality criterion pays special attention to A's high number of first preferences. But on the other hand voters would like to elect C instead of A with large majority (C>A voters would not be happy with the result). How about C then? Plurality criterion accepts C too, but using the high number of first preference votes of A as an argument that supports C does not make much sense. My conclusion is that this is a typical mess that we can get with c
ircular preferences. Our voters were quite stupid when they didn't sufficiently rank the potential winners. There are many different possible scenarios on what the truncated opinions might have been, and different results emerging from that. In this example my recommendation would be to tell to the voters that they should rank all potential winners (except maybe the worst one). I don't see any need to start blaming (or praising) margins on what happened. Maybe you have some realistic examples in your mind, that would give better justification to the Plurality criterion.

Juho


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Election-Methods mailing list - see http://electorama.com/em for list info

[Juho Laatu]

That was a good summary of the weaknesses of the Plurality criterion. I wonder if the Plurality criterion could be reformulated so that it would not refer to the first preferences at all, and it would make its message on the implicit approvals clearer.

Juho

Post by Toby Pereira
I think I basically agree with Juho on this. The plurality criterion sounds like a reasonable criterion on the surface, but think about it more and it's arguably less so. To summarise, in a pairwise method, first place on a ballot doesn't hold any special status, nor does indeed last place (or joint last place or "unranked"). And a criterion shouldn't be used to impose an approval cut-off on a method that doesn't have one in its definition.
So while it sounds like a good criterion, removing the special status of these positions means that we are left with just saying that a candidate who pairwise beats another candidate should finish ahead in the overall ranking. Which is what all Condorcet methods do - except when there's a cycle.
Toby
Sent: Thursday, 27 April 2017, 22:57
Subject: Re: [EM] Fwd: Ordering defeats in Minimax

Post by Kristofer Munsterhjelm
Do you consider Plurality a strategic criterion? It seems to me to be
more of a "natural behavior" criterion: if A gets more first preferences
than B gets any preferences, then B shouldn't win. This seems reasonable
from a natural behavior perspective because A dominates B in some
Approval-ish sense.
If that's a "natural behavior" criterion, then you could say that
margins is more natural from a descriptive point of view (no
discontinuities) while wv is more natural from a criterion point of
view. Though, if we're to go by the apparent popularity of IRV, it seems
that descriptive clarity weighs heavier than criterion clarity.

First of all, my thinking when it comes to practical election methods is not very criterion oriented. I tend to see criteria and criterion compatibility as important theoretical results that are mostly too far from practical election method considerations to be applied directly on them as viability criteria. The relevance of different criteria to practical election methods is almost as low as the relevance of latest mathematical inventions to practical everyday economic calculations (well, not quite, but something in that direction). I'm about at the level of accepting Condorcet criterion if we seriously want to have a neutral majority based method for consensus oriented single winner elections. One has to take also into account the fact that all election methods are bound to break some potentially useful criteria. All this means that I classify Plurality and most other criteria as an interesting discussion points but not something to be followed categorically. There are many
criteria that are useful in the sense that most elections should have strong orientation in the described direction, but no need, or possibly with strong reasons to deviate from some criteria in some special (usually marginal) situations.
I think Plurality is a bit strange. Actually it is not even a criterion of of ranked methods. It is a criterion for ranked methods with implicit approval cutoff. It makes the assumption that a voter that casts a short vote has somehow approved those candidates that he marked, and not approved the others. In different elections the behaviour of voters with respect to which candidates will be marked on the ballot may vary a lot, and that may have nothing to do with how much the voters support or approve those candidates. In order to make any sense of the Plurality criterion we are thus tied to having an assumption of implicit approval in the ballots, where marking a candidate means approving that candidate at some level.
One reason why I don't like implicit approval in general (as a fact that is known by the voters) is that it encourages voters not to rank candidates that they don't like. Ranked methods work well only if most voters do rank explicitly at least all the potential winners (or all of them except one). If there is an approval cutoff, it would be better if it was an explicit one (this comment is not Plurality criterion specific but a general one).
Plurality criterion is a "heuristic" criterion in the sense that its message somehow sounds good (e.g. to people that do not regularly deal with election methods and their peculiarities). People would like also criterion "if voters would prefer A to B, then B should not win". But EM experts know that this criterion would not be a very good one, although it states something that we all would like to be true in all elections. What I'm trying to say here is only that we should be careful with cyclic group opinions. They will contain some nasty features. Instead of trying to pick a set of criteria that should be met 100%, my preferred approach is to see what kind of problems each method would be likely to face in real elections (typically but not necessarily large public elections with many different kind of voters that the strategists can not control), and evaluate them based on their performance in such real life situations.
I'm not well prepared to comment how margins can handle Plurality criterion but I'll address one basic (but theoretical and extreme, i.e. unlikely to happen in typical elections) example. 35:A, 34:B>C, 31:C. A has more first preferences than B has ballots where B is marked. B's worst defeat margin is however smallest (1), so it will win in typical margins based methods. Plurality criterion says that B should not win. B is however two votes short of being a Condorcet winner, so it can't be the worst of the worst. What if A would win? Plurality criterion pays special attention to A's high number of first preferences. But on the other hand voters would like to elect C instead of A with large majority (C>A voters would not be happy with the result). How about C then? Plurality criterion accepts C too, but using the high number of first preference votes of A as an argument that supports C does not make much sense. My conclusion is that this is a typical mess that we can get with c
ircular preferences. Our voters were quite stupid when they didn't sufficiently rank the potential winners. There are many different possible scenarios on what the truncated opinions might have been, and different results emerging from that. In this example my recommendation would be to tell to the voters that they should rank all potential winners (except maybe the worst one). I don't see any need to start blaming (or praising) margins on what happened. Maybe you have some realistic examples in your mind, that would give better justification to the Plurality criterion.
Juho
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[Andrew Myers]

Thanks for all the useful feedback from everyone on this topic.

I decided to implement Minimax with the following ordering: defeats are
ordered by margins (W-L), and by ratios (W/L) when margins are tied.
Further, two candidates are compared first by their weakest defeats;
then, if tied on those, by their 2nd weakest defeats, and so on. This
comparison method was suggested by Richard Darlington. It seems to work
well in practice -- the results seem intuitive and reasonable, and the
algorithm is also efficient.

-- Andrew

Post by Juho Laatu
That was a good summary of the weaknesses of the Plurality criterion.
I wonder if the Plurality criterion could be reformulated so that it
would not refer to the first preferences at all, and it would make its
message on the implicit approvals clearer.
Juho

Post by Toby Pereira
I think I basically agree with Juho on this. The plurality criterion
sounds like a reasonable criterion on the surface, but think about it
more and it's arguably less so. To summarise, in a pairwise method,
first place on a ballot doesn't hold any special status, nor does
indeed last place (or joint last place or "unranked"). And a
criterion shouldn't be used to impose an approval cut-off on a method
that doesn't have one in its definition.
So while it sounds like a good criterion, removing the special status
of these positions means that we are left with just saying that a
candidate who pairwise beats another candidate should finish ahead in
the overall ranking. Which is what all Condorcet methods do - except
when there's a cycle.
Toby
------------------------------------------------------------------------
*Sent:* Thursday, 27 April 2017, 22:57
*Subject:* Re: [EM] Fwd: Ordering defeats in Minimax

On 27 Apr 2017, at 10:25, Kristofer Munsterhjelm
Do you consider Plurality a strategic criterion? It seems to me to be
more of a "natural behavior" criterion: if A gets more first

preferences

than B gets any preferences, then B shouldn't win. This seems

reasonable

from a natural behavior perspective because A dominates B in some
Approval-ish sense.
If that's a "natural behavior" criterion, then you could say that
margins is more natural from a descriptive point of view (no
discontinuities) while wv is more natural from a criterion point of
view. Though, if we're to go by the apparent popularity of IRV, it

seems

that descriptive clarity weighs heavier than criterion clarity.

First of all, my thinking when it comes to practical election methods
is not very criterion oriented. I tend to see criteria and criterion
compatibility as important theoretical results that are mostly too
far from practical election method considerations to be applied
directly on them as viability criteria. The relevance of different
criteria to practical election methods is almost as low as the
relevance of latest mathematical inventions to practical everyday
economic calculations (well, not quite, but something in that
direction). I'm about at the level of accepting Condorcet criterion
if we seriously want to have a neutral majority based method for
consensus oriented single winner elections. One has to take also into
account the fact that all election methods are bound to break some
potentially useful criteria. All this means that I classify Plurality
and most other criteria as an interesting discussion points but not
something to be followed categorically. There are many
criteria that are useful in the sense that most elections should
have strong orientation in the described direction, but no need, or
possibly with strong reasons to deviate from some criteria in some
special (usually marginal) situations.
I think Plurality is a bit strange. Actually it is not even a
criterion of of ranked methods. It is a criterion for ranked methods
with implicit approval cutoff. It makes the assumption that a voter
that casts a short vote has somehow approved those candidates that he
marked, and not approved the others. In different elections the
behaviour of voters with respect to which candidates will be marked
on the ballot may vary a lot, and that may have nothing to do with
how much the voters support or approve those candidates. In order to
make any sense of the Plurality criterion we are thus tied to having
an assumption of implicit approval in the ballots, where marking a
candidate means approving that candidate at some level.
One reason why I don't like implicit approval in general (as a fact
that is known by the voters) is that it encourages voters not to rank
candidates that they don't like. Ranked methods work well only if
most voters do rank explicitly at least all the potential winners (or
all of them except one). If there is an approval cutoff, it would be
better if it was an explicit one (this comment is not Plurality
criterion specific but a general one).
Plurality criterion is a "heuristic" criterion in the sense that its
message somehow sounds good (e.g. to people that do not regularly
deal with election methods and their peculiarities). People would
like also criterion "if voters would prefer A to B, then B should not
win". But EM experts know that this criterion would not be a very
good one, although it states something that we all would like to be
true in all elections. What I'm trying to say here is only that we
should be careful with cyclic group opinions. They will contain some
nasty features. Instead of trying to pick a set of criteria that
should be met 100%, my preferred approach is to see what kind of
problems each method would be likely to face in real elections
(typically but not necessarily large public elections with many
different kind of voters that the strategists can not control), and
evaluate them based on their performance in such real life situations.
I'm not well prepared to comment how margins can handle Plurality
criterion but I'll address one basic (but theoretical and extreme,
i.e. unlikely to happen in typical elections) example. 35:A, 34:B>C,
31:C. A has more first preferences than B has ballots where B is
marked. B's worst defeat margin is however smallest (1), so it will
win in typical margins based methods. Plurality criterion says that B
should not win. B is however two votes short of being a Condorcet
winner, so it can't be the worst of the worst. What if A would win?
Plurality criterion pays special attention to A's high number of
first preferences. But on the other hand voters would like to elect C
instead of A with large majority (C>A voters would not be happy with
the result). How about C then? Plurality criterion accepts C too, but
using the high number of first preference votes of A as an argument
that supports C does not make much sense. My conclusion is that this
is a typical mess that we can get with c
ircular preferences. Our voters were quite stupid when they didn't
sufficiently rank the potential winners. There are many different
possible scenarios on what the truncated opinions might have been,
and different results emerging from that. In this example my
recommendation would be to tell to the voters that they should rank
all potential winners (except maybe the worst one). I don't see any
need to start blaming (or praising) margins on what happened. Maybe
you have some realistic examples in your mind, that would give better
justification to the Plurality criterion.
Juho
----
Election-Methods mailing list - see http://electorama.com/em
<http://electorama.com/em>for list info

[Kevin Venzke]

Hi all,
Kristofer wrote:>Do you consider Plurality a strategic criterion? It seems to me to be>more of a "natural behavior" criterion
FWIW I don't consider Plurality a strategy criterion. We can bring up strategy criteriaif we wanted to, but they are more obscure than the Woodall criteria. The best knownone worth bringing up is favorite betrayal, but WV methods don't completely satisfy it,so I would be stuck talking about simulations instead of firm guarantees.
(You may ask why does favorite betrayal come into it? Because the same incentives thatare supposed to discourage margins voters from truncating at the bottom, also discouragethem from equal-ranking a set of favorites at the top. And there isn't a mechanism ensuringthat ideal strategy is to simply rank them sincerely.)
I would say margins' largest issues are strategy-related, but its most obvious issuesaren't, so I prefer to talk about "natural behavior" when I have a choice.
To Juho:
You feel criteria are "too far from practical election method considerations to be applieddirectly on them as viability criteria"; that is actually very close to how I view yourcriteria (even if you don't use the term "criteria"). You say the "strongest argument" formargins is that it is a relatively natural and continuous preference function.
I guess that you don't say that this involves "practical considerations," and it's justan aesthetic preference. I give you credit for consistency in not even mentioning mono-add-top, which could easily be argued to be a practical consideration. On the otherhand you seem to believe WV has effective strategy incentives that result in things you don't like, so you don't seem to completely dismiss practical considerations either.
I find it more accurate when you complain that WV seems like an approval hybrid thanwhen you suggest that interest in WV stems from strategic defense concerns. When peopleinvent random new methods on EM they frequently behave like WV (or IRV); it's very hard toemulate margins' results without actually being margins. Methods that show approval-likebehavior stem from a relatively common expectation that expressed votes are a goodindication of viability/merit. There may be good historical reasons to portray WV as ahorrified reaction to margins... And I can imagine the FPP supporter who says interest inIRV "comes mainly from strategic defense reasons." But that seems like a limited way oflooking at it.
You write:>I think Plurality is a bit strange. Actually it is not even a criterion >of ranked methods. It is a criterion for ranked methods with implicit>approval cutoff. It makes the assumption that a voter that casts a short>vote has somehow approved those candidates that he marked, and not approved>the others. In different elections the behaviour of voters with respect>to which candidates will be marked on the ballot may vary a lot, and that>may have nothing to do with how much the voters support or approve those >candidates. In order to make any sense of the Plurality criterion we are >thus tied to having an assumption of implicit approval in the ballots, >where marking a candidate means approving that candidate at some level.
I think voters expect this behavior, and that's why it's important, for example, forthe long-term viability of the method's adoption. Now, you may say that we could convince voters not to expect this. You might even (though I'm still not 100% sure)manage to do this by forbidding voters from truncating at all. In that case, I woulddrop all my objections dealing with naturalness and what voters expect. My remainingcomplaints at that point would be the strategy-related ones.

One reason why I don't like implicit approval in general (as a fact that>is known by the voters) is that it encourages voters not to rank candidates>that they don't like.

Sure, I would rather criticize how margins addresses this than the fact that it triesto address it. IRV does this, for instance: You can rank the worse frontrunner in asincere way and you know that it won't hurt you. In margins we "want" you to rank theworse frontrunner, but it's not expected to be of any use to you, and it can hurt thebetter frontrunner by making "worse" look like your compromise choice.

I'm not well prepared to comment how margins can handle Plurality>criterion but I'll address one basic (but theoretical and extreme,>i.e. unlikely to happen in typical elections) example. 35:A, 34:B>C,>31:C. A has more first preferences than B has ballots where B is>marked. B's worst defeat margin is however smallest (1), so it will>win in typical margins based methods. Plurality criterion says that B>should not win. B is however two votes short of being a Condorcet>winner, so it can't be the worst of the worst. What if A would win?>Plurality criterion pays special attention to A's high number of first>preferences. But on the other hand voters would like to elect C>instead of A with large majority (C>A voters would not be happy with>the result). How about C then? Plurality criterion accepts C too, but>using the high number of first preference votes of A as an argument >that supports C does not make much sense. My conclusion is that this>is a typical mess that we can get with circular preferences. Our>voters were quite stupid when they didn't sufficiently rank the >potential winners. There are many different possible scenarios on what>the truncated opinions might have been, and different results emerging>from that. In this example my recommendation would be to tell to the>voters that they should rank all potential winners (except maybe the>worst one). I don't see any need to start blaming (or praising) margins>on what happened. Maybe you have some realistic examples in your mind,>that would give better justification to the Plurality criterion.

1. I just note that "fewest votes short of being a Condorcet winner" need notstrike one as a particularly less arbitrary standard than Plurality. I do not knowwhat stops one from dismissing yours as a criterion whose "message somehow soundsgood to people that do not regularly deal with election methods." It does "soundgood," I agree with that.
2. I'm not sure what is your basis for calling these voters "stupid." Are you(rhetorically) employing Plurality's assumption that voters didn't like theoutcome? I get the sense that you don't like the outcome yourself.
3. I do understand feeling that Plurality is strange. I don't love it. My view isthat Plurality is an easily articulated subset of a larger principle. Essentially,if the voters were instead legislators selecting an outcome, could B ever prevail?It seems quite unlikely, because at the moment that C is the status quo and the Bvoters wish to assert their win over C, they can't because they are outnumbered bythe A voters. The pairwise contest doesn't occur in a vacuum. In this case Pluralityconveys what I would want.
A more thorough version of Plurality (in my opinion, to my taste) wouldn't talkabout first preferences or votes in total. I doubt this language is necessary toexpress the idea. (The criterion we do have is easy to apply, though.)
Kevin

[Juho Laatu]

In another recent mail I said that I am not a criterion oriented person, and that often there is no need to require 100% compliance to all the numerous criteria. I however gave in an earlier mail (see below) some criteria for (pairwise) preference functions, and I'm about to present some more such criteria here. :-)

I already listed two criteria that typical "natural" preference functions could be requited to have.
P(x,x) = 0
P(x,1-x) = 2x-1

I'll add two monotonicity related requirements.
if a > b then P(a,y) > P(b,y)
if a > b then P(x,a) < P(x,b)

Alternatively one could satisfy with less, and allow also equal results.
if a > b then P(a,y) >= P(b,y)
if a > b then P(x,a) <= P(x,b)

Symmetry is also one natural requirement.
P(x,y) = -P(y,x)

One more requirement could be that the preference functions must be continuous. I'm sure that you'll forgive me that some of the functions in the preference function family that I gave are not defined at (0,0) although the first requirement says that the value of the preference function must be 0 there :-).

Juho

Post by Juho Laatu

1. WV: (W1, L1) > (W2, L2) if W1 > W2 or (W1=W2 and L2 > L1) [currently implemented]
2. Margins: (W1, L1) > (W2, L2) if W1 - L1 > W2 - L2
3. LV: (W1, L1) > (W2, L2) if L1 < L2 or (L1 = L2 and W1 > W2)

Those functions make sense to me. I would maybe separate the basic WV, margins and LV definitions from the additional tie breaker definitions ("W1=W2 and L2 > L1" and "L1 = L2 and W1 > W2").

I'm usually a wv person, but I think Minmax is more classically
associated with margins. Or perhaps I think that because Juho is here
and he prefers margins :-)

The strongest argument in favour of margins must be that it is a relatively natural preference function. WV and LV are discontinuous functions and therefore can not really be called natural. Interest in using them comes mainly form strategic defence reasons, not from studying what would be a natural way of measuring strengths of preference. In addition the results that you get close to those discontinuities may appear strange (one additional vote may change the outcome radically).
Preference function between two candidates (A, B) can be given as a function of x and y, where x is the proportion of votes (0..1) ranking A over B, and y is the proportion of votes (0..1) ranking B over A. The values of the function range from 1 (100% of voters rank A over B) to -1 (100% of voters rank B over A). Value 0 refers to a tie.
Margins preference function is x-y
WV preference function is 0 if x=y, x if x>y, -y if y>x
LV preference function is 0 if x=y, 1-y if x>y, x-1 if y>x
WV and LV are not continuous around the x=y line. It is for example strange that in WV result 51-49 is considered a strong victory to A (0.51), while 50-50 gives 0 and 49-51 gives -0.51.
There are also other possible preference functions. One could measure for example the proportion of A>B preferences against all given preferences (A>B or B>A). This one is close to margins in the sense that it can be seen as one natural preference function. It is also smooth and continuous, except that at point 0-0 it is not even defined. The value of result 1-0 is 1, and the value of result 0-1 is -1, which is a quite radical approach.
Margins and proportions have different philosophy with respect to votes that have not given any preference between A and B (indifferent voters). Margins thinks that indifferent voters gave half a vote to support A>B and half a vote to support B>A. Preferences thinks that indifferent voters want to vote in favour of A vs B in same proportion as those voters did that gave a preference. Both approaches can thus be explained as natural approaches to explaining how the indifferent votes should be read.

The desire to say that a 35-0 win is stronger than a 51-49 win could
make sense if a strong win in itself was of some value.

This (comparison of different results) is a good approach to evaluating how the indifferent votes should be handled. I already wrote above on how proportions could be considered bad around the 0-0 result. In margins it is a good question if 2-0 should be considered to have equal preference strength to 51-49.
I'll define some additional preference strength functions (P). I start from the assumption that margins philosophy can be taken as the starting point for results where all voters have expressed preference (= no indifferent votes). As a result preference value for 100-0 is 1 (for all preference functions of this group of P functions), i.e. P(100,0)=1, and P(50,50)=0, and P(75,25)=0.5. The preference function is thus linear at that line (y = 1-x). Preference value should also always be 0 at line x=y. More formally, P(x,x)=0 and P(x,1-x)=2x-1.
One family of preference functions that meets these criteria is (x-y)*(x+y)^k. We get margins when k=0. We get proportion when k=-1. The next interesting possibility is to use value k=1. This one is interesting because it has some WV like properties without introducing the weird discontinuities of WV. I'll study this function (k=1) a bit more.
(Note that when k=1 the function becomes quite simple, (x-y)*(x+y)^1 = x^2 - y^2.)
First few words about sincere votes. In margins the preference values of 50-0 and 75-25 are equal. Pm(50,0) = Pm(75,25). If one doesn't think this is ideal, one can adjust this relation by adjusting the value of k. When k=1 (P1) we have P1(75,25) = 0.5 (by definition). P1(50,0) = 0.25, Pm(50,0) = 0.5 and Pp(50,0) = 1 (p = proportion). The point of this paragraph is to demonstrate that if you want to have a P that gives best possible results with sincere votes, one can adjust k to reach best performance (within this family of preference functions). One parameter may be enough to address the most typical concerns (?).
What about defence against strategic voting then. In many large public elections such defences may be unnecessary. But for for people that like the WV properties P1 may be of interest also for strategy defence related reasons. It for example gives P1(10,0) = 0.01 while P1(55,45) = 0.1. I will not go further into details although it could be interesting to study the impact of parameters to strategic defence capabilities. The point here is that there are also continuous "natural" preference functions that can reach some of the targets of discontinuous functions like WV.
If one uses parameterized preference functions like the one described above, one can also adjust the parameters (k) so that the function reaches the required strategy resistance, but at the same time deviates from the preferred sincere preference function only as little as possible.

On a side note, Minmax can produce a lot of ties if there are few voters
involved, so sometimes I prefer to break ties by second strongest defeat
(and then third strongest, fourth strongest, etc). That isn't
*classical* Minmax, but it shouldn't break any of Minmax's criteria.

I just note that the parameterized versions may also reduce the probability of ties (e.g. if one uses value k=0.00001 instead of k=0).
Juho

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[Juho Laatu]

Here are some more thoughts on preference functions, and especially on the those preference functions that can be considered natural measures of strength of preference (of two candidates, by a group of voters, using ranked ballots).

The value of a preference function P(x,y) may range from -1 to 1. Parameters x and y get values from 0 to 1. Parameter x refers to the proportion of votes that rank candidate X over candidate Y. Parameter y refers to the proportion of votes that rank candidate Y over candidate X. The proportion of votes that do not rank either candidate above the other is 1-x-y. Function P gets value 1 when all votes rank candidate X over candidate Y. Function P gets value -1 when all votes rank candidate Y over candidate X. Value 0 refers to a tie. The strengths of preferences can be compared by comparing the results of the PFs.

I'll define first some criteria for all "sensible" preference functions (PF).
P(x,y) = -P(y,x)
- symmetric handling of x and y
P(x,x) = 0
- equal amount of preferences in both directions shall always be a tie
P(1,0) = 1
- unanimous support to X
- the target of this requirement is just to normalise the presentation (and preference strength values) of different PFs
P(0,1) = -1
- unanimous support to Y
P shall be monotonic
- grows or stays equal when x grows
- diminishes or stays equal when y grows

The result of a PF is a tie or a victory (with strength) to either candidate. Note that there are comparison methods like Pairwise Opposition that don't give or care about such results (ties, pairwise victories). PFs are thus just a subset of all comparison methods. Pairwise Opposition can't meet the first two requirements above. Pairwise Opposition could be called a strength function (SF). SFs can measure e.g. opposing votes or votes in favour. Their values could be from 0 to 1 (instead of -1 to 1). Symmetric sensible SFs can be defined as functions that can be presented as sensible PFs.

Then some possible criteria for "natural" PFs.
P(x,1-x) = 2x-1
- this one may be valid for all natural PFs
- this criterion normalises the presentation of different PFs (to a scale that feels natural and obvious)
- note that most election methods care only about which preference is stronger, not about how much the values differ (i.e. this criterion has no impact on their operation)
- note that winning votes can not meet this criterion (= can not be normalised) since there is a big value gap between "strong preference" 51-49 and "strong preference" 49-51
P(x+a,y-a) = P(x,y)+k*a
- most natural PFs might respect this criterion
- the idea is that in addition to having linear values when x+y=1 (P(x,1-x) = 2x-1), the values should be linear also when the indifferent voters are excluded (when x+y is constant)
- the value of k may be different for different "lines" (= for different values of x+y)
All natural PFs shall be continuous
- PFs with some kind of thresholds might violate this rule (they could be said to be "natural threshold PFs", but maybe not "natural PFs")
- exceptions to this rule are allowed at point (0,0) since we want to allow functions like proportions / ratio to be called natural PFs

Next I'll present a family of preference functions that meet all of the criteria above. Function f is the modifying parameter that generates the family.
P1(0,0) = 0
P1(x,y) = (x-y)/(x+y)*f(x+y) when x>0 or y>0

Function f can be any function, but it shall meet some requirements.
f is defined in range 0<x≤1
f is monotonic (rising) in range 0<x≤1
f is continuous in range 0<x≤1 (you could skip this one if you really want, and the system still works, maybe just losing the "natural" status)
f(1) = 1
f(x)≥0 when 0<x≤1

Any continuous monotonic function will thus do if it is ≥0 and ends at 1. You'll get margins when f(x)=x. You'll get proportions / ratio when f(x)=1.

Note that when y=0 P1(x,y) becomes (x-0)/(x+0)*f(x+0), and that is f(x). This helps the 3D visualisation of different functions of this preference function family. The 3D function can be thought to consist of a series of straight lines that are parallel to the x+y=1 line. All of them are at height 0 at the point where x=y. Only the tilting angle and length of the lines changes. Their end points of the lines form function f at plane y=0. Function f can make whatever monotonic curves within the rectangle (defined by points (0,0) and (1,1)). Plane x=0 has a corresponding pattern (rotated 180°, with non-positive values, z ≤ 0). If you have a program than can display these functions in 3D, use it. That helped me to understand these functions better.

The smaller family of preference functions (with one parameter) that I gave earlier can be defined in this framework as f(x) = x^n, where n≥0. Within each f you can have also other modifiers (than n). The first additional one that I found interesting is one that changes the angle of the first "lines" next to point (0,0) and line at x+y=1 (see parameters up and down). The next one was parameter turn, that can flip a function e.g. from the bottom right triangle (below line f(x)=x) to the top left triangle (or somewhere in-between). This makes it easier to generate functions with wanted shape also at "the other side" of the f(x))x line. All these modifications will maintain the "natural" properties of the function. I'll give the definition (one version) of the modifier function below. It modifies the results of another function (f) that is expected to meet the same requirements that were given to f above.

f1(x) = up*x + (1 - up*x - down*(1-x)) * ( (1-turn)*f(x)^bend + turn*(1 - f(1-a)^bend + f(0)^bend) )
0 ≤ bend neutral value = 1 (bend=n)
0 ≤ up ≤ 1 neutral value = 0
0 ≤ down ≤ 1 neutral value = 0
0 ≤ turn ≤ 1 neutral value = 0
f is any function that meets the criteria (for f) above

That's enough for now. Any opinions on the value of this kind of natural preference functions? Or on those preference functions that I classified as non-natural? Note that some of the natural preference functions may be quite similar to other non-natural functions. For example proportions / ratio is quite similar to losing votes. I wonder how much also their strategic properties correlate. And I wonder how much the flexibility of these natural preference functions can be used to defend against whatever strategic threats one might assume to exist in the elections. Parameterized functions are good because one can adjust them in a balanced way to protect against each of the identified treats only at suitable level (leaving space for other modifications too, thereby allowing better total defence). The number one use for the parameters may still be to define the fairest possible preference function for sincere votes.

Juho


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[Markus Schulze]

Hallo,

in section 2.1 and in section 6 of my paper, I discuss
the different definitions for the strength of a defeat:

http://m-schulze.9mail.de/verylong.pdf

I my opinion, another natural definition is ratios:

(W1, L1) > (W2, L2) if W1*L2 > W2*L1.

In any case, every definition for the strength of
a defeat should satisfy at least the following
properties:

(2.1.1)
((W1 > W2 and L1 <= L2) or (W1 >= W2 and L1 < L2)) => (W1, L1) > (W2, L2).
[In my paper, I call this property "positive responsiveness"
because it says (a) that the strength of a defeat should
respond to a change of its support or its opposition
and (b) that it should respond in the correct direction.
The term "monotonicity" would only imply that it
responds in the correct direction.]

(2.1.2)
(W1, L1) > (W2, L2) => (L2, W2) > (L1, W1).
[In my paper, I call this property "reversal symmetry".]

(2.1.3)
(c1*W1, c1*L1) > (c1*W2, c1*L2) => (c2*W1, c2*L1) > (c2*W2, c2*L2).
[In my paper, I call this property "homogeneity"
because this property is necessary to guarantee
that the resulting election method satisfies
homogeneity.]

Markus Schulze

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[robert bristow-johnson]

 
Markus, i am happy nearly every time you chip in with an idea.  (Sorry, I just can't read all of the lit, including your writings.)


---------------------------- Original Message ----------------------------

Subject: Re: [EM] Ordering defeats in Minimax

From: "Markus Schulze" <***@alumni.tu-berlin.de>

Date: Fri, April 28, 2017 12:46 am

To: election-***@lists.electorama.com

--------------------------------------------------------------------------

Post by Markus Schulze
Hallo,
in section 2.1 and in section 6 of my paper, I discuss
http://m-schulze.9mail.de/verylong.pdf
(W1, L1) > (W2, L2) if W1*L2 > W2*L1.

this is cool.  it's like margins of the logarithms of the votes.  or, if i may coin a term, the "Geometric Margins"
   W1*L2  >  W2*L1        implies
   W1/L1  >  W2/L2
 
 log(W1) - log(L1)   >   log(W2) - log(L2) 
maybe that is better than the simple "Arithmetic Margins":
   W1 - L1   >   W2 - L2
i've always been dissatisfied by using only Winning Votes (instead of Margins).  i think the
number of Losing Votes should also say something in an election.
one thing that the Arithmetic Margins has over the Geometric Margins (if i may call it that) is that the Geometric Margins care only about the percentage defeat strength, and the number of people voting does not count.
 Arithmetic Margins is the product of the percentage defeat strength times the number of voters weighing in on a race, which *should* (in my opinion) make that race more salient and another race with an equal percentage defeat strength but fewer voters who care about it.

Post by Markus Schulze
In any case, every definition for the strength of
a defeat should satisfy at least the following
(2.1.1)
((W1 > W2 and L1 <= L2) or (W1 >= W2 and L1 < L2)) => (W1, L1) > (W2, L2).
[In my paper, I call this property "positive responsiveness"
because it says (a) that the strength of a defeat should
respond to a change of its support or its opposition
and (b) that it should respond in the correct direction.
The term "monotonicity" would only imply that it
responds in the correct direction.]
(2.1.2)
(W1, L1) > (W2, L2) => (L2, W2) > (L1, W1).
[In my paper, I call this property "reversal symmetry".]
(2.1.3)
(c1*W1, c1*L1) > (c1*W2, c1*L2) => (c2*W1, c2*L1) > (c2*W2, c2*L2).
[In my paper, I call this property "homogeneity"
because this property is necessary to guarantee
that the resulting election method satisfies
homogeneity.]

those are all very reasonable requirements.  seems to me that the simple Arithmetic Margins also have these properties.  maybe not.
thanks for weighing in on this, Markus.  still not *totally* convinced it's better than the conventional definition of
defeat strength with (arithmetic) margins.  but it's something to think about.

--
r b-j                  ***@audioimagination.com
"Imagination is more important than knowledge."

[Markus Schulze]

Hallo,

Darlington's paper ("Minimax is the Best Electoral System
After All") is very interesting:

https://arxiv.org/ftp/arxiv/papers/1606/1606.04371.pdf

There are many papers where some author makes presumptions
about the distribution of the voters and the candidates,
about the used strategies, about how the performance of an
election method is measured in concrete test cases, etc..
The author then proves that his favorite election method
performs better than every other known election method.

However, this is not surprising. The purpose of an
election method is to find the best candidate according
to some heuristic. So you can always use test cases where
this election method's heuristic happens to be met exactly
and then claim that you have proven with random simulations
that your favorite method is the best.

Therefore, a more interesting question is which election
method performs the second best. Here, Darlington writes
that the Schulze method performs the second best, only
slightly worse than his favorite method.

Markus Schulze

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[Andrew Myers]

To follow up on this, the method implemented by CIVS is Darlington's T3
method, described in the paper Markus mentions. The main criterion by
which he judges methods is _minimum change_; that is, the candidate who
is closest to becoming a Condorcet winner if some votes are changed.
This criterion is attractive because it makes the results tend to be
stable with respect to adding or subtracting voters. The biggest
downside is that, as he demonstrates in Section 1.2, a Condorcet loser
can be the candidate who is closest being a Condorcet winner. His
corresponding example can be found here:

http://civs.cs.cornell.edu/cgi-bin/results.pl?id=E_e5c3c20972af0ab5

-- Andrew

Post by Markus Schulze
Hallo,
Darlington's paper ("Minimax is the Best Electoral System
https://arxiv.org/ftp/arxiv/papers/1606/1606.04371.pdf
There are many papers where some author makes presumptions
about the distribution of the voters and the candidates,
about the used strategies, about how the performance of an
election method is measured in concrete test cases, etc..
The author then proves that his favorite election method
performs better than every other known election method.
However, this is not surprising. The purpose of an
election method is to find the best candidate according
to some heuristic. So you can always use test cases where
this election method's heuristic happens to be met exactly
and then claim that you have proven with random simulations
that your favorite method is the best.
Therefore, a more interesting question is which election
method performs the second best. Here, Darlington writes
that the Schulze method performs the second best, only
slightly worse than his favorite method.
Markus Schulze

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[Kristofer Munsterhjelm]

Post by Markus Schulze
Hallo,
Darlington's paper ("Minimax is the Best Electoral System
https://arxiv.org/ftp/arxiv/papers/1606/1606.04371.pdf

[snip]

Post by Markus Schulze
Therefore, a more interesting question is which election
method performs the second best. Here, Darlington writes
that the Schulze method performs the second best, only
slightly worse than his favorite method.

If the best method ends up being Minmax, wouldn't the second best
presumably be the most Minmax-ish of what's left? If so, which method
ends up being second best might not be all that more interesting than
which method ends up being best.

Post by Markus Schulze

Green-Armytage (2014) compared 8 electoral systems
on 5 forms of strategic manipulability. He
found that all 8 were somewhat manipulable, but Borda
was worst while minimax was one of the less
manipulable systems.

Page 17 of that paper shows that there are broadly speaking three
classes of strategy resistance. The least resistant methods (Borda,
Approval, Range), general Condorcet methods (and Plurality), and then
Hare and the Hare hybrids.

Minmax belongs to the middle class, so it's only "one of the less
manipulable" in that it's not in the least resistant class
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[Juho Laatu]

Some quick observations on the paper.

I agree that those criteria that do not allow electing the Minmax winner D of the example should not be considered as criteria that should always be true.

The paper aimed at using continuous and appropriately monotonic functions as preference functions. They fall within the families of natural preference functions that I described in a recent post. Or actually in the smaller family (W-L)*(W+L)^k or (W-L)/(W+L)*(W+L)^k. I.e. methods in a continuous range from proportions/ratio to the proposed square root based approach, and finally to Minmax, but not beyond that point, although methods beyond that point might be interesting too.

The approach of using the second preferences as tie breakers may be problematic because of problems with having or not having clones. Also the approach of using e.g. a square root based method to solve the ties of basic Minmax is a bit ad hoc. One simple approach to solving most of the ties in Minmax is simply to compare the W+L values of the tied candidates (to break ties in pairwise comparisons). That's what k values very close to 0 (e.g. -0,0001) would do anyway in (W-L)*(W+L)^k.

Don't take these comments too seriously since I skimmed the paper already few days ago, and this is about as much as I can remember of the comments that I had then :-).

Juho

Post by Markus Schulze
Hallo,
Darlington's paper ("Minimax is the Best Electoral System
https://arxiv.org/ftp/arxiv/papers/1606/1606.04371.pdf
There are many papers where some author makes presumptions
about the distribution of the voters and the candidates,
about the used strategies, about how the performance of an
election method is measured in concrete test cases, etc..
The author then proves that his favorite election method
performs better than every other known election method.
However, this is not surprising. The purpose of an
election method is to find the best candidate according
to some heuristic. So you can always use test cases where
this election method's heuristic happens to be met exactly
and then claim that you have proven with random simulations
that your favorite method is the best.
Therefore, a more interesting question is which election
method performs the second best. Here, Darlington writes
that the Schulze method performs the second best, only
slightly worse than his favorite method.
Markus Schulze
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