Discussion:
first-wave Condorcet versions for public election
James Green-Armytage
2005-03-13 11:48:33 UTC
Permalink
Dear election methods fans,

In a recent message, I noted that there is no broad consensus among
Condorcet supporters as to which completion methods would be most
appropriate for a few key scenarios. I don't really expect to establish
such a consensus, but I would at least like to address some of the issues
involved, and hear where some of the other Condorcet supporters are coming
from.
There are at least three areas of possible divergence:
1. The base method: Minimax (candidate whose worst loss is least bad),
sequential dropping (drop the weakest defeat that's in a cycle until a
candidate is unbeaten) ranked pairs, river, beatpath, Condorcet completed
by another method, approval hybrids, etc.
2. Measures of defeat strength: margins, winning votes, or something else
(cardinal-weighted pairwise (CWP), approval-weighted pairwise (AWP), etc.)
3. Whether to use an anti-strategy measure (candidate withdrawal option
(CWO), CWP, AERLO/ATLO, iterative procedure, etc.)

Area (1) is not necessarily the most contentious; i.e. most people who
like beatpath like ranked pairs just about as much, and so on. However, I
would not feel especially good about a method that isn't Smith-efficient,
even to start out with. So that cuts out plain minimax as far as I'm
concerned.
I prefer winning votes for area (2), entirely for anti-strategic reasons.
This starts to bring us toward area (3), i.e. strategy. I agree that
winning votes has a better protection against the burying strategy than
margins, but I still suspect it to be somewhat unstable in certain
situations. If I am correct (which is debatable, of course), this brings
us into slightly uncomfortable terrain. CWO is the simplest anti-strategy
method, but some voters might be intuitively uncomfortable with the idea.
CWP has an intuitive interface, but one which requires very sophisticated
ballots, and the tally rule is complex. AWP, AERLO/ATLO, and similar
methods have a somewhat confusing interface, and while the tally rules are
not terribly complex, they are not brilliantly easy to explain, either.
I know that Mike Ossipoff has said that we should all come together
around a winning votes method without an additional anti-strategy measure.
But I'd like to hear what some other people think.
I'm not even sure what I would recommend, if I was in a position to
recommend something for public elections. I lean towards starting out with
a winning votes version of sequential dropping (or any one of ranked
pairs, beatpath, river, if there isn't an intense need for simplicity)
with a CWO. But that's subject to change, with further discussion.

my best,
James

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Russ Paielli
2005-03-14 07:54:04 UTC
Permalink
Post by James Green-Armytage
Dear election methods fans,
In a recent message, I noted that there is no broad consensus among
Condorcet supporters as to which completion methods would be most
appropriate for a few key scenarios. I don't really expect to establish
such a consensus, but I would at least like to address some of the issues
involved, and hear where some of the other Condorcet supporters are coming
from.
1. The base method: Minimax (candidate whose worst loss is least bad),
sequential dropping (drop the weakest defeat that's in a cycle until a
candidate is unbeaten) ranked pairs, river, beatpath, Condorcet completed
by another method, approval hybrids, etc.
The method that I tentatively call "Ranked Approval Voting" (RAV) is not
simply Condorcet "completed" with Approval. (Condorcet completed with
Approval would simply choose the Approval winner from the Smith set or
from the entire set of candidates.) RAV uses Approval as an integral
part of the rules rather than as an afterthought. As I said before, the
approval scores naturally fill in the diagonal elements of the pairwise
matrix. To my way of thinking, RAV is how Condorcet should work (or is
at least one good way it could work).

<cut>
Post by James Green-Armytage
I know that Mike Ossipoff has said that we should all come together
around a winning votes method without an additional anti-strategy measure.
But I'd like to hear what some other people think.
If the EM community adopts this approach, you will be no further ahead
in 30 years than you are today. I guarantee it.
Post by James Green-Armytage
I'm not even sure what I would recommend, if I was in a position to
recommend something for public elections. I lean towards starting out with
a winning votes version of sequential dropping (or any one of ranked
pairs, beatpath, river, if there isn't an intense need for simplicity)
with a CWO. But that's subject to change, with further discussion.
Your last sentence leaves some hope.

Regards,
Russ
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James Green-Armytage
2005-03-14 09:34:00 UTC
Permalink
Post by James Green-Armytage
Post by James Green-Armytage
I know that Mike Ossipoff has said that we should all come together
around a winning votes method without an additional anti-strategy
measure.
Post by James Green-Armytage
But I'd like to hear what some other people think.
If the EM community adopts this approach, you will be no further ahead
in 30 years than you are today. I guarantee it.
Now, I write:
What exactly do you think is wrong with that approach? Please don't say
that defeat-dropping completion methods are too difficult to understand,
because I won't be convinced that your Condorcet/approval method is easier
to understand. Is it the winning votes part that you have a problem with,
or the no additional anti-strategy measure part? My own reservations are
primarily with the latter (strategy) part, as I mentioned.
my best,
James

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Juho Laatu
2005-03-14 08:00:41 UTC
Permalink
Dear All,



One more formulation of the IRV or Condorcet question could be: Why is Condorcet less popular than IRV?





One reason for this is that experts that support Condorcet have not yet agreed which completion method is the best. Another reason is that explaining the differences of alternative Condorcet completion methods leads to quite detailed technical discussions. These two together mean that it is difficult to make simple and concrete proposals that would be backed up by "strong academic support".





IRV has also the additional benefit that the vote counting process looks pretty much like an exciting real life fight where some candidates at some point have to give up and donate their votes to the other candidates. To many people this kind of dramatic nature of the vote counting process may be more interesting than e.g. the relatively complex technical terms that are used on this mailing list to compare different Condorcet alternatives.





The following mechanism is my favourite single winner mechanism for two reasons: 1) technical merits (it is simple and it makes a good pick), 2) it is easy to explain and understand. I think this is about the level of simplicity that would be required to make Condorcet methods more understandable and acceptable to other than the hard core experts.





Least Additional Votes:

"Elect the candidate that wins all others. If there is no such candidate, elect the one that needs least additional votes to win all others."





Not a word about cycles and cycle breaking, not even about pairwise comparison matrixes. This is not really a new method but maybe a new way to describe the rules.





Any support to this kind of thinking and the voting method in question in this group?





- - -





I'll write also few other observations here to give some background to why I like this particular voting method (and this style of defining the voting method).
However, I would not feel especially good about a method that isn't Smith-efficient, even to start out with.
I both agree and disagree with this. I don't feel good about methods that elect an alternative that is not in the Smith set. But on the other hand I similarly do not like methods that create preference loops even in situations where all voter preferences are all non-cyclic. I have however learned that laws of nature and mathematics are such that preference loops occur in group opinions and I can't do anything about it. Condorcet methods are thus still maybe the best single winner methods although they have to cope with this loop problem somehow. For similar reasons I question the value of the Smith set. Sometimes the poor option of electing someone outside the Smith set may still be the best option.





I'll use one concrete example.

101: a>b>x>c

101: b>c>x>a

101: c>a>x>b

100: x

Let's say that we have here four parties of about equal size, and each party has one candidate. Candidate x is a Condorcet loser but, using terminology of the voting method I described above, candidate x would need only two additional votes to become a Condorcet winner. Candidates a, b and c would each need 102 additional votes to become Condorcet winners.





Most people on this list agree that Condorcet winner should always win. Although candidate x is a Condorcet loser, it is very close to being a Condorcet winner (two votes missing). The structure of the graph describing the results must thus in some sense be very flat. If one draws a graph that describes the results of the election, Smith set is typically drawn on top and candidate x below it. This leads to thinking that that "candidate x is clearly below the Smith set and should therefore not be elected". I however claim that the visual structure of such a graph impacts our thinking too strongly here. Graph based visualizations are in general not a very useful tool when discussing voting related matters that involve cyclic preferences.





I guess often also the wish to make election results a linear preference order is present. This happens although we (in theory) already know that group preferences can not be presented as a linear preference order (although individual preferences maybe can). For this reason I don't feel quite comfortable with Condorcet completion rules that try to re-establish this linear structure of individual preferences also in the final results (since that simply is not natural for group preferences).





I like to see the Least Additional Votes method description in the light of "real life impact" (instead of trying to "re-establish a linear preference order" or using other order based measures to justify the method). In the voting example above the election could have been held in order to elect a captain for a pirate ship whose crew consists of pirates that are citizens of four very different countries (maybe about 10 from each country instead of the 100 in the example to be more practical :-) ). Electing pirate x as the captain would be a rather good option since in case of a mutiny planned by a, b or c they would maybe not dare to try it since they would not be able to persuade sufficient majority of the crew to participate in the mutiny (51+% majority with some uncertainty of the plans of few individuals and/or their fighting skills is too risky). Mutiny against captain a, b or c wo
uld be easier. Same rules apply of course also in politics. "Least additional votes" may t
hus
sometimes have a real meaning and impact in the real world (=getting two additional pirates in the ship to eliminate the risk of mutiny in this case). (There may be also other "real life" criteria than this "mutiny criterion" but I won't go further in that direction now.)





In the election methods mailing list I have in the recent months observed lots of discussion on criteria that are related to making the voting methods as strategy free as possible. Sometimes I have even gotten the impression that when electing the winner from the candidates in the top loop (Smith set) it could be anyone in the top loop, as long as the numerous strategy criteria are fulfilled. I guess this has not really been the case, but my point is that one should give high priority to selecting the candidate that we think is best, and maybe a bit less priority to all the strategical considerations. This is based on the assumption that strategical voting is not that easy in real life, at least not in elections where the number of voters is large. Many of the strategical voting cases are problematic only in situations where the voting behaviour of the voters is known. In real life this
is seldom the case. (And cycles are also rare.) With this I want to say that sometimes sim
plicity
and/or "real life need" based rules may be more sensible than detailed strategy based criteria.





All the comments above were written in order to explain why the Least Additional Votes method is so good (possibly in the "fight against IRV" :-), for the non-experts, as well as just in general). James Green-Armytage presented a number of number of good tools and arguments that could be used when trying to achieve consensus within the community on the best single winner method. I didn't consider the Smith set as critical as he did, and as a result I'm leaning in a somewhat different direction when trying to locate the best Condorcet method. Any comments appreciated.





Best Regards,

Juho Laatu

(long time follower but not so active participant of the election methods list :-)



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James Green-Armytage
2005-03-14 09:44:51 UTC
Permalink
Hi Juho, and welcome to the list.
Post by Juho Laatu
"Elect the candidate that wins all others. If there is no such candidate,
elect the one that needs least additional votes to win all others."
I'd like to clarify this, especially the second part. What exactly is an
"additional vote" in this context? A single ballot that lists this
candidate as the first choice, with all others tied for last? A reversal
of a pairwise preference in favor of this candidate?

my best,
James

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James Green-Armytage
2005-03-14 13:10:14 UTC
Permalink
Hi Juho,
Very interesting post; glad you to decided to write. My preliminary
thoughts on three topics...

1. The Smith set.
My attachment to the Smith set stems in part from a desire to satisfy
majority rule to the maximum possible extent. If you are willing to agree
that majority rule should be upheld, then it doesn't matter whether the
majority is small (e.g. a margin of only a few votes) or large (e.g. a 2:1
ratio). If you agree that majority rule should be upheld, you can only
reasonably ignore a majority preference if it is contradicted by another
majority preference. In your ABCX example, there is in each case a clear
majority who prefer A>X, B>X, and C>X. It is true that these majorities
are narrow, but the important thing is that they are not contradicted by
other majorities. Keep in mind that if X ran in an election with any of
the other candidates, X would lose.
This is the nature of the beast, i.e. the democracy beast: majority rule
is obviously imperfect, but once you have accepted the need to vote, it
seems necessary to accept the will of the majority, so long as majority
can be distinguished from minority. Among candidates A, B, and C, this
distinction cannot be made. However, it can be made between any of these
candidates and candidate X. Hence, I think that selecting X would violate
majority rule.

2. Pirates
I like your pirate example. :-)

3. Strategy
Post by Juho Laatu
In the election methods mailing list I have in the recent months observed
lots of discussion on criteria that are related to making the voting
methods as strategy free as possible. Sometimes I have even gotten the
impression that when electing the winner from the candidates in the top
loop (Smith set) it could be anyone in the top loop, as long as the
numerous strategy criteria are fulfilled. I guess this has not really
been the case, but my point is that one should give high priority to
selecting the candidate that we think is best, and maybe a bit less
priority to all the strategical considerations.
I am perhaps more actively interested in voter strategy than most voting
theorists. I consider strategy resistance to be a very high priority for a
method that will be used in contentious elections, although I don't rely
heavily on criteria in my strategic analyses.
Again, I am assuming that the first priority is majority rule, which
dictates that we should select a member of the top cycle. So, I think that
it is extremely important to have a methods that not only identify Smith
members when voting is sincere, but also prevent sincere Smith members
from being obscured by strategic incursion. This is the first priority.
However, that said, I am interested in the question of how to determine
which of the Smith set members is the "best". I'm hoping that you might be
interested in my "cardinal pairwise" method, which attempts to get a rough
measure of the relative priority of different defeats to the voters. Given
a sincere majority rule cycle, I suggest that this gives us a more
meaningful way to determine the "best" candidate. However, the method
requires cardinal ballots (e.g. 0-100) and the tally rule takes a bit of
explaining, which is why I don't consider it to be a likely "first wave"
Condorcet method. Anyway, here is a link to my write-up (and to my web
site in general).
http://fc.antioch.edu/~james_green-armytage/cwp13.pdf
http://fc.antioch.edu/~james_green-armytage/voting.htm
Post by Juho Laatu
This is based on the assumption that strategical voting is not that easy
in real life, at least not in elections where the number of voters is
large. Many of the strategical voting cases are problematic only in
situations where the voting behaviour of the voters is known. In real
life this is seldom the case.
I am skeptical of the statements above. First, the prevalence of
strategic voting depends on how broadly you define strategy. Many would
define it to include voting for a Democrat or Republican when you actually
prefer a third party candidate. This kind of strategy is obviously quite
common, and it has a significant impact on the political landscape. I
follow Blake Cretney in referring to this generally as the "compromising
strategy", which I define as follows:
"Insincerely ranking an option higher in order to decrease the
probability that a less preferred option will win. For example, if my
sincere preferences are R>S>T, a compromising strategy would be to vote
S>R>T or R=S>T, raising S’s ranking in order to decrease T’s chances of
winning. (The drawback is that this often decreases R’s chances of winning
as well.)"
The nice thing about Condorcet-efficient methods is that they tend to
minimize the need/incentive for compromising strategies. The tradeoff is
that we have to consider the possibility of "burying" strategies, which I
define as follows:
"Insincerely ranking an option lower in order to increase the probability
that a more-preferred option will win. For example, if my sincere
preferences are R>S>T, a burying strategy would be to vote R>T>S or R>S=T,
lowering S’s ranking in order to increase R’s chances of winning. (The
drawback is that this often increases T’s chances of winning as well.)"
There is no incentive for the burying strategy in plurality, two-round
runoff, or IRV. The incentive does exist, however, in Condorcet methods,
as well as in Bucklin and Borda. This makes it somewhat more of a
theoretical entity (difficult to study empirically), because there is much
less real public election data for these methods. (Although I can tell you
that the college where I went as an undergraduate uses Borda, and I talked
to several people who admitted (often with some embarrassment) to using
the burying strategy, although of course they didn't use that terminology)
Since we lack empirical data, I think it is premature to conclude that
burying will not be a problem if Condorcet methods do rise to use in
highly contentious elections. Of course I hope that it will not be, but I
prefer to err on the side of caution. This means keeping an eye on the
problem, and identifying methods that keep the possibility for a
successful burying within acceptable bounds. If regular winning votes
methods are found to not be sufficiently strategy resistant, then I would
advocate an additional anti-strategy measure.
Post by Juho Laatu
(And cycles are also rare.)
Sincere cycles may be rare (there is debate over this point, but I tend
to agree, at least when there is not a huge number of candidates), but the
frequency of strategically created cycles may depend on the method in use,
i.e. whether it gives incentives to create false cycles.

all my best,
James

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Juho Laatu
2005-03-15 09:00:37 UTC
Permalink
Hello James,

Here is some feedback on point 1. I didn't find yet time to write a proper answer also to point 3 but I'm planning to comment also that.


1. Majority and Smith set

Yes, one should respect the majority opinion. My thinking however goes so that in some situations some majority opinion has to be violated.

In the ABCX example majority says that instead of X one should elect e.g. A. But if A is elected, then a larger majority says that one should elect C instead of A. And then C would be changed to B, and B to A, A to C etc.

One viewpoint to the Smith set problem is that although there is no majority that would change A (or B or C) back to X, there is a large majority that is unhappy with the situation after X has been changed to A (="from bad to worse"). If one wants to violate majority opinions as little as possible, one could consider keeping X (against the smallest majority opinion).

It is true that majority would change X to any other of the candidates. I'm having problems trying to explain why violating this type of majority opinion would be a smaller problem than violating a stronger majority opinion that would change the candidate in question only to one of the other candidates (e.g. A -> C). The mutiny example however offers one quite clear argument. If one wants the election method to produce a stable result, then electing X seems to be the correct thing to do. Condorcet is known to elect good compromise candidates. X is a compromise candidate in the same spirit => "least threat of mutiny". This "least threat of mutiny" could btw be seen as one possible ("real life") criterion that is actually so strict that it already defines the whole election method ("least threat of mutiny" = "least additional votes").

Summary: If one selects the viewpoint in an appropriate way it is possible to claim that electing X respects the majority opinion, maybe even in the best possible way.

I still violate your rule that says that one would need a majority decision loop leading back to X in order to elect X. I based my support to X only on the strength of majority opinions without considering if they form loops that include X or not. This logic corresponds to the mutiny example. The Smith set logic would maybe correspond to a real life example where the crowds would elect A and B and C in turn and never remember that also X exists (good candidate missed? or maybe just happy to leave this passive candidate in the corner? :-) ).

Btw, I think you referred to majority in the sense that "majority makes a change that no other majority will change back" while I used it more in the spirit of "majority not happy with proposed election outcome". I could claim that the majority electing one of the the Smith set candidates is just stupid since they are unable to loop back to the best option, while you could claim that majority rule would lead to the Smith set solution in any case after few rounds of fighting. Theorist vs. pragmatist?? :-)

I'm not sure if I have provided any additional viewpoints that would convince you of the merits of the non-Smith-set candidates. I hope at least some viewpoints that show that there may be some sensible threads of thought also on the other side of the fence. I.e. just trying to prove that Smith set is not as obvious requirement as often thought.

I think that there exists one natural set of real world criteria for an election method (best characterized as "least threat of mutiny"), and to this set of requirements an election method that violates the Smith set rule is the correct solution. There may be other useful single winner election methods too in principle (for other purposes than defending against mutiny) but this one looks pretty useful to me.

Based on this chain of thoughts my question to you is: what would be your favourite captain in the pirate example? Let's assume that the pirates have requested for a stable compromise captain (or a stable compromise producing voting method) because they have had lots of problems with mutinies recently. I'm just asking for a solution for one particular need. And if you say that X would be a good solution in this particular case, then you would say that there are reasonable needs for election methods that do not respect the Smith set. Remember that the life of the sailors is at your hands :-).

Best Regards,
Juho


James Green-Armytage <***@antioch-college.edu> wrote:

Hi Juho,
Very interesting post; glad you to decided to write. My preliminary
thoughts on three topics...

1. The Smith set.
My attachment to the Smith set stems in part from a desire to satisfy
majority rule to the maximum possible extent. If you are willing to agree
that majority rule should be upheld, then it doesn't matter whether the
majority is small (e.g. a margin of only a few votes) or large (e.g. a 2:1
ratio). If you agree that majority rule should be upheld, you can only
reasonably ignore a majority preference if it is contradicted by another
majority preference. In your ABCX example, there is in each case a clear
majority who prefer A>X, B>X, and C>X. It is true that these majorities
are narrow, but the important thing is that they are not contradicted by
other majorities. Keep in mind that if X ran in an election with any of
the other candidates, X would lose.
This is the nature of the beast, i.e. the democracy beast: majority rule
is obviously imperfect, but once you have accepted the need to vote, it
seems necessary to accept the will of the majority, so long as majority
can be distinguished from minority. Among candidates A, B, and C, this
distinction cannot be made. However, it can be made between any of these
candidates and candidate X. Hence, I think that selecting X would violate
majority rule.

2. Pirates
I like your pirate example. :-)

3. Strategy
Post by Juho Laatu
In the election methods mailing list I have in the recent months observed
lots of discussion on criteria that are related to making the voting
methods as strategy free as possible. Sometimes I have even gotten the
impression that when electing the winner from the candidates in the top
loop (Smith set) it could be anyone in the top loop, as long as the
numerous strategy criteria are fulfilled. I guess this has not really
been the case, but my point is that one should give high priority to
selecting the candidate that we think is best, and maybe a bit less
priority to all the strategical considerations.
I am perhaps more actively interested in voter strategy than most voting
theorists. I consider strategy resistance to be a very high priority for a
method that will be used in contentious elections, although I don't rely
heavily on criteria in my strategic analyses.
Again, I am assuming that the first priority is majority rule, which
dictates that we should select a member of the top cycle. So, I think that
it is extremely important to have a methods that not only identify Smith
members when voting is sincere, but also prevent sincere Smith members
from being obscured by strategic incursion. This is the first priority.
However, that said, I am interested in the question of how to determine
which of the Smith set members is the "best". I'm hoping that you might be
interested in my "cardinal pairwise" method, which attempts to get a rough
measure of the relative priority of different defeats to the voters. Given
a sincere majority rule cycle, I suggest that this gives us a more
meaningful way to determine the "best" candidate. However, the method
requires cardinal ballots (e.g. 0-100) and the tally rule takes a bit of
explaining, which is why I don't consider it to be a likely "first wave"
Condorcet method. Anyway, here is a link to my write-up (and to my web
site in general).
http://fc.antioch.edu/~james_green-armytage/cwp13.pdf
http://fc.antioch.edu/~james_green-armytage/voting.htm
Post by Juho Laatu
This is based on the assumption that strategical voting is not that easy
in real life, at least not in elections where the number of voters is
large. Many of the strategical voting cases are problematic only in
situations where the voting behaviour of the voters is known. In real
life this is seldom the case.
I am skeptical of the statements above. First, the prevalence of
strategic voting depends on how broadly you define strategy. Many would
define it to include voting for a Democrat or Republican when you actually
prefer a third party candidate. This kind of strategy is obviously quite
common, and it has a significant impact on the political landscape. I
follow Blake Cretney in referring to this generally as the "compromising
strategy", which I define as follows:
"Insincerely ranking an option higher in order to decrease the
probability that a less preferred option will win. For example, if my
sincere preferences are R>S>T, a compromising strategy would be to vote
S>R>T or R=S>T, raising S’s ranking in order to decrease T’s chances of
winning. (The drawback is that this often decreases R’s chances of winning
as well.)"
The nice thing about Condorcet-efficient methods is that they tend to
minimize the need/incentive for compromising strategies. The tradeoff is
that we have to consider the possibility of "burying" strategies, which I
define as follows:
"Insincerely ranking an option lower in order to increase the probability
that a more-preferred option will win. For example, if my sincere
preferences are R>S>T, a burying strategy would be to vote R>T>S or R>S=T,
lowering S’s ranking in order to increase R’s chances of winning. (The
drawback is that this often increases T’s chances of winning as well.)"
There is no incentive for the burying strategy in plurality, two-round
runoff, or IRV. The incentive does exist, however, in Condorcet methods,
as well as in Bucklin and Borda. This makes it somewhat more of a
theoretical entity (difficult to study empirically), because there is much
less real public election data for these methods. (Although I can tell you
that the college where I went as an undergraduate uses Borda, and I talked
to several people who admitted (often with some embarrassment) to using
the burying strategy, although of course they didn't use that terminology)
Since we lack empirical data, I think it is premature to conclude that
burying will not be a problem if Condorcet methods do rise to use in
highly contentious elections. Of course I hope that it will not be, but I
prefer to err on the side of caution. This means keeping an eye on the
problem, and identifying methods that keep the possibility for a
successful burying within acceptable bounds. If regular winning votes
methods are found to not be sufficiently strategy resistant, then I would
advocate an additional anti-strategy measure.
Post by Juho Laatu
(And cycles are also rare.)
Sincere cycles may be rare (there is debate over this point, but I tend
to agree, at least when there is not a huge number of candidates), but the
frequency of strategically created cycles may depend on the method in use,
i.e. whether it gives incentives to create false cycles.

all my best,
James



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James Green-Armytage
2005-03-15 11:42:49 UTC
Permalink
Hi Juho,

About your "least additional votes" method: Correct me if I'm wrong, but
I think that your method is equivalent to minimax (margins). Adding an
additional "vote" will decrease the margin of each of a candidates defeats
by one. So, the candidate whose widest-margin defeat is less wide than the
widest-margin defeat of all other candidates will be the one who requires
the fewest votes to be "filled up" by this process.
By the way, I just wrote an in-depth post about the strategic instability
of margins methods
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015125.html
Post by Juho Laatu
Yes, one should respect the majority opinion. My thinking however goes so
that in some situations some majority opinion has to be violated.
In the ABCX example majority says that instead of X one should elect e.g.
A. But if A is elected, then a larger majority says that one should elect
C instead of A. And then C would be changed to B, and B to A, A to C etc.
Just clarifying... When you say a larger majority, you seem to mean a
majority with a wider margin. But I would prefer to define the *size of a
majority* by the number of voters who prefer R to S (when more prefer R to
S than S to R). Hence size of the A>X majority is 202. 202 people are
pleased with the change, and 201 people are displeased. If we change the
winner from A to C, 202 people are pleased with the change, 101 people are
displeased, and 100 are indifferent.
Post by Juho Laatu
One viewpoint to the Smith set problem is that although there is no
majority that would change A (or B or C) back to X, there is a large
majority that is unhappy with the situation after X has been changed to A
(="from bad to worse").
A large majority who is unhappy with the change? I would say that there
is a large *minority* (201 voters) that is unhappy with the change. As to
how many voters are unhappy with candidate A in general, it's hard to say,
because we only have ordinal information here, nothing about utility,
strength of preference, 'approval', etc.
Perhaps voters only like their first choice, and disapprove of all the
rest, perhaps because of national differences (pirates from 4 separate
countries). This means that a majority coalition will be hard to form.
Perhaps no matter who is the captain, at least 302 pirates will be
significantly unhappy. Perhaps it is just not practical for these pirates
to share a boat!
Post by Juho Laatu
If one wants to violate majority opinions as little as possible, one
could consider keeping X (against the smallest majority opinion).
Again, it might be more clear to say the 'narrowest' majority rather than
the 'smallest'.
Post by Juho Laatu
It is true that majority would change X to any other of the candidates.
I'm having problems trying to explain why violating this type of majority
opinion would be a smaller problem than violating a stronger majority
opinion that would change the candidate in question only to one of the
other candidates (e.g. A -> C).
Violating an unambiguous majority preference (e.g. A>X) is a *larger*
problem than violating a majority preference that is contradicted by
another majority preference (e.g. A>C), because the former is always
avoidable, and the latter is unavoidable in the case of a majority rule
cycle.
Post by Juho Laatu
The mutiny example however offers one quite clear argument. If one wants
the election method to produce a stable result, then electing X seems to
be the correct thing to do. Condorcet is known to elect good compromise
candidates.
It can only elect a compromise candidate if there is a compromise
candidate in the running. In your pirate example, there are no compromise
candidates; the pirate electorate is very badly polarized.
Post by Juho Laatu
X is a compromise candidate in the same spirit => "least threat of
mutiny". This "least threat of mutiny" could btw be seen as one possible
("real life") criterion that is actually so strict that it already
defines the whole election method ("least threat of mutiny" = "least
additional votes").
= the candidate with the most narrow defeats. Okay, so if a potential
mutiny started to form around ONE particular candidate (let's say
candidate A), then it would be the closest possible fight of this nature
(201 vs. 202). But what if multiple dissatisfied groups arose at once?
Then the X supporters would be in desperate trouble (as would supporters
of any other candidate in a similar situation).
Post by Juho Laatu
I.e. just trying to prove that Smith set is not as obvious requirement as
often thought.
Actually, it's kind of a new thing for me to be emphasizing the Smith set
as much as I do now. It's been in my head for about six months, and I've
just begun to articulate it quite recently. I began to feel that there was
something logically inconsistent about insisting on the Condorcet winner,
but abandoning all strict majority rule requirements when no Condorcet
winner exists. It makes it seem as if the pairwise method loses its
meaning when there is no CW. I feel that insisting on the Smith set makes
for a less wishy-washy definition of majority rule, and a less wishy-washy
election system proposal. A Smith method has more logical unity than a
non-Smith Condorcet method; no matter what, it elects a Smith member,
whether the set has one member or more than one.
Post by Juho Laatu
Based on this chain of thoughts my question to you is: what would be your
favourite captain in the pirate example? Let's assume that the pirates
have requested for a stable compromise captain (or a stable compromise
producing voting method) because they have had lots of problems with
mutinies recently. I'm just asking for a solution for one particular
need. And if you say that X would be a good solution in this particular
case, then you would say that there are reasonable needs for election
methods that do not respect the Smith set. Remember that the life of the
sailors is at your hands :-).
I would say none of the above candidates are a sufficient compromise
candidate. I would suggest that the pirates try a bit harder to find a
compromise captain (perhaps someone who has spent several years in each
country). Failing that, I would suggest that the four factions should go
their separate ways, finding boats that are manned by more like-minded
seafarers.

my best,
James

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Juho Laatu
2005-03-16 14:58:10 UTC
Permalink
Hello James,

I wrote a long mail. Sorry about that. No need to reply on everything
word in it. I however felt that it is worth writing all the text, just
in case it would trigger some useful thoughts. Simple answer "thanks
but I'm not convinced of the merits of non-Smith-set candidates yet" is
also enough :-).

Best Regards,
Juho
Post by James Green-Armytage
About your "least additional votes" method: Correct me if I'm wrong, but
I think that your method is equivalent to minimax (margins).
Correct. Didn't want to reveal that right away. Fresh thinking
requested. :-)

If the maximum defeat margin of some candidate is n, she needs exactly
n+1 additional votes to become a Condorcet winner.
Post by James Green-Armytage
Just clarifying... When you say a larger majority, you seem to mean a
majority with a wider margin.
Yes, sorry about not being more exact. All my terms in the mail (e.g.
"large majority") referred to margins. (And yes, term "narrowest
majority" is more appropriate than "smallest majority".)

I tend to see margins as "natural" and winning votes as something that
deviates from the more natural margins but that might be used somewhere
to eliminate strategic voting. (not a very scientific description but I
don't have any better short explanation available :-) )
Post by James Green-Armytage
A large majority who is unhappy with the change? I would say that there
is a large *minority* (201 voters) that is unhappy with the change.
I meant that when X was the captain people wanted to change him to A, B
or C with a small margin of votes. But later when e.g. C became the
captain people wanted to change him to B with a large margin. Only a
minority wanted to change C to X. But the point is that people
(majority of them) are now "less happy" or "more mutinous" because of
the problematic B>C relationship. I'm thus just measuring general
happiness and risk of mutiny without paying attention to whom people
would elect as captain in the current situation. The election method
could be so clever that it would elect X (the candidate with least risk
of mutiny) even if the people would not make the switch themselves in a
mutiny. (Are election methods allowed to be more clever than the voters
when picking up the winner?)
Post by James Green-Armytage
it's hard to say,
because we only have ordinal information here, nothing about utility,
strength of preference, 'approval', etc.
I think it is the nature of (basic) Condorcet methods not to take into
account how strong the preferences are. Taking also strengths into
account would be wonderful but I guess it is the problems with
strategical voting that have kept us away from this ideal target. When
talking about Condorcet based methods I tend to limit myself to this
"order only" mode.

(I however think that your cardinal pairwise method adds something to
this plain Condorcet tradition without taking all the rating related
problems in => worth another discussion.)
Post by James Green-Armytage
Violating an unambiguous majority preference (e.g. A>X) is a *larger*
problem than violating a majority preference that is contradicted by
another majority preference (e.g. A>C), because the former is always
avoidable, and the latter is unavoidable in the case of a majority rule
cycle.
I think all the majorities are unambiguous (because that is what the
voters told us). A>X could be called "loopless", if we want to describe
how it is different from the others. Both electing X and electing A
violate a majority opinion. One can avoid violating A>X by not electing
X (= select one of the Smith candidates). But one can also avoid
violating e.g. A>B by not electing B. All of the individual preferences
are thus avoidable. And all the Smith loop violations can be avoided by
electing X. I guess the key target of my pirate example is to
demonstrate that in some (rare) situations violating A>X could be a
smaller crime than violating one of the Smith loop preferences. (And my
thinking is not based that much on paths but on utility of each captain
candidate separately.)
Post by James Green-Armytage
In your pirate example, there are no compromise
candidates; the pirate electorate is very badly polarized.
I agree. The basic setting is four parties of about equal size. I think
this situation is quite normal. What is exceptional is the strength of
the loop. My understanding however is that strong loops may occur also
in real life - considerably stronger than ones between three parties of
equal size as a result of some random votes. Also sincere, not only as
a result of a voting strategy.
Post by James Green-Armytage
But what if multiple dissatisfied groups arose at once?
Then the X supporters would be in desperate trouble (as would
supporters
of any other candidate in a similar situation).
Yes. I think now we come to the question if "mutiny" is the "only
correct" real life criterion or if there are also others. I claim that
"mutiny" is one well defined criterion that is useful is some
situations and directly points out the correct voting method (MinMax
with margins).

Mutiny of everyone against one is one candidate for another real life
criterion. I think mutiny to replace one with one is however the most
useful and typical case (both in the ship and in politics). This
"mutiny for anyone else" would also give support to sticking to the
Smith set when electing the winner. I'm however afraid that these
majorities can not be summed up (=> not a strong case to support
sticking to the Smith set). (Note also that a Condorcet winner that has
not been the #1 favourite of any of the voters has a risk of yet
another type of mutiny ("everyone thinks he is not the best").)

There may be also other real life criteria that could be used to
characterise (or define) different alternative single winner election
types / needs. I think the current paradigm is that there are only one
type of single winner elections (i.e. rules are the same irrespective
of what the context is (e.g. captain, president, holiday resort or
favourite fruit election); one method serves all single winner needs).
I tried to prove that eliminating risk of mutiny is one such need, but
I don't have any evidence that it is the only one that is needed.
Post by James Green-Armytage
I began to feel that there was
something logically inconsistent about insisting on the Condorcet winner,
but abandoning all strict majority rule requirements when no Condorcet
winner exists.
In my mind one important borderline is cycles. Newtonian physics
(=linear ordering) applies as long as there are no loops. Condorcet
winner is a very natural concept in this world. But when loops emerge
the ideal linear ordering is broken. To me the linear order of Smith
sets (the top cycle + bigger ones) (or "loop groupings") is not the
most tempting way forward since it seems to hide possibly bigger group
preferences inside the "loop groupings" than what the strength of
preferences between the groupings are. As I mentioned earlier, there is
a risk of trying to make the group opinions look like linear (personal)
preferences. I think the drawing (and imagining) techniques may lead us
to false conclusions. As a result I have been interested also in
criteria that simply evaluate candidates one by one.
Post by James Green-Armytage
I would say none of the above candidates are a sufficient compromise
candidate. I would suggest that the pirates try a bit harder to find a
compromise captain (perhaps someone who has spent several years in each
country). Failing that, I would suggest that the four factions should go
their separate ways, finding boats that are manned by more like-minded
seafarers.
That is not allowed :-). We had an election with four candidates. And
elections are not supposed to cause countries to break into separate
smaller countries. The best single winner election method must be
capable of electing one (the best) of these candidates. Since you say
that you want to stick to the Smith set, I guess your answer must be A,
B or C. That would violate the "least risk of mutiny" criterion. Does
this mean that there is no need for election methods that try find the
optimal candidate by minimizing the risk of mutiny.

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James Green-Armytage
2005-03-17 07:51:00 UTC
Permalink
Hi Juho,
My critique of your pro-minimax(margins) argument follows...
Post by Juho Laatu
I tend to see margins as "natural" and winning votes as something that
deviates from the more natural margins but that might be used somewhere
to eliminate strategic voting. (not a very scientific description but I
don't have any better short explanation available :-) )
No, that's more or less how I think of it. However, when you say that wv
might be needed "somewhere" to reduce (not eliminate) strategic voting, I
suggest that most public elections will fall within the region of
"somewhere". (Please see my 3/14 post.)
copying your pirate example for reference:
101: a>b>x>c
101: b>c>x>a
101: c>a>x>b
100: x
...
Post by Juho Laatu
I meant that when X was the captain people wanted to change him to A, B
or C with a small margin of votes. But later when e.g. C became the
captain people wanted to change him to B with a large margin. Only a
minority wanted to change C to X.
I'm with you this far.
Post by Juho Laatu
But the point is that people
(majority of them) are now "less happy"
...you don't know how happy they are with any of these candidates...
Post by Juho Laatu
or "more mutinous" because of
the problematic B>C relationship.
Okay, let's get to the bottom of this.
No matter who wins, 202 pirates would rather have some other candidate in
particular. If X wins, this still holds, but 201 pirates strictly
disagree. In the other cases, e.g. A wins, 202 pirates would rather have
C, and only 101 pirates strictly disagree (the remaining 100 are
indifferent).
Your logic is as follows: If X wins, and a group of 202 pirates who
preferred another candidate rather than X wanted to mutiny, there would be
201 pirates ready to stand in their way, serving as an effective
deterrent. However, if A wins, and the 202 C>A pirates (101: B>C>X>A, 101:
C>A>X>B) mutiny in favor of C, there won't be sufficiently many pirates to
fight to defend A.
Here's what I'd like you to consider: Let's say that A is the initial
winner, these 202 C>A pirates declare mutiny, and the 100 X pirates stay
neutral. There may or may not be a scuffle, but anyway the 101 A>B>X>C
pirates back down. Okay fine; C is the captain. But now the B>C pirates
will be emboldened to mutiny against C. The process repeats, and B is the
captain. Now it will be the A>B pirates' turn, and A will be captain once
more. This idiotic process could go on indefinitely, so that the captain
might shift several times in the duration of any given voyage, causing
general irritation. Or, it could result in serious violence, and there is
no guarantee that C will be on top when the dust settles.
I suggest to you that this is a relatively intelligent bunch of pirates.
(This is evidenced by the fact they are using Condorcet's method to make
decisions.) If so, I suggest that the 202 C>A pirates will see the
risk/futility of their mutiny ahead of time. (I'm assuming that all the
pirates know each other's expressed ranked preferences, as would be the
case in any real public election.) Sure, they could oust A in favor of C
by force if the X voters sat on their hands. Maybe they could even kill
candidate A, so as to finalize his defeat. But if they did that, a pro-B
mutiny would be likely to follow, and perhaps this new coalition would
murder candidate C, for good measure. Half of the C>A voters (101:
B>C>X>A) would be all the more delighted with this second mutiny, but the
other half (101: C>A>X>B) would rather have A than B, and they would mourn
for C's death.
So I ask you, would the B>C>X>A voters participate in the first mutiny
against A? I suggest that they would not, because they would realize that
a victory for C so reached would be unlikely to last. In short, you
neglected to assign foresight to your imaginary pirates, and foresight
would prevent a mutiny against a Smith set member. Would foresight prevent
a mutiny against a non-Smith member, in favor of a Smith member? Not
necessarily! Example:

Preferences:
35: R>S>T>Z
33: S>T>R>Z
32: T>R>S>Z
71: Z>R=S=T
Pairwise comparisons:
R>S 67-33
S>T 68-32
T>R 65-35
R>Z 100-71
S>Z 100-71
T>Z 100-71

Candidate Z is the minimax(margins) winner. However, he is in no wise the
most mutiny-proof candidate. If Z is the initial winner, then all 100 of
the R/S/T faction will have a common cause in ousting him. Perhaps if they
change the winner to R, there could conceivably be further mutiny, but no
matter what, such further mutiny will not lead to another result that the
R/S/T pirates like less than Z. (Hence they can happily mutiny against Z
without worrying that it will hurt them in the long run.) More likely,
however, there will be no further mutiny. The R/S/T faction would do well
to first choose whom they prefer among themselves (let's say that they
settle on R), and to then march over to the Z faction and announce the
change of leadership. The odds are running heavily in favor of the R/S/T
faction if a fight breaks out.
Again, once Captain R (as in "ARRR!") takes over, any potential mutiny
coalition has to face the prospect of subsequent mutinies that cause a
result that they like less than Captain R. So I argue that Captain R would
suffer less risk of mutiny than Captain Z.
I hope that I have disrupted your assumptions concerning the "risk of
mutiny" concept.
Post by Juho Laatu
I think all the majorities are unambiguous (because that is what the
voters told us). A>X could be called "loopless", if we want to describe
how it is different from the others. Both electing X and electing A
violate a majority opinion. One can avoid violating A>X by not electing
X (= select one of the Smith candidates). But one can also avoid
violating e.g. A>B by not electing B. All of the individual preferences
are thus avoidable. And all the Smith loop violations can be avoided by
electing X.
If there is a majority rule cycle, then one cannot avoid ignoring at
least one majority preference. However, one can always avoid ignoring a
majority preference that is not contradicted by another majority
preference (via a cycle).
Post by Juho Laatu
Post by James Green-Armytage
In your pirate example, there are no compromise
candidates; the pirate electorate is very badly polarized.
I agree. The basic setting is four parties of about equal size. I think
this situation is quite normal.
Four parties of equal size. Okay, that's not very common, but there's no
particular reason why it couldn't happen. What I'm calling your attention
to is not the relative size of the parties, but the intensity of the
polarization between them. We have intense political polarization in
countries that have voting systems that encourage polarization. In
Condorcet systems, we should not assume that this polarization will
remain; rather, it seems logical that compromise candidates will emerge,
which they haven't done in your example.
Post by Juho Laatu
I claim that
"mutiny" is one well defined criterion that is useful is some
situations and directly points out the correct voting method (MinMax
with margins).
Please read and consider my recent post about strategic vulnerability in
"margins" methods before you state so unequivocally that it is "the
correct voting method". Actually, even then you might want to be careful
about calling anything "the correct voting method" without some sort of
qualification.
Post by Juho Laatu
Mutiny of everyone against one is one candidate for another real life
criterion. I think mutiny to replace one with one is however the most
useful and typical case (both in the ship and in politics). This
"mutiny for anyone else" would also give support to sticking to the
Smith set when electing the winner.
If your second criterion is to select the candidate who is not the first
choice of the fewest voters, this is equivalent to selecting the candidate
with the most first choice votes, a.k.a. plurality.
Post by Juho Laatu
That is not allowed :-). We had an election with four candidates. And
elections are not supposed to cause countries to break into separate
smaller countries. The best single winner election method must be
capable of electing one (the best) of these candidates.
Sure, but if all of the candidates are highly divisive (as they are in
your example), you can't blame the method for choosing a divisive
candidate. Based on the information available, A, B, and C are equally
good choices, which is to say that they are equally bad choices. X is a
slightly worse choice, because choosing X unnecessarily violates majority
rule.

all my best,
James
http://fc.antioch.edu/~james_green-armytage/voting.htm

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Juho Laatu
2005-03-18 06:05:59 UTC
Permalink
Hello James,

Thanks for the excellent mail. I still found some points where
different definitions lead to different conclusions. See (lengthy)
comments below.

BR, Juho
I suggest that most public elections will fall within the region of
"somewhere". (Please see my 3/14 post.)
Ok. I don't have any firm opinion (due to lack of sufficient
understanding) although I'm trying to seek evidence of unusable
strategies and hoping that the best method would be close to the "best
sincere method". I'd maybe not even try to fight some (non fatal)
strategies in the hope that many people would vote sincerely just
because they are supposed to do so, or because they are lazy or not
aware of the strategies.
101: a>b>x>c
101: b>c>x>a
101: c>a>x>b
100: x
Your logic is as follows: If X wins, and a group of 202 pirates who
preferred another candidate rather than X wanted to mutiny, there would be
201 pirates ready to stand in their way, serving as an effective
C>A>X>B) mutiny in favor of C, there won't be sufficiently many pirates to
fight to defend A.
Yes, that's what I thought.
(I'm assuming that all the
pirates know each other's expressed ranked preferences, as would be the
case in any real public election.)
My assumption was that the fact that there are four parties of about
equal size was known. Since I at some point said that these pirates
would be from different countries, maybe also the exact number of
people in each party is known. In most elections that is not known. The
fact that there is a cycle and the direction and strength of it and the
fact that one party is not part of the cycle may or may not be known
(or guessed) in advance. (Pirate example is of course just one example
to demonstrate the generic idea that in some elections preference
margins inside the Smith set are stronger than preference margins
towards the other candidates.)
So I ask you, would the B>C>X>A voters participate in the first mutiny
against A? I suggest that they would not, because they would realize that
a victory for C so reached would be unlikely to last.
I'm afraid I don't have a clear answer to this. But I do my best and
try to explain at least something.

First one obvious counter question: What if X was elected in the first
round? Maybe no strong mutiny tendencies at all.

If they would have foresight and they would guess that there is a loop
of preferences, and the Smith set parties would be able to find each
others and agree, my proposal to the Smith set parties would be to toss
a three sided coin before the first election and leave X party out of
this process based on the fact that it is expected to get one vote less
than the other parties. (I leave it open if the pirates also believe
that it is correct to pick the winner from the Smith set.) Then all
Smith set party voters would vote the lucky winner (A,B or C).

I think cycles of three are really vicious. The next possible strategy
of B party would be to agree with C party that A will be thrown out
together, and B party voters will after that satisfy with and defend
their second best alternative C. This is already a partial answer to
your question. If someone at B party would invent this strategy and
convince others about its benefits, they would participate in the
mutiny against A. On the other hand, if they would invent the logic
your described first, maybe they wouldn't participate in the mutiny.

There are really many options - and finding an easy solution for a
cycle of three is not easy. My best guess is that it is all up to luck
and negotiation skills and quick actions.

Although I took the mutiny case up, answering your question is a bit
tricky also because in normal Condorcet elections there are no second
rounds. Well, maybe some countries could have a law saying that new
election must be arranged when majority of voters is not happy with the
achieved result. But in that case probably also all old candidates
would participate in the new election. I think it is characteristic to
the Condorcet methods that all necessary information will be collected
already in the first and only election round. Maybe the correct
interpretation to the term "mutiny" is not to expect people to change
the result but to ask who would be the best such first choice that
there would be no interest to change the result. I'm a bit biased here.
Also any other reasoning (than those favouring X) for picking the
winner of the election are ok.

Now back to the question of X vs. Smith set.

What do you say about the following viewpoints:
1) candidate A is good if there is a strong interest to change some
other candidate to A
2) candidate A is good if there is a weak interest to change A to some
other candidate

From a stability oriented point of view 2) looks more tempting. The
path oriented thinking seems to favour 1). If 1) is used, X has no
chance. If 2) is used, X has a strong chance.

One type of foresight requiring logic for the pirates would be to elect
X. Assuming that their thinking was in line with 2).

I have made some studies above and, of course, came back to defending
X. The best constructive comment I can make at this point is that the
voting method should elect the best candidate right away so that the
selection would be done once and for all. I picked mutiny resistance as
a requirement since it seems to favour X. Also other
criteria/requirements on which candidate is the best may exist.

My answer to your question is: Don't know. Maybe there is no answer
since it is all up to tactics.

I think it is a mathematical fact that if mutiny resistance is accepted
by a country as the target of the election, one must elect the
Condorcet loser in some cases. And MinMax (margins) is the correct
voting method if votes are sincere. In real life votes are not
necessarily sincere and some other variant may be more useful. But this
does not contradict the fact that in some cases the Condorcet loser
should be elected. (Before shooting me because of my strong claims,
please see also below how I defined the mutiny to mean the first mutiny
:-).)
35: R>S>T>Z
33: S>T>R>Z
32: T>R>S>Z
71: Z>R=S=T
R>S 67-33
S>T 68-32
T>R 65-35
R>Z 100-71
S>Z 100-71
T>Z 100-71
Candidate Z is the minimax(margins) winner. However, he is in no wise the
most mutiny-proof candidate.
Here our thinking differs. I'm thinking about the probability of the
first mutiny, which can be said to correspond to (one measure of)
dissatisfaction with the election results (in countries where
revolutions are unlikely and term "mutiny" therefore would mean only
mutiny in some debates and votings (other votings than what we are
talking about here), not really throwing out the elected person). For Z
the probability of first mutiny is still the smallest. Chain of
mutinies may not lead back to Z, but that does not worry me if there
will be no mutiny in the first place.
(Hence they can happily mutiny against Z
without worrying that it will hurt them in the long run.)
This is a good argument in the pirate world if there are sequential
mutinies, but as I said, I'm mostly focusing on avoiding mutinies
altogether (and consider it a problem of the election if there is even
one).
So I argue that Captain R would
suffer less risk of mutiny than Captain Z.
Yes, in the meaning that you described. Z has however slightly smaller
risk of first mutiny.
I hope that I have disrupted your assumptions concerning the "risk of
mutiny" concept.
Yes you did to some extent. I however still hide behind the argument
that the risk of first mutiny is the parameter that some election
organizers may want to minimize.

Another threatening argument in your example could be the fact that R,
S and T supporters could be seen as one big party. If that was the
case, then they would beat Z clearly 100 against 71. What would my
argument be against this. I think the best explanation in that case is
that people inside the RST party are not able to agree internally which
candidate is best and therefore electing Z from the other party might
be appropriate. It is possible to seek voting methods that would allow
people to express their opinions in more detail than in the basic
ranking based methods. In this case RST party members maybe would like
to have a rule that would somehow eliminate the negative effect of
loops within each party. But for the time being this is ffs for me and
I stick to the basic Condorcet rules. => Least first mutiny risk is a
least mutiny risk, without considering if party internal mutiny risk
should be considered smaller than mutiny risk between parties.

One hint for the RST party, in case we end up using MinMax (margins),
is that they should consider setting only two candidates, and maybe
arrange a pre-election within the party before the actual election.
Note that I keep looking alternative strategy reduction methods that
would allow me to still use the sincere method (or something close to
that) and sincere votes in the elections.

I might mention here also how I want to disrupt your thinking. There
are at least three points.
1) One should consider separately what is the best ideal / strategy
free / sincere method, and after that what is the method that is best
in real life. The latter differs from the former because it tries to
defend against various strategies.
2) "Least first mutiny risk" is a possible and rational target (= as
the ideal case of the previous point) for some elections (if some
country wants to emphasize this aspect)
3) If one accepts point 2) then in those elections Smith set is not a
target. It could be used for defensive purposes as described in point
1) above but better if we could do without it.

Maybe you can comment which ones of these you find ok.
If there is a majority rule cycle, then one cannot avoid ignoring at
least one majority preference. However, one can always avoid ignoring a
majority preference that is not contradicted by another majority
preference (via a cycle).
Why is it more important to avoid the loopless majority opinions than
the looped ones? One can always avoid the loopless ones but then one
has to violate one of the Smith set internal majorities (that might be
stronger). (I'm back to square one. Don't want to end up in a debate
loop though :-).)
In
Condorcet systems, we should not assume that this polarization will
remain; rather, it seems logical that compromise candidates will emerge,
which they haven't done in your example.
I agree. And my example is an extreme case. I would expect that in most
elections there are no loops. If there is a top loop, then it is
probable that it is weaker than the preferences between the top loop
and the other candidates. As a result the pirate case is highly
unlikely to occur in real elections.

Furthermore I don't want ever to face the situation where a Condorcet
loser or anyone outside the Smith set is elected. (But is extreme cases
that may be the least bad option.) Actually my target is to prove that
these strange cases are so rare that we probably need not care about
them to much. The most probable reason why we might have loops is
intentional strategies. As you know, also here I hope that most of them
would be so unusable that we could simply forget most of them. If you
want to shake my world a bit more, I could be most vulnerable to
attacks that would show practical use cases where strategies could be
useful in normal elections (typically without detailed information of
the preferences of the voters). Your recent mail on one vulnerability
of margins was a good one. I hope to come back to that.
Please read and consider my recent post about strategic vulnerability in
"margins" methods before you state so unequivocally that it is "the
correct voting method". Actually, even then you might want to be careful
about calling anything "the correct voting method" without some sort of
qualification.
I note that I already restated that claim earlier in this mail. Sorry
for using strong terms, but I did that because I believe that is a
mathematical fact and I wanted to point that out. In my sentence I
however missed the assumption that this requirement points out the
correct _sincere_ voting method, i.e. I was talking about the ideal
case and strategies were excluded in this claim. Fight against
strategies may lead to deviation from the ideal sincere method. Another
point that was certainly confusing here is the definition of risk of
mutiny. I meant the first mutiny after election.
X is a
slightly worse choice, because choosing X unnecessarily violates majority
rule.
I'm still a bit confused about the use of term "unnecessarily". It
seems to mean that in the loops violation is necessary and in linear
preference chains unnecessary. This makes sense as long as we have a
Condorcet winner and we can pick the candidate that at the better end
of the linear chain. Then it would be an unnecessary violation to pick
someone else than the Condorcet winner. But if there is a loop at the
end of the chain (Smith set), then avoiding violation of majority
preference in the linear structure leads (now necessarily!) to
violation of a majority preference in the loop. And in this situation
where we must violate some majority preferences we could as well
violate the linear ones.

(In the pirate example we would need to violate only one but strong
majority (margin) preference or alternatively three weak linear
preferences.)

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James Green-Armytage
2005-03-18 08:10:19 UTC
Permalink
Hi, this is James G-A replying to Juho...
Post by Juho Laatu
My assumption was that the fact that there are four parties of about
equal size was known. Since I at some point said that these pirates
would be from different countries, maybe also the exact number of
people in each party is known. In most elections that is not known. The
fact that there is a cycle and the direction and strength of it and the
fact that one party is not part of the cycle may or may not be known
(or guessed) in advance.
I'm not talking about knowing it in advance, I'm talking about knowing it
after the votes have been cast.
Let me clarify, for you seem to have missed my major point. I assume that
the pirates have already taken a ranked vote, the result of the vote (the
exact numbers that you printed initially (101 A>B>X>C, etc....) are made
known to all of them, and then a winner is chosen based on our choice of
Condorcet completion method. (This is obviously the most realistic
scenario, when you replace "pirate captains" with presidents, etc.) Then,
with the pirates knowing how many votes of each kind there were, and
knowing how the winner was arrived at by the voting method, the question
is how likely is a mutiny under a) minimax(margins) b) a Smith-efficient
method.
Let's say that a Smith method chose A in this example. You argued that A
would be mutiny-prone because there is a large-margin defeat against him.
My counter argument is that the pirates can read the election result
carefully, and see that yes indeed, a C>A mutiny could succeed, but that
it would lead naturally to a B>C mutiny, and possibly later an A>B mutiny,
and so on. Hence, the C>A pirates would realize the futility/risk of their
potential mutiny, and probably they would not do it. Especially the
C>A>X>B voters, who would be especially wary of the second B>C mutiny.
This is what you didn't take into account when you formulated your "risk
of mutiny" principle, and this oversight is really a fatal to your theory.
You assume that voters will look exactly one mutiny ahead, but there is no
basis for this assumption. The knowledge of where further mutinies might
go should tend to stop an mutiny within the Smith set.
However, it will not necessarily prevent a mutiny against a non-Smith
candidate, in favor of a Smith candidate, as in my RSTZ example.
Post by Juho Laatu
I think it is a mathematical fact that if mutiny resistance is accepted
by a country as the target of the election, one must elect the
Condorcet loser in some cases.
You can only say that if you totally ignore my argument.
Post by Juho Laatu
And MinMax (margins) is the correct
voting method if votes are sincere.
Why?
Post by Juho Laatu
Here our thinking differs. I'm thinking about the probability of the
first mutiny
That's just what I'm saying! I'm saying that the first mutiny won't occur
if those who would potentially engage in it realize that it leads them
into a potentially endless cycle of mutinies, with no guarantee of a more
preferable result, and a real chance of a less preferable result. Your
failure to take this into account is frustrating.
Post by Juho Laatu
For Z
the probability of first mutiny is still the smallest.
Only based on your arbitrary use of defeat margin as the sole determinant
of mutiny probability. As I understand it, mutiny against Z far, far more
likely than mutiny against R, S, or T. 100 voters favor R/S/T. 71 voters
favor Z. The 100 R/S/T voters realize that they outnumber the Z voters
100-71. They realize that no matter which of the R/S/T candidates ends up
ahead, the result will be preferable to Z. I suggest that they will feel
that the method has not satisfied majority rule, and I suggest that they
will be entirely correct in feeling this. Thus, they will feel justified
in taking matters into their own hands. Since they know that they have
common cause in a mutiny, they will probably pause to decide which
candidate they would like to replace Z with. Once they figure this out,
they can happily mutiny. Z will go down, their new captain will go up, and
there will be no further mutinies.
If R, S, or T is the initial winner, potential mutineers will be soundly
discouraged by the possibility of further mutinies, as discussed.
Post by Juho Laatu
This is a good argument in the pirate world if there are sequential
mutinies, but as I said, I'm mostly focusing on avoiding mutinies
altogether (and consider it a problem of the election if there is even
one).
Yes, of course, that's what we're both interested in. This provides
further proof that you didn't understand my argument.
Post by Juho Laatu
Yes you did to some extent. I however still hide behind the argument
that the risk of first mutiny is the parameter that some election
organizers may want to minimize.
"
Post by Juho Laatu
Another threatening argument in your example could be the fact that R,
S and T supporters could be seen as one big party. If that was the
case, then they would beat Z clearly 100 against 71. What would my
argument be against this. I think the best explanation in that case is
that people inside the RST party are not able to agree internally which
candidate is best and therefore electing Z from the other party might
be appropriate.
Voting methods should minimize the need for outside coordination.
...
Sorry to be so harsh. It's just that I spent a lot of time and effort on
that e-mail to you, and the fact that you didn't seem to follow the main
argument is frustrating to me.

my best,
James
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Juho Laatu
2005-03-18 19:33:22 UTC
Permalink
Hello James,

Sorry about causing some gray hair to you. I think the problem is that
we drove into two alternative tracks in the discussion and my text,
when trying to address both of these, was not clear. I hope this mail
improves the situation a bit.

The two tracks that I see are one where we talk about dynamics of
sequential mutinies and how the voters may stop the process already
before the first mutiny when they see the votes and understand the
rules of the game, and another one where we try to do the decision just
once and then live with the result until the next election day (few
years ahead).

I re-read my mail and noted that I had at least made quite bad use of
term "first mutiny" since that term has a meaning in the first track
but I used it also in the framework of the second track. Maybe I should
talk separately abouth these two tracks to avoid any further confusion
caused by handling both phenomena and criteria simultaneously.


First track related comments:

I think your conclusions on the first track made all the sense, so
let's consider them agreed.

I identified also some possible additional scenarios:
- An alternative model where the cost of mutiny is low and therefore
mutinies could continue forever (instead of stopping when pirates
understand that the cost of mutinies is too high). Accepting one of the
Smith candidates to take permanent lead may thus be more painful than
"sharing the leadership" by making continuous mutinies.
- B and C could join forces and make just one revolution where A would
be changed to C (202 against 101) and stop there. This case I mentioned
also in the previous mail. Revolution of two Smith set members against
X would be also possible (202 against 201). A could also try to make a
deal with C in order to avoid revolution. But C would become the
captain if it made a deal with B instead. Knowing this, A could make a
deal with B, make a revolution against herself, and let B be the
captain.


Second track relatd comments:

In track two one should maybe talk more about mutiny against elected
captain's initiatives instead of talking about replacing the captain
herself. In politics the next elections typically come after a fixed
amount of time. The winner must thus start working with all the voters
and try to make the best of what trust and support she has.

Let's say that X is the captain. She makes an "X style" proposal. A
makes an "A style" counter proposal. 201 pirates support proposal "X"
but 202 pirates support proposal "A". Let's assume that X is a good
speaker (or has a musket) and can convince few additional pirates to
vote for the proposal (note close links to "additional votes", that
were however defined to come from outside of the current crew of 403
pirates). Majority achieved. Job well done.

Captain A would have more problems driving her policy through since C
could always make counter proposals that would be supported 202 against
101 and A would need better speaking skills than X (or a cannon).

I used the pirate example here but also the RSTZ example could be used.
Any key observations?
Post by James Green-Armytage
I'm not talking about knowing it in advance, I'm talking about knowing it
after the votes have been cast.
Sorry, I mixed voting and mutinies and your intentions here.
Post by James Green-Armytage
Post by Juho Laatu
I think it is a mathematical fact that if mutiny resistance is accepted
by a country as the target of the election, one must elect the
Condorcet loser in some cases.
You can only say that if you totally ignore my argument.
Or alternatively made a mess of the two different tracks. Please
condsider this theory (and MinMax (margins) as the solution) in light
of track two.


Best Regards,
Juho



ANNEX 1: The pirate example.

101: a>b>x>c
101: b>c>x>a
101: c>a>x>b
100: x


ANNEX 2: The RSTZ example.

Preferences:
35: R>S>T>Z
33: S>T>R>Z
32: T>R>S>Z
71: Z>R=S=T
Pairwise comparisons:
R>S 67-33
S>T 68-32
T>R 65-35
R>Z 100-71
S>Z 100-71
T>Z 100-71

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James Green-Armytage
2005-03-19 02:38:37 UTC
Permalink
Hi Juho,
Further replies follow on the topic of Smith methods vs.
minimax(margins)...
Post by Juho Laatu
Sorry about causing some gray hair to you.
Sorry about being peevish in my reply.

============
track one
============
Post by Juho Laatu
one where we talk about dynamics of
sequential mutinies and how the voters may stop the process already
before the first mutiny when they see the votes and understand the
rules of the game,
...
Post by Juho Laatu
I think your conclusions on the first track made all the sense, so
let's consider them agreed.
Does this mean you agree that foresight of potential further mutinies is
likely to deter mutinies against Smith set candidates?
Does it mean you acknowledge that this foresight will not necessarily
protect non-Smith candidates?
Does it mean you agree that candidate Z (the non-Smith Condorcet loser)
is likely to be the most mutiny-vulnerable candidate in my RSTZ example?
Does it mean you are willing to abandon the claim that minimax(margins)
winners are less vulnerable to mutiny than Smith winners, when they differ?
Post by Juho Laatu
- An alternative model where the cost of mutiny is low and therefore
mutinies could continue forever (instead of stopping when pirates
understand that the cost of mutinies is too high). Accepting one of the
Smith candidates to take permanent lead may thus be more painful than
"sharing the leadership" by making continuous mutinies.
In real life government/election scenarios, the cost of mutiny is always
high.
Post by Juho Laatu
- B and C could join forces and make just one revolution where A would
be changed to C (202 against 101) and stop there.
You suggest that the B>C>X>A and C>A>X>B pirates may join forces to
change A to C. In forming this coalition, the B>C>X>A pirates would
promise the C>A>X>B pirates that they would not mount a further mutiny
against C. But why should the C>A>X>B faction trust them on this, mutinous
pirates that they are? Once the first mutiny has occurred, the B>C>X>A
pirates could join forces with the disgruntled A>B>X>C faction, to get
their man B at the helm.
To be fair, I acknowledge that some mutinies might have more "sticking
power" than others. I suggest that this will depend on the strength of the
preferences involved, and so I suggest that cardinal pairwise may do
better in this sort of situation than any strictly ordinal method.

=============
track 2
=============
Post by Juho Laatu
and another one where we try to do the decision just
once and then live with the result until the next election day (few
years ahead).
...
Post by Juho Laatu
Captain A would have more problems driving her policy through since C
could always make counter proposals that would be supported 202 against
101 and A would need better speaking skills than X (or a cannon).
This doesn't make a whole lot of sense to me so far, perhaps because I
don't understand the scenario. To begin with, we're assuming that there is
an extremely strong sincere cycle in the initial vote. I doubt that this
will happen very often (probably never to the extent of your example), but
I can accept the premise for the sake of argument. But then, are we
assuming that there would be a comparably strong cycle in the sincere
preferences of the voters on most public issues? I think that this is much
less probable.
Let's dump the pirate metaphor for track 2, and start talking about
actual government institutions. Is A the president now? What do you mean,
"problems driving her policy through"? Is the president supposed to write
legislation, and then rely on a popular ranked vote to have it passed? Who
says that the president has to win the vote on every issue? If A is
president, but the X faction wins the vote on several issues, that's fine
with me.

my best,
James Green-Armytage
http://fc.antioch.edu/~james_green-armytage/voting.htm



===========
annex
===========

ANNEX 1: The pirate example.

101: a>b>x>c
101: b>c>x>a
101: c>a>x>b
100: x

ANNEX 2: The RSTZ example.

Preferences:
35: R>S>T>Z
33: S>T>R>Z
32: T>R>S>Z
71: Z>R=S=T
Pairwise comparisons:
R>S 67-33
S>T 68-32
T>R 65-35
R>Z 100-71
S>Z 100-71
T>Z 100-71




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Juho Laatu
2005-03-23 06:29:18 UTC
Permalink
Hello James,

Some further comments on the two tracks (= two scenarios on what mutiny
may mean in elections). Sorry that the mail is long (maybe too long and
difficult to read for those who have not followed the discussion).

Best Regards,
Juho
Post by James Green-Armytage
============
track one
============
Post by Juho Laatu
one where we talk about dynamics of
sequential mutinies and how the voters may stop the process already
before the first mutiny when they see the votes and understand the
rules of the game,
...
Post by Juho Laatu
I think your conclusions on the first track made all the sense, so
let's consider them agreed.
Does this mean you agree that foresight of potential further mutinies is
likely to deter mutinies against Smith set candidates?
With the "considerable cost of mutiny" (to the mutineers and/or
defenders and/or neutrals?) assumption you seemed to have, yes. People
may however hope that it is someone else who has to give up and stop
making mutinies, not me.

This deterrence applies also to non-Smith-set candidates, particularly
since mutinies after entering the Smith set are in the two examples
easier than before entering the Smith set (and results of a mutiny
requiring hard work could easily be lost to another easier mutiny).
There are however other psychological reasons, like no risk of beaten
captain taking part in the cyclic majority revolutions, why people may
be more eager to attack them, as you pointed out.
Post by James Green-Armytage
Does it mean you acknowledge that this foresight will not necessarily
protect non-Smith candidates?
As mentioned above, there seem to be both reasons that support and are
against this. I don't have a 100% clear picture of all possible mutiny
scenarios and their psychological impacts so that I could now give a
firm opinion on the strengths of different mutiny cases.
Post by James Green-Armytage
Does it mean you agree that candidate Z (the non-Smith Condorcet loser)
is likely to be the most mutiny-vulnerable candidate in my RSTZ example?
Not yet. I'll make one question to understand your thinking.

Case 1: The voting method elects Z. R, S and T supporters make an
agreement to replace Z with (e.g.) R and then forget further
revolutions.
Case 2: The voting method elects R. S and T supporters make an
agreement to replace R with T and then forget further revolutions.
Revolution of case 2 is easier to implement (if margins are used to
measure difficulty of revolutions) and S and T have the motivation.
Would that make R more vulnerable to a mutiny than Z?

- after the mutiny situation is about the same in both cases ("cycle of
three")
- before the mutiny situation was not satisfactory to any of the
mutineers
- the candidate that was replaced may feel more angry or more beaten
after the mutiny
- mutineers may feel more or less ready for new mutinies after one
revolution
- I didn't evaluate the possible cost of mutinies in this example
- I didn't address the possibility of R, S and T being members of the
same party (clones?) => separate parties that don't like each others so
far

I tried to construct this example so that it would help me seeing the
difference between the "foresight" based mutiny tendencies that you
brought up and the simpler mutiny tendencies that I used (mainly for
track 2, but in interesting in track 1 too). So, if you find the rest
of my comments repetitive or otherwise less interesting, clear comments
on how you see the difference between these two cases might help me
forward.
Post by James Green-Armytage
Does it mean you are willing to abandon the claim that
minimax(margins)
winners are less vulnerable to mutiny than Smith winners, when they differ?
We are now on track 1 and that claim addresses track 2. I believe it is
valid there. I don't want to claim anything on track 1 yet.
Post by James Green-Armytage
Post by Juho Laatu
- An alternative model where the cost of mutiny is low and therefore
mutinies could continue forever (instead of stopping when pirates
understand that the cost of mutinies is too high). Accepting one of the
Smith candidates to take permanent lead may thus be more painful than
"sharing the leadership" by making continuous mutinies.
In real life government/election scenarios, the cost of mutiny is always
high.
Yes, in government level elections. But there are also other cases. In
track 1 we talk about possibility of continuous mutinies/elections.
Therefore track 1 is maybe not the best model for large elections where
cost of new rounds is high (e.g. normal presidential elections). I
guess we are more likely talking about some smaller elections when
talking about track one. If we are talking about election of a captain
of a pirate ship, then cost of mutiny could be human lives, which is
high (well, maybe some pirates do not value human life very much). On
the other hand the pirates could be civilized or we could talk about
electing a new chairman for a board. In these cases the cost of mutiny
would be only few pieces of paper for the ballots and 15 minutes of
time, and maybe some disappointments.
Post by James Green-Armytage
Post by Juho Laatu
- B and C could join forces and make just one revolution where A would
be changed to C (202 against 101) and stop there.
You suggest that the B>C>X>A and C>A>X>B pirates may join forces to
change A to C. In forming this coalition, the B>C>X>A pirates would
promise the C>A>X>B pirates that they would not mount a further mutiny
against C. But why should the C>A>X>B faction trust them on this, mutinous
pirates that they are?
In politics deals like this are very common. Pirate style politicians
that are not trustworthy may also exist. I think the stopping problem
is pretty much the same in all scenarios => deals, getting bored, risk
of further revolutions eating the benefits and cost of mutinies may
stop them.
Post by James Green-Armytage
Once the first mutiny has occurred, the B>C>X>A
pirates could join forces with the disgruntled A>B>X>C faction, to get
their man B at the helm.
Yes, but there are also some limiting factors like the deal and other
reasons listed in the previous answer, and the fact that B supporters
already have their second best alternative as the captain.
Post by James Green-Armytage
To be fair, I acknowledge that some mutinies might have more "sticking
power" than others. I suggest that this will depend on the strength of the
preferences involved, and so I suggest that cardinal pairwise may do
better in this sort of situation than any strictly ordinal method.
Yes, and cardinal pairwise style methods could at least in theory dig
some additional useful additional information out. (Sorry, haven't made
good enough analysis of it yet to give better comments but the basic
idea seems sound.)


One more generic comment: The reason why I don't feel comfortable with
track one style voting methods that may consist of two or more rounds
is that when the voting behaviour of the earlier rounds is known, the
possibility and probability of strategic voting increases, the need to
defend against them increases, and the more probable it becomes that we
don't get the sincere votes and the algorithm can not pick the sincere
(= best candidate based on the agreed targets of the election) winner.
Post by James Green-Armytage
=============
track 2
=============
Post by Juho Laatu
and another one where we try to do the decision just
once and then live with the result until the next election day (few
years ahead).
...
Post by Juho Laatu
Captain A would have more problems driving her policy through since C
could always make counter proposals that would be supported 202 against
101 and A would need better speaking skills than X (or a cannon).
This doesn't make a whole lot of sense to me so far, perhaps because I
don't understand the scenario. To begin with, we're assuming that there is
an extremely strong sincere cycle in the initial vote. I doubt that this
will happen very often (probably never to the extent of your example), but
I can accept the premise for the sake of argument. But then, are we
assuming that there would be a comparably strong cycle in the sincere
preferences of the voters on most public issues? I think that this is much
less probable.
Example of a possible real life strong cycle:
- candidate A spends 70% of her campaign time to talk about low taxes
and 30% of her time to talk about good social security
- candidate B spends 70% of her campaign time to talk about good
education and 30% of her time to talk about low taxes
- candidate C spends 70% of her campaign time to talk about good social
security and 30% of her time to talk about good education
- 33% of the voters are unemployed and they want good social security.
They vote C>A>B.
- 33% of the voters are students or academic and they want good
education. They vote B>C>A.
- 33% of the voters are factory and office workers and they want low
taxes. They vote A>B>C.
Conclusion: The selected strategies of three candidates lead to a
strong cycle in the votes although the voters themselves are sincere
and as normal as they can be. Strong cycles are quite possible in real
life (although not usually as common and strong as this example tries
to demonstrate).

If strong sincere loops are not probable, then defending against some
strategies is maybe not needed. Same comment about strong loops that
are a result of strategic voting.
Post by James Green-Armytage
Let's dump the pirate metaphor for track 2, and start talking about
actual government institutions. Is A the president now?
My claim was that if low risk of mutiny (in the sense of track 2) is
selected as the main target of the elections, then X should be the
president. But let's continue commenting with A as the president. That
doesn't make any difference here I guess.
Post by James Green-Armytage
What do you mean,
"problems driving her policy through"? Is the president supposed to write
legislation, and then rely on a popular ranked vote to have it passed? Who
says that the president has to win the vote on every issue? If A is
president, but the X faction wins the vote on several issues, that's fine
with me.
Ok, there is no clear relationship between the voting results and
opinions on some individual questions. The president could get varying
support to her different initiatives.

But on the other hand one can claim that politicians represent some
certain set of values and voters tend to pick their side and then
sympathize with their chosen candidates in many questions. Maybe they
even rely on their favourite so much that they change some of their old
opinions in line with what their favourite candidate says. Politics may
thus get very personalized.

In this case "mutiny" might demonstrate itself in the form of public
demonstrations. Former presidential candidate C could arrange a
campaign against the policy that president A drives. She would be able
to collect 10% of the 202 voters that support her criticism in a public
demonstration against C's policy. C would get 10% of the 101
participants that support the opposite view in the counter
demonstration in the following day. TV watchers would notice that C had
10 more people in the demonstration than what A had (is this a good
measure of the strength of the mutiny?). Based on this they would make
their conclusions on whether A is a strong mother of the country or a
loser. Rest of the term of A would either suffer or benefit of the
conclusions that people made.


One general (maybe clarifying) comment on track 1 vs. track 2: To me
the main difference between these two tracks is that in track 2 the
target is a "one shot election" where the (hopefully sincere) votes of
the voters will be evaluated and winner decided. Track one seems to
contain the possibility that voters could change the result of the
election by arranging a new election (of all candidates) or a
revolution (where x will be replaced with y).
Post by James Green-Armytage
===========
annex
===========
ANNEX 1: The pirate example.
101: a>b>x>c
101: b>c>x>a
101: c>a>x>b
100: x
ANNEX 2: The RSTZ example.
35: R>S>T>Z
33: S>T>R>Z
32: T>R>S>Z
71: Z>R=S=T
R>S 67-33
S>T 68-32
T>R 65-35
R>Z 100-71
S>Z 100-71
T>Z 100-71
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Stephane Rouillon
2005-05-27 04:43:53 UTC
Permalink
Pirates should, after some repetitive election,
see the wisdom of defining a mandate length before
knowing who wins...

Criterias and electoral methods hare not meant to
cope for a fractionated electorate. An electoral system
goal is to get the electorate will, whatever it is. Stability
is a further issue that should be dealt with separately,
either before by consensual agreement (over a mandate
length for example) or after with a winner's bonus when
comes time to take decisions in exchange for other
advantages to losers (as a reduction of the mandate length
for example: this is the "crutch option" proposed within SPPA).

Steph.
Post by James Green-Armytage
Hi Juho,
My critique of your pro-minimax(margins) argument follows...
Post by Juho Laatu
I tend to see margins as "natural" and winning votes as something that
deviates from the more natural margins but that might be used somewhere
to eliminate strategic voting. (not a very scientific description but I
don't have any better short explanation available :-) )
No, that's more or less how I think of it. However, when you say that wv
might be needed "somewhere" to reduce (not eliminate) strategic voting, I
suggest that most public elections will fall within the region of
"somewhere". (Please see my 3/14 post.)
101: a>b>x>c
101: b>c>x>a
101: c>a>x>b
100: x
...
Post by Juho Laatu
I meant that when X was the captain people wanted to change him to A, B
or C with a small margin of votes. But later when e.g. C became the
captain people wanted to change him to B with a large margin. Only a
minority wanted to change C to X.
I'm with you this far.
Post by Juho Laatu
But the point is that people
(majority of them) are now "less happy"
...you don't know how happy they are with any of these candidates...
Post by Juho Laatu
or "more mutinous" because of
the problematic B>C relationship.
Okay, let's get to the bottom of this.
No matter who wins, 202 pirates would rather have some other candidate in
particular. If X wins, this still holds, but 201 pirates strictly
disagree. In the other cases, e.g. A wins, 202 pirates would rather have
C, and only 101 pirates strictly disagree (the remaining 100 are
indifferent).
Your logic is as follows: If X wins, and a group of 202 pirates who
preferred another candidate rather than X wanted to mutiny, there would be
201 pirates ready to stand in their way, serving as an effective
C>A>X>B) mutiny in favor of C, there won't be sufficiently many pirates to
fight to defend A.
Here's what I'd like you to consider: Let's say that A is the initial
winner, these 202 C>A pirates declare mutiny, and the 100 X pirates stay
neutral. There may or may not be a scuffle, but anyway the 101 A>B>X>C
pirates back down. Okay fine; C is the captain. But now the B>C pirates
will be emboldened to mutiny against C. The process repeats, and B is the
captain. Now it will be the A>B pirates' turn, and A will be captain once
more. This idiotic process could go on indefinitely, so that the captain
might shift several times in the duration of any given voyage, causing
general irritation. Or, it could result in serious violence, and there is
no guarantee that C will be on top when the dust settles.
I suggest to you that this is a relatively intelligent bunch of pirates.
(This is evidenced by the fact they are using Condorcet's method to make
decisions.) If so, I suggest that the 202 C>A pirates will see the
risk/futility of their mutiny ahead of time. (I'm assuming that all the
pirates know each other's expressed ranked preferences, as would be the
case in any real public election.) Sure, they could oust A in favor of C
by force if the X voters sat on their hands. Maybe they could even kill
candidate A, so as to finalize his defeat. But if they did that, a pro-B
mutiny would be likely to follow, and perhaps this new coalition would
B>C>X>A) would be all the more delighted with this second mutiny, but the
other half (101: C>A>X>B) would rather have A than B, and they would mourn
for C's death.
So I ask you, would the B>C>X>A voters participate in the first mutiny
against A? I suggest that they would not, because they would realize that
a victory for C so reached would be unlikely to last. In short, you
neglected to assign foresight to your imaginary pirates, and foresight
would prevent a mutiny against a Smith set member. Would foresight prevent
a mutiny against a non-Smith member, in favor of a Smith member? Not
35: R>S>T>Z
33: S>T>R>Z
32: T>R>S>Z
71: Z>R=S=T
R>S 67-33
S>T 68-32
T>R 65-35
R>Z 100-71
S>Z 100-71
T>Z 100-71
Candidate Z is the minimax(margins) winner. However, he is in no wise the
most mutiny-proof candidate. If Z is the initial winner, then all 100 of
the R/S/T faction will have a common cause in ousting him. Perhaps if they
change the winner to R, there could conceivably be further mutiny, but no
matter what, such further mutiny will not lead to another result that the
R/S/T pirates like less than Z. (Hence they can happily mutiny against Z
without worrying that it will hurt them in the long run.) More likely,
however, there will be no further mutiny. The R/S/T faction would do well
to first choose whom they prefer among themselves (let's say that they
settle on R), and to then march over to the Z faction and announce the
change of leadership. The odds are running heavily in favor of the R/S/T
faction if a fight breaks out.
Again, once Captain R (as in "ARRR!") takes over, any potential mutiny
coalition has to face the prospect of subsequent mutinies that cause a
result that they like less than Captain R. So I argue that Captain R would
suffer less risk of mutiny than Captain Z.
I hope that I have disrupted your assumptions concerning the "risk of
mutiny" concept.
Post by Juho Laatu
I think all the majorities are unambiguous (because that is what the
voters told us). A>X could be called "loopless", if we want to describe
how it is different from the others. Both electing X and electing A
violate a majority opinion. One can avoid violating A>X by not electing
X (= select one of the Smith candidates). But one can also avoid
violating e.g. A>B by not electing B. All of the individual preferences
are thus avoidable. And all the Smith loop violations can be avoided by
electing X.
If there is a majority rule cycle, then one cannot avoid ignoring at
least one majority preference. However, one can always avoid ignoring a
majority preference that is not contradicted by another majority
preference (via a cycle).
Post by Juho Laatu
Post by James Green-Armytage
In your pirate example, there are no compromise
candidates; the pirate electorate is very badly polarized.
I agree. The basic setting is four parties of about equal size. I think
this situation is quite normal.
Four parties of equal size. Okay, that's not very common, but there's no
particular reason why it couldn't happen. What I'm calling your attention
to is not the relative size of the parties, but the intensity of the
polarization between them. We have intense political polarization in
countries that have voting systems that encourage polarization. In
Condorcet systems, we should not assume that this polarization will
remain; rather, it seems logical that compromise candidates will emerge,
which they haven't done in your example.
Post by Juho Laatu
I claim that
"mutiny" is one well defined criterion that is useful is some
situations and directly points out the correct voting method (MinMax
with margins).
Please read and consider my recent post about strategic vulnerability in
"margins" methods before you state so unequivocally that it is "the
correct voting method". Actually, even then you might want to be careful
about calling anything "the correct voting method" without some sort of
qualification.
Post by Juho Laatu
Mutiny of everyone against one is one candidate for another real life
criterion. I think mutiny to replace one with one is however the most
useful and typical case (both in the ship and in politics). This
"mutiny for anyone else" would also give support to sticking to the
Smith set when electing the winner.
If your second criterion is to select the candidate who is not the first
choice of the fewest voters, this is equivalent to selecting the candidate
with the most first choice votes, a.k.a. plurality.
Post by Juho Laatu
That is not allowed :-). We had an election with four candidates. And
elections are not supposed to cause countries to break into separate
smaller countries. The best single winner election method must be
capable of electing one (the best) of these candidates.
Sure, but if all of the candidates are highly divisive (as they are in
your example), you can't blame the method for choosing a divisive
candidate. Based on the information available, A, B, and C are equally
good choices, which is to say that they are equally bad choices. X is a
slightly worse choice, because choosing X unnecessarily violates majority
rule.
all my best,
James
http://fc.antioch.edu/~james_green-armytage/voting.htm
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James Gilmour
2005-05-27 10:25:26 UTC
Permalink
Stephane Rouillon Sent: Friday, May 27, 2005 5:44 AM
Post by Stephane Rouillon
Criterias and electoral methods hare not meant to
cope for a fractionated electorate. An electoral system
goal is to get the electorate will, whatever it is.
This may be true for single-winner elections, eg city mayor, state governor, but fractionated electorates are the
realities of politics in the real world.

For elections to councils, assemblies and legislatures it is only one view of the goal of an electoral system. Those
steeped in social choice theory believe that the purpose of a voting system should be to maximise representation of
consensus among the electors. But there is a much older view: that the purpose of a voting system should be to maximise
representation of the diversity among the electors.

James Gilmour

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Abd ul-Rahman Lomax
2005-05-27 19:29:45 UTC
Permalink
Post by James Gilmour
Those
steeped in social choice theory believe that the purpose of a voting
system should be to maximise representation of
consensus among the electors. But there is a much older view: that the
purpose of a voting system should be to maximise
representation of the diversity among the electors.
Those two goals could support each other. However, many voting systems
accomplish neither purpose.

The goals are compatible because the best way to ensure the widest
consensus is to have as many players at the table as possible. You may
increase meeting efficiency by excluding minority factions, but at the cost
of potentially excluding them in deliberations toward consensus.

Proportional Representation, of course, advances the diversity position,
but also is based on a party system. Unless, of course, voting becomes
proportional rather than number of members. I.e., proxy representation. And
Delegable Proxy makes the concentration of proxies into a council or
working group almost automatic. The idea is to reduce meeting size to the
ideal. What that ideal is, again, would depend on the nature of the
organization.

One point to be realized is that a 20-member council with delegable proxy
would be far more diverse than one with, say PR. This is because a few
proxies would likely hold many votes, and thus proxy-holders with many
fewer votes might still qualify for the council. In other words, a
20-member council would likely have members on it representing much less
than 1% of the electorate. But I don't think we can predict the results.

Delegable Proxy could fail if introduced prematurely into a highly
polarized election process, and where people have no expectation of being
able to personally communicate with their proxy. What would happen here is
that people would give their proxy to highly-visible, media-savvy
candidates, who would then have great power. The problem is that we don't
really know those people! This is why delegable proxy will work best when
the direct proxy assignment scale is quite small. The exact number would
vary with the nature of the organization, but in an active organization,
with broad interest among its members, I'd think that twenty direct proxies
might be about right. Then delegability allows proxies to be further
concentrated without creating a big step, without breaking the personal
links of trust that would make delegable proxy work.

Once again, this failure mode for Delegable Proxy is why I think it crucial
to introduce it into Free Associations -- which can't, by design, be
hijacked -- rather than into necessarily more stable institutions. If those
FAs don't work, little will be lost, and the networking created will still
be valuable.

(Free Association is a term which formalizes certain characteristics of
ad-hoc peer organizations, common when they start, much less common, indeed
rare, when they grow. Delegable Proxy theoretically makes it possible for
Free Associations and Direct Democracy to scale, to become quite large
without losing the freedom and full participation of direct democracy in
young organizations.)


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James Gilmour
2005-05-27 21:46:00 UTC
Permalink
On Behalf Of Abd ul-Rahman Lomax Sent: Friday, May 27, 2005 8:30 PM
Proportional Representation, of course, advances the diversity position,
but also is based on a party system.
You are considering only one version of PR, ie party PR. With STV-PR (choice voting) there need be no parties nor is
there any need to assume the existence of parties. Of course, STV-PR works equally well when the candidates are
nominated by parties, but importantly, the relationships are different from those created by party-PR. (I recognise
this is a multi-seat election intrusion into what is almost exclusively a single-winner election discussion, but my
original comment was prompted by Stephane's completely general assertion about the goal of an electoral system.)

James Gilmour

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Juho Laatu
2005-05-27 20:56:47 UTC
Permalink
Hello James,

In the pirate example one could take a step in the direction of
proportional representation and give up the original idea of single
winner elections. It is the captain that is to be elected, and there is
a tradition of having only one captain on a ship. In this situation one
could consider arranging the proportional representation in a serial
mode, not in the traditional parallel mode. What I mean is that the
community could agree (beforehand) to divide the post in time, let's
say in n consecutive terms. I'm not proposing any particular method,
nor to do this in real life (just presenting ideas popping in my head),
but this would anyway be one way of dealing with the fractioned
electorate.

BR, Juho

P.S. To increase proportionality one could even consider n terms of
different lengths.
Post by James Gilmour
Stephane Rouillon Sent: Friday, May 27, 2005 5:44 AM
Post by Stephane Rouillon
Criterias and electoral methods hare not meant to
cope for a fractionated electorate. An electoral system
goal is to get the electorate will, whatever it is.
This may be true for single-winner elections, eg city mayor, state
governor, but fractionated electorates are the
realities of politics in the real world.
For elections to councils, assemblies and legislatures it is only one
view of the goal of an electoral system. Those
steeped in social choice theory believe that the purpose of a voting
system should be to maximise representation of
consensus among the electors. But there is a much older view: that
the purpose of a voting system should be to maximise
representation of the diversity among the electors.
James Gilmour
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Stephane Rouillon
2005-05-31 02:17:04 UTC
Permalink
Juho just showed another way of using time to get some efficiency
without sacrifying fairness. A better example than any I could provide...

My sincere congratulations,
Steph.
Post by Juho Laatu
Hello James,
In the pirate example one could take a step in the direction of
proportional representation and give up the original idea of single
winner elections. It is the captain that is to be elected, and there is
a tradition of having only one captain on a ship. In this situation one
could consider arranging the proportional representation in a serial
mode, not in the traditional parallel mode. What I mean is that the
community could agree (beforehand) to divide the post in time, let's
say in n consecutive terms. I'm not proposing any particular method,
nor to do this in real life (just presenting ideas popping in my head),
but this would anyway be one way of dealing with the fractioned
electorate.
BR, Juho
P.S. To increase proportionality one could even consider n terms of
different lengths.
Post by James Gilmour
Stephane Rouillon Sent: Friday, May 27, 2005 5:44 AM
Post by Stephane Rouillon
Criterias and electoral methods hare not meant to
cope for a fractionated electorate. An electoral system
goal is to get the electorate will, whatever it is.
This may be true for single-winner elections, eg city mayor, state
governor, but fractionated electorates are the
realities of politics in the real world.
For elections to councils, assemblies and legislatures it is only one
view of the goal of an electoral system. Those
steeped in social choice theory believe that the purpose of a voting
system should be to maximise representation of
consensus among the electors. But there is a much older view: that
the purpose of a voting system should be to maximise
representation of the diversity among the electors.
James Gilmour
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Stephane Rouillon
2005-05-31 01:40:35 UTC
Permalink
James,

I never said that the electorate will was to identify itself
to some political parties.

You mix the fact that I use political parties in SPPA to simplify ballot treatment
in order to get nearer our common objective (a representative chamber that is
independent of party lines) and the fact that other people (not me) consider
that proportionality is only measured using party distributions.

Yes I lose something with SPPA (using party affiliation to transfer votes)
compared to STV-PR using only individually expressed transfers.
But I gain more because SPPA results in a proportionailty equivalent
to a single district STV-PR, a level STV-PR cannot reach because ballots
with hundreds of names scares the electorate. This is "the realities of
politics in the real world."

Steph.
PS: Please note that I will never repeat it enough: STV-PR is in my humble
opinion the best multiple-winner electoral system among the ones actually
used in the world. It should not stop us to search for a better one.
Post by James Gilmour
Stephane Rouillon Sent: Friday, May 27, 2005 5:44 AM
Post by Stephane Rouillon
Criterias and electoral methods hare not meant to
cope for a fractionated electorate. An electoral system
goal is to get the electorate will, whatever it is.
This may be true for single-winner elections, eg city mayor, state governor, but fractionated electorates are the
realities of politics in the real world.
For elections to councils, assemblies and legislatures it is only one view of the goal of an electoral system. Those
steeped in social choice theory believe that the purpose of a voting system should be to maximise representation of
consensus among the electors. But there is a much older view: that the purpose of a voting system should be to maximise
representation of the diversity among the electors.
James Gilmour
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James Gilmour
2005-05-31 07:28:28 UTC
Permalink
Stephane Rouillon Sent: Tuesday, May 31, 2005 2:41 AM
Post by Stephane Rouillon
I never said that the electorate will was to identify itself
to some political parties.
I never said you did. MY comments (in full below) made absolutely no mention of political parties.

I was concerned only to draw the distinction in multi-winner elections between the view that the voting system should
maximise representation of consensus and the view that the voting system should maximise representation of diversity.
Post by Stephane Rouillon
You mix the fact that I use political parties in SPPA to
simplify ballot treatment in order to get nearer our common
objective (a representative chamber that is independent of
party lines) and the fact that other people (not me) consider
that proportionality is only measured using party distributions.
I made no comment about your SPPA voting system, nor did I have it in mind when I wrote my comments about consensus and
diversity.

My comment was intended to be a completely general one, relating to issues that overtly or covertly run through much of
the discussion about the purposes of elections. The only voting system I had in mind was STV-PR: it has implementations
that maximise diversity (Dáil Éireann rules) and implementations that maximise consensus (Meek rules).

James
Post by Stephane Rouillon
Yes I lose something with SPPA (using party affiliation to
transfer votes) compared to STV-PR using only individually
expressed transfers. But I gain more because SPPA results in
a proportionailty equivalent to a single district STV-PR, a
level STV-PR cannot reach because ballots with hundreds of
names scares the electorate. This is "the realities of
politics in the real world."
Steph.
PS: Please note that I will never repeat it enough: STV-PR is
in my humble opinion the best multiple-winner electoral
system among the ones actually used in the world. It should
not stop us to search for a better one.
Post by James Gilmour
Stephane Rouillon Sent: Friday, May 27, 2005 5:44 AM
Post by Stephane Rouillon
Criterias and electoral methods hare not meant to
cope for a fractionated electorate. An electoral system goal is to
get the electorate will, whatever it is.
This may be true for single-winner elections, eg city mayor, state
governor, but fractionated electorates are the realities of politics
in the real world.
For elections to councils, assemblies and legislatures it is only one
view of the goal of an electoral system. Those steeped in social
choice theory believe that the purpose of a voting system should be to
maximise representation of consensus among the electors. But there is
a much older view: that the purpose of a voting system should be to
maximise representation of the diversity among the electors.
James Gilmour
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Abd ulRahman Lomax
2005-05-27 16:26:34 UTC
Permalink
Criterias and electoral methods [...] are not meant to
cope for a fractionated electorate. An electoral system
goal is to get the electorate will, whatever it is.
Actually, the goal of electoral systems is to reduce the electorate will to
a decision. One of the basic problems is the lack of clarity of what we
mean by "the electorate will."

Sensible persons, in the presence of contradictory impulses in their own
internal process, will take one of several possible courses of action:

(1) If the issue is not important, they may allow the "majority" impulse to
rule. Or they might, as an experiment, allow a hunch to control action,
even if there are plenty of arguments against it.

(2) They will take no action and wait for clarity. This presumes that the
situation is not urgent.

(3) Again, if the issue is not urgent, they will take the time to
investigate and to carefully compare the various options. An equivalent of
Condorcet Voting is sometimes used.

(4) If the situation is important and urgent, they will use an internal
equivalent of either Plurality or Approval voting. The tiger is at your
heels and there are three doors, about which you have no information but
what you see. I'm really not sure which of the two systems the brain will
use in that case, though, in the end, Approval might be hard-wired and
plurality then rules. And this is what is done in Approval Voting. There is
a preliminary process which determines Approval ratings and then plurality
within the ratings wins. Approval in an election process might indeed
require a majority approval or even a supermajority approval, or else the
election remains suspended, perhaps there is some kind of runoff (forcing
supporters of largely unapproved candidates to cast an approval vote for
the remaining candidates or abstain).

A sane electoral system would ordinarily avoid considering an election for
an important office done merely because of a simple majority approval.
That's a divided electorate, the equivalent of a divided mind. And there is
no efficient way beyond this other than a more sophisticated process than
what are ordinarily considered election methods.

This is the origin of the name Beyond Politics, for htt://beyondpolitics.org.

Delegable Proxy, if used as an election method, does not resolve conflict
in the electorate in the secret ballot phase; rather it reserves the
decision for a deliberative body in which every voter may either
participate or be represented by a representative of choice. One might call
the assignment of votes to electors an "election," except that in a proxy
system there are no losers. All remain represented, regardless of the
relative vote counts.

This is, indeed, how higher consciousness functions. We could take a hint
from our biology.

And my major point is that there is nothing stopping the formation of this
more coherent entity than our inertia and political cynicism. It does not
take convincing the public at large before such organizations could be up
and running and exerting substantial influence. Thus, such organizations
could be used as part of an electoral reform process.

Instead of trying to reform elections by using the existing election
process, one reforms the organization of voters to create a deliberative
body, through an organizational technology that, by its nature, attempts to
discover consensus; once there is a consensus, *then* it will be easy to
change election methods.

Even a relatively small delegable proxy political action group could exert
influence beyond its size. This is because the existing system allows
relatively small special interest groups to dominate the election process.

If one small DP organization is able to do this, it will be imitated by
others. And if these are FA/DP, i.e., Free Associations with Delegable
Proxy, they will almost automatically merge.

This is because merger does not require the acceptance or resolution of
competing ideas. It simply allows these ideas to meet on a level playing
field. FAs don't collect funds which are then spent without the individual
consent of the members. Rather, if a majority of members want to take some
action, a special fund is created for that action, including its own
management mechanism, and members voluntarily contribute to it. There might
be other members who oppose it, and they remain free -- and automatically
organized -- and in a position to do the same. So if there is a situation
where the electorate is divided, the competing conclusions may remain
balanced. As they should be.

Thus joining an FA/DP organization does not prejudice the outcomes toward
some particular position. FA/DP may start among progressives, for example,
and it would thus initially help progressive causes, but ultimately it will
create an environment which is "beyond progressive." Rather it might be
called integrative.

Absent emergencies, important decisions should be made from a position of
relative unity.




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Juho Laatu
2005-05-27 20:55:27 UTC
Permalink
Hello Stephane,

Yes. Electoral methods should aim at electing the candidate that is
best for the planned period (based on the will of the electors as
expressed in the ballots). Repetitive mutinies are thus something one
need not normally prepare for.

If the community can agree what the "utility function" (that sets the
criteria and determines which candidate is best) is, then the
calculating the election results is quite straight forward (((although
maybe computationally complex))). There is of course one important
thing to take into account when agreeing the utility function (or
electoral method). The electoral method should be sufficiently strategy
resistant (= the reason why often only ranking based methods are
considered, and why also between these there is lots of discussion
about the smaller granularity strategy questions).

BR, Juho
Post by Stephane Rouillon
Pirates should, after some repetitive election,
see the wisdom of defining a mandate length before
knowing who wins...
Criterias and electoral methods hare not meant to
cope for a fractionated electorate. An electoral system
goal is to get the electorate will, whatever it is. Stability
is a further issue that should be dealt with separately,
either before by consensual agreement (over a mandate
length for example) or after with a winner's bonus when
comes time to take decisions in exchange for other
advantages to losers (as a reduction of the mandate length
for example: this is the "crutch option" proposed within SPPA).
Steph.
Hi Juho,
        My critique of your pro-minimax(margins) argument follows...
Post by Juho Laatu
I tend to see margins as "natural" and winning votes as something
that
Post by Juho Laatu
deviates from the more natural margins but that might be used
somewhere
Post by Juho Laatu
to eliminate strategic voting. (not a very scientific description
but I
Post by Juho Laatu
don't have any better short explanation available :-) )
        No, that's more or less how I think of it. However, when you
say that wv
might be needed "somewhere" to reduce (not eliminate) strategic voting, I
suggest that most public elections will fall within the region of
"somewhere". (Please see my 3/14 post.)
101: a>b>x>c
101: b>c>x>a
101: c>a>x>b
100: x
...
Post by Juho Laatu
I meant that when X was the captain people wanted to change him to
A, B
Post by Juho Laatu
or C with a small margin of votes. But later when e.g. C became the
captain people wanted to change him to B with a large margin. Only a
minority wanted to change C to X.
        I'm with you this far.
Post by Juho Laatu
But the point is that people
(majority of them) are now "less happy"
        ...you don't know how happy they are with any of these
candidates...
Post by Juho Laatu
or "more mutinous" because of
the problematic B>C relationship.
        Okay, let's get to the bottom of this.
        No matter who wins, 202 pirates would rather have some other
candidate in
particular. If X wins, this still holds, but 201 pirates strictly
disagree. In the other cases, e.g. A wins, 202 pirates would rather have
C, and only 101 pirates strictly disagree (the remaining 100 are
indifferent).
        Your logic is as follows: If X wins, and a group of 202
pirates who
preferred another candidate rather than X wanted to mutiny, there would be
201 pirates ready to stand in their way, serving as an effective
C>A>X>B) mutiny in favor of C, there won't be sufficiently many pirates to
fight to defend A.
        Here's what I'd like you to consider: Let's say that A is the
initial
winner, these 202 C>A pirates declare mutiny, and the 100 X pirates stay
neutral. There may or may not be a scuffle, but anyway the 101 A>B>X>C
pirates back down. Okay fine; C is the captain. But now the B>C pirates
will be emboldened to mutiny against C. The process repeats, and B is the
captain. Now it will be the A>B pirates' turn, and A will be captain once
more. This idiotic process could go on indefinitely, so that the captain
might shift several times in the duration of any given voyage, causing
general irritation. Or, it could result in serious violence, and there is
no guarantee that C will be on top when the dust settles.
        I suggest to you that this is a relatively intelligent bunch
of pirates.
(This is evidenced by the fact they are using Condorcet's method to make
decisions.) If so, I suggest that the 202 C>A pirates will see the
risk/futility of their mutiny ahead of time. (I'm assuming that all the
pirates know each other's expressed ranked preferences, as would be the
case in any real public election.) Sure, they could oust A in favor of C
by force if the X voters sat on their hands. Maybe they could even kill
candidate A, so as to finalize his defeat. But if they did that, a pro-B
mutiny would be likely to follow, and perhaps this new coalition would
B>C>X>A) would be all the more delighted with this second mutiny, but the
other half (101: C>A>X>B) would rather have A than B, and they would mourn
for C's death.
        So I ask you, would the B>C>X>A voters participate in the
first mutiny
against A? I suggest that they would not, because they would realize that
a victory for C so reached would be unlikely to last.   In short, you
neglected to assign foresight to your imaginary pirates, and foresight
would prevent a mutiny against a Smith set member. Would foresight prevent
a mutiny against a non-Smith member, in favor of a Smith member? Not
35: R>S>T>Z
33: S>T>R>Z
32: T>R>S>Z
71: Z>R=S=T
R>S 67-33
S>T 68-32
T>R 65-35
R>Z 100-71
S>Z 100-71
T>Z 100-71
        Candidate Z is the minimax(margins) winner. However, he is in
no wise the
most mutiny-proof candidate. If Z is the initial winner, then all 100 of
the R/S/T faction will have a common cause in ousting him. Perhaps if they
change the winner to R, there could conceivably be further mutiny, but no
matter what, such further mutiny will not lead to another result that the
R/S/T pirates like less than Z. (Hence they can happily mutiny against Z
without worrying that it will hurt them in the long run.) More likely,
however, there will be no further mutiny. The R/S/T faction would do well
to first choose whom they prefer among themselves (let's say that they
settle on R), and to then march over to the Z faction and announce the
change of leadership. The odds are running heavily in favor of the R/S/T
faction if a fight breaks out.
        Again, once Captain R (as in "ARRR!") takes over, any
potential mutiny
coalition has to face the prospect of subsequent mutinies that cause a
result that they like less than Captain R. So I argue that Captain R would
suffer less risk of mutiny than Captain Z.
        I hope that I have disrupted your assumptions concerning the
"risk of
mutiny" concept.
Post by Juho Laatu
I think all the majorities are unambiguous (because that is what the
voters told us). A>X could be called "loopless", if we want to
describe
Post by Juho Laatu
how it is different from the others. Both electing X and electing A
violate a majority opinion. One can avoid violating A>X by not
electing
Post by Juho Laatu
X (= select one of the Smith candidates). But one can also avoid
violating e.g. A>B by not electing B. All of the individual
preferences
Post by Juho Laatu
are thus avoidable. And all the Smith loop violations can be avoided
by
Post by Juho Laatu
electing X.
        If there is a majority rule cycle, then one cannot avoid
ignoring at
least one majority preference. However, one can always avoid ignoring a
majority preference that is not contradicted by another majority
preference (via a cycle).
Post by Juho Laatu
Post by James Green-Armytage
In your pirate example, there are no compromise
candidates; the pirate electorate is very badly polarized.
I agree. The basic setting is four parties of about equal size. I
think
Post by Juho Laatu
this situation is quite normal.
        Four parties of equal size. Okay, that's not very common, but
there's no
particular reason why it couldn't happen. What I'm calling your attention
to is not the relative size of the parties, but the intensity of the
polarization between them. We have intense political polarization in
countries that have voting systems that encourage polarization. In
Condorcet systems, we should not assume that this polarization will
remain; rather, it seems logical that compromise candidates will emerge,
which they haven't done in your example.
Post by Juho Laatu
I claim that
"mutiny" is one well defined criterion that is useful is some
situations and directly points out the correct voting method (MinMax
with margins).
        Please read and consider my recent post about strategic
vulnerability in
"margins" methods before you state so unequivocally that it is "the
correct voting method". Actually, even then you might want to be careful
about calling anything "the correct voting method" without some sort of
qualification.
Post by Juho Laatu
Mutiny of everyone against one is one candidate for another real life
criterion. I think mutiny to replace one with one is however the most
useful and typical case (both in the ship and in politics). This
"mutiny for anyone else" would also give support to sticking to the
Smith set when electing the winner.
        If your second criterion is to select the candidate who is
not the first
choice of the fewest voters, this is equivalent to selecting the candidate
with the most first choice votes, a.k.a. plurality.
Post by Juho Laatu
That is not allowed :-). We had an election with four candidates. And
elections are not supposed to cause countries to break into separate
smaller countries. The best single winner election method must be
capable of electing one (the best) of these candidates.
        Sure, but if all of the candidates are highly divisive (as
they are in
your example), you can't blame the method for choosing a divisive
candidate. Based on the information available, A, B, and C are equally
good choices, which is to say that they are equally bad choices. X is a
slightly worse choice, because choosing X unnecessarily violates majority
rule.
all my best,
James
http://fc.antioch.edu/~james_green-armytage/voting.htm
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Juho Laatu
2005-03-17 06:29:39 UTC
Permalink
Hello James,

As more or less promised, here are some comments on the rest of your
mail.

BR,
Juho



3. Condorcet and strategies

Condorcet is close to a dream come true in the sense that it almost
provides a perfect solution that eliminates all strategies from
elections and frees people to giving sincere votes only. Ok, there is
the problem with the loops and there are no strategy free election
methods. But when comparing Condorcet to many of the methods that are
commonly used today I would claim that Condorcet solves >90% of the
strategical voting problems. Being strategy free is thus a key
requirement. But is it already solved if Condorcet methods are used or
do we need further protection?

The remaining <10% of the problems (~= "the loop cases") need further
attention. Out of these <10% some problems are incurable. For the
remaining ones my approach is such that in order to avoid "shooting
flies with artillery" I would like to see concrete examples of cases
where in _real_world_election_situations_ strategical voting is a real
risk (and opportunity). If such cases are not clearly demonstrated for
each strategy eliminating fix/method, then we take the risk of picking
an election method that has features that are good in theory but never
needed in practice.

It is possible that the strategies against which we are protecting
ourselves are not used in practice and the voters simply give us their
sincere preferences. In such situations the strategy protection
supporting method may actually give an outcome that deviates from the
ideal solution that we would have picked if we had trusted all (or most
of) the votes to be sincere (I'm writing in parallel a reply to Mike
Ossipoff => some more notes there). These cases are naturally quite
marginal, but that is just the point => playing with marginal threats
that change the outcome will probably make the system more complex and
could even make the outcome worse in some (marginal) situations. If we
believe that certain voting strategies, although possible, are not
probable, it may be worth considering leaving those strategies out of
consideration when planning the best system.

Summary: Simple examples of use cases where strategies are a real
threat are needed to justify adding such defense mechanisms in the
election system.

I'll write one very basic use case to show what I mean.
"There are three parties of equal size and one candidate from each
party. There is a possibility for a single voter to try to bury one of
the two non-favourite candidates. But the voter has no idea which one
to bury. => She will vote sincerely. => This use case doesn't seem to
set new requirements on adding strategy elimination mechanisms."

Some classifications that may be useful when analysing the seriousness
of different voting strategy threats:

How detailed information of the voter opinions does the voting strategy
need before it can be efficiently used?
a1) complete set of preferences, a2) detailed, a3) statistical, a4) no
information needed

Is the strategy useful when the number of voters is b1) small, b2)
large?

Is the strategy useful when the number of candidates is c1) small, c2)
large?

Can the strategy be applied d1) independently by individuals, d2) only
by coordinated groups

Is the strategy e1) same for all, e2) different for different
individuals ("I vote this way, you vote that way and he votes that
way")

Can the strategy be applied f1) secretly, f2) will the strategy be
noticed after the elections, f3) noticed before the elections, f4)
already known and guessed by all?

g) Are there counter strategies or defensive methods that can be
applied by others?

h) Is the strategy morally acceptable to people? Of course we often can
not start judging and don't even know which opinions are sincere and
which not, but there are cases like "if all would start doing this, the
whole election would be a mess", "I don't want to admit that I did so",
"I voted strategically since I expect everyone else did so, and it
would be therefore stupid not to do so, and lose the elections".

What is the risk of strategy i1) turning against me, i2) having no
effect?

j) How easy to use?

k) How easy to explain to voters?

One example strategy that I find interesting (because it is not so easy
to ignore) is one where voters try to create a loop that includes only
the candidates of a competing party. All voters add at the end of their
ballot a list of candidates of the competing party in certain order. I
think this case is a4 (quite bad), d2 (this makes the risk smaller), e2
(someone votes "ABCDE" someone else "DEABC"), maybe f4, g => everyone
else does the same, i1=0 (bad), i2 very high but lower if well
coordinated, j not easy, k not easy.

Do we need to defend against this? What would be the best method? (Note
btw that there are also methods outside the vote counting phase. If we
make the ballot forms such that voter can only use limited number of
preference values (e.g. from 1 to 5) (several candidates can be given
the same value), then there is not much space for making such loops.)

Another interesting area is the recent discussion on this mailing list
on withdrawal after the elections. This is a very risky case since now
everyone knows exactly what the votes are unlike before the election
when they probably only had wild guesses and few Gallups.


I think this is enough for now. Have to rush to other business again. I
didn't yet comment many things properly like the cardinal pairwise
method (interesting although I haven't any firm opinions yet). I hope I
didn't miss too many points where you would like to squeeze and answer
out of me. :-)

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James Green-Armytage
2005-03-17 10:59:55 UTC
Permalink
Hi Juho,
Various replies follow, on the subject of voter strategy.
Post by Juho Laatu
Condorcet is close to a dream come true in the sense that it almost
provides a perfect solution that eliminates all strategies from
elections and frees people to giving sincere votes only.
This is true only in terms of the"compromising" strategy, which Condorcet
methods minimize. However, they open the door to the "burying" strategy,
which does not exist in plurality or IRV. I already defined these terms
for you. See also Blake Cretney's web site, for a list of which methods
are haunted by which strategies.
http://condorcet.org/
The burying strategy is more of a theoretical phenomenon than the
compromising strategy, because methods that invite the burying strategy
are not yet used in large-scale contentious elections. Hence it's hard to
say exactly how common it will be. However, I feel that we can say with
some confidence that it will be more common in some methods than others.
E.g. more common in margins than winning votes; more common in winning
votes than in any of the following: cardinal pairwise, approval-weighted
pairwise, wv with CWO or AERLO/ATLO.
Have you read my 3/14 post yet?
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015125.html
Post by Juho Laatu
I would like to see concrete examples of cases
where in _real_world_election_situations_ strategical voting is a real
risk (and opportunity).
It's hard to find real-world data about voter behavior given voting
systems like Condorcet that are predominantly theoretical. I suppose we
could try to take ranked ballots from a STV elections and see what sort of
strategic possibilities would have existed if it had been a Condorcet
election instead. That's not quite the same thing, but it might be fun
anyway.
Post by Juho Laatu
If such cases are not clearly demonstrated for
each strategy eliminating fix/method, then we take the risk of picking
an election method that has features that are good in theory but never
needed in practice.
It's far better to err on the side of caution, especially when the
integrity of the electoral process and the credibility of pairwise count
methods are at stake.
Post by Juho Laatu
Summary: Simple examples of use cases where strategies are a real
threat are needed to justify adding such defense mechanisms in the
election system.
I have provided several made-up examples along these lines. If you want
real examples, you have to wait for the method to be adopted for
contentious elections.
Post by Juho Laatu
Some classifications that may be useful when analysing the seriousness
...
Your "a" through "k" code system is perhaps not necessary, but the
questions you are asking are largely the right ones to ask.
Post by Juho Laatu
One example strategy that I find interesting (because it is not so easy
to ignore) is one where voters try to create a loop that includes only
the candidates of a competing party. All voters add at the end of their
ballot a list of candidates of the competing party in certain order. Do
we need to defend against this?
Yes, among other forms of the burying strategy.
Post by Juho Laatu
What would be the best method?
To begin with, the method should be Smith-efficient. That way, if none of
the strategizers' party's (party B's) candidates actually beat the other
party's (party A's) candidates, the winner will come from party A. With
minimax, party A could be a party of clones with a mutual majority, and
still fall victim to party B's strategy.
Second, the method should at least be a wv method, if not something
stronger (cardinal pairwise, AWP, CWO, AERLO/ATLO, etc.). I've explored
this idea in other places, and will continue to do so...
Post by Juho Laatu
(Note
btw that there are also methods outside the vote counting phase. If we
make the ballot forms such that voter can only use limited number of
preference values (e.g. from 1 to 5) (several candidates can be given
the same value), then there is not much space for making such loops.)
There are better ways to curtail strategy; reducing preference spaces is
not necessary.
Post by Juho Laatu
Another interesting area is the recent discussion on this mailing list
on withdrawal after the elections. This is a very risky case since now
everyone knows exactly what the votes are unlike before the election
when they probably only had wild guesses and few Gallups.
The concept of CWO (candidate withdrawal option) is that there is only
one public vote, but after the initial tally, candidates have the option
of having a new tally with their names deleted from the ballot. We can
only hope that the candidates will usually have enough information to tell
sincere cycles apart from strategically created cycles, and that they will
primarily use the CWO to correct strategically altered results. CWO is one
of the more rough anti-strategy measures, but it has the advantage of not
complicating the ballot and keeping the tally method proper as simple as
possible.

my best,
James
http://fc.antioch.edu/~james_green-armytage/voting.htm


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Juho Laatu
2005-03-18 07:05:14 UTC
Permalink
Hello James,

You wondered how familiar I am with different strategies etc. I have
studied the voting methods for quite some time and I have visited also
Blake Cretney's web site. I think I know most of the basic stuff but
unfortunately have not had time to follow all the details of the
discussions on this mailing list, so I don't master all of the
abbreviations of three and four letters.
Post by James Green-Armytage
Have you read my 3/14 post yet?
http://lists.electorama.com/pipermail/election-methods-electorama.com/
2005-March/015125.html
I'm off-line at the moment so I can't check. I guess yes but if I
haven't, I'll do that.
Post by James Green-Armytage
I suppose we
could try to take ranked ballots from a STV elections and see what sort of
strategic possibilities would have existed if it had been a Condorcet
election instead.
Yes, that would be a good check against real life data. I'd be
interested in doing the tests (at least in theory) so that before
opening the ballot files we would read the local newspapers from the
time before the elections and then make strategy recommendations to
different type of voters. It is important that the strategies would be
applied before knowing the actual outcome of the election and the
ballots. This method would help seeing which strategies can be applied
in real life an which not.
Post by James Green-Armytage
It's far better to err on the side of caution, especially when the
integrity of the electoral process and the credibility of pairwise count
methods are at stake.
I agree that risk analysis must be done and serious risks must be
eliminated (if possible) by selecting appropriate voting methods.
Post by James Green-Armytage
I have provided several made-up examples along these lines. If you want
real examples, you have to wait for the method to be adopted for
contentious elections.
Made-up examples are fine with me. What I often would like to see more
is to make the voters less clairvoyant and limit their information
better to what they are likely to have available in a real voting
situation. It is thus not enough if some voting result could have been
manipulated by appropriate strategical voting. The strategy must be
usable also in real life to be a real threat.
Post by James Green-Armytage
Post by Juho Laatu
One example strategy that I find interesting (because it is not so easy
to ignore) is one where voters try to create a loop that includes only
the candidates of a competing party. All voters add at the end of their
ballot a list of candidates of the competing party in certain order. Do
we need to defend against this?
Yes, among other forms of the burying strategy.
I'm particularly interested in strategies that can be implemented
without any prior knowledge of the expected outcome of the election.
That's why I picked this strategy. This category of strategies is
dangerous in the sense that it makes my target/hope of keeping the
voting methods close to the best sincere methods harder to achieve.
Post by James Green-Armytage
To begin with, the method should be Smith-efficient. That way, if none of
the strategizers' party's (party B's) candidates actually beat the other
party's (party A's) candidates, the winner will come from party A. With
minimax, party A could be a party of clones with a mutual majority, and
still fall victim to party B's strategy.
Let's say that because of the applied strategies both A and B
candidates have a loop within the party. If party B is a bit smaller
than party A, then the loop within party A must be weaker than the loop
within party B. In this case there would be no need for a defence (=>
also basic MinMax would be fine).

I'm worried about the possibility that all voters would have to apply
strategies in their ballots or otherwise they would lose the election.
A voting method that forces people to follow complex unintuitive
strategies surely is not a good voting method. If only party B applies
the strategy, then party A could lose the election if basic MinMax was
used.

I have sometimes played with the idea that if there are rules that try
to eliminate party internal loops, maybe those rules should apply to
parties only and not to other, maybe sincere loops. One could solve
this by using a method that takes into account which candidates have
been declared as belonging to the same party. Loops among them would
not be used against them. I don't know if such methods have already
been discussed somewhere. I haven't analysed these well enough to have
any firm opinon. And I understand that there are also malicious burying
loops between that involve several parties.

One big weakness of the loop voting strategy is that one has to agree
how to construct the loop. Is it ABCDA or is it ADCBA or something
else. Also voters have to be quite educated to understand that they
should pick a random starting point of the loop and create the loop
based on this information. In large public elections these problems may
be enough to make the strategy useless and defensive methods
unnecessary.
Post by James Green-Armytage
Second, the method should at least be a wv method, if not something
stronger (cardinal pairwise, AWP, CWO, AERLO/ATLO, etc.). I've explored
this idea in other places, and will continue to do so...
I can't comment since I can not estimate the risks and need for defence
yet.
Post by James Green-Armytage
There are better ways to curtail strategy; reducing preference spaces is
not necessary.
I agree that reducing preference spaces is quite violent. On the other
hand in practical elections sometimes simple ballots are a benefit. But
maybe it is also simple enough to write a ranking number next to each
candidate.

Best Regards,
Juho

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Juho Laatu
2005-03-14 10:16:57 UTC
Permalink
Hello James,

I think your first guess ("A single ballot that lists this candidate as the first choice, with all others tied for last") is enough to do the job.

In the example I gave I was thus thinking of additions like

101: a>b>x>c
101: b>c>x>a
101: c>a>x>b
100: x
2: x

or

101: a>b>x>c
101: b>c>x>a
101: c>a>x>b
100: x

102: a

It is possible to add other candidates names after the first one (e.g. "2: x>c>b>a") but those additions will not have any impact since x is now in any case a Condorcet winner, and the relative preference of the other candidates doesn't matter much since this is a single winner election.

Best Regards,
Juho


James Green-Armytage <***@antioch-college.edu> wrote:

Hi Juho, and welcome to the list.
Post by Juho Laatu
"Elect the candidate that wins all others. If there is no such candidate,
elect the one that needs least additional votes to win all others."
I'd like to clarify this, especially the second part. What exactly is an
"additional vote" in this context? A single ballot that lists this
candidate as the first choice, with all others tied for last? A reversal
of a pairwise preference in favor of this candidate?

my best,
James


Send instant messages to your online friends http://uk.messenger.yahoo.com
Fan de Condorcet
2005-03-14 20:53:08 UTC
Permalink
James,
Post by James Green-Armytage
Dear election methods fans,
In a recent message, I noted that there is no broad consensus among
Condorcet supporters as to which completion methods would be most
appropriate for a few key scenarios. I don't really expect to establish
such a consensus, but I would at least like to address some of the issues
involved, and hear where some of the other Condorcet supporters are coming
from.
1. The base method: Minimax (candidate whose worst loss is least bad),
sequential dropping (drop the weakest defeat that's in a cycle until a
candidate is unbeaten) ranked pairs, river, beatpath, Condorcet completed
by another method, approval hybrids, etc.
Like many others here, I'm a big fan of Ranked Pairs (RP), Schulze, and
River. To a great extent this is because I value approximations of IIA,
so I want a method that meets Smith-IIA and Independence of Clones.
Post by James Green-Armytage
2. Measures of defeat strength: margins, winning votes, or something else
(cardinal-weighted pairwise (CWP), approval-weighted pairwise (AWP), etc.)
I recently re-read your paper on CWP. I must confess that I didn't see
much justification for it at first, but I now find it to be well
justified and elegant. Unfortunately, there's the matter of the
complications this will create when it comes to creating and using
ballots. Perhaps over time I'll come to appreciate CWP more and think
it's worth the trouble, but for now I remain partial to margins.

To what I've said in regards to (1) and (2) so far I'd like to add that
for some time I've had difficulty deciding which of the big three
methods I prefer. Similarly I've had trouble finding any criterion that
makes either margins or winning votes the obvious choice. I've recently
become partial to RP(m). I'll post more about this in the days to come.
Post by James Green-Armytage
3. Whether to use an anti-strategy measure (candidate withdrawal option
(CWO), CWP, AERLO/ATLO, iterative procedure, etc.)
I'll briefly reiterate an idea I presented to this list some time ago:
Give runners-up a role within the institution. One modest example would
be that the bylaws of an organization could state that when an officer
becomes incapacitated, the runner-up will assume the role until
re-election or the officer is able to serve again. This might dissuade
people from (some) insincere ranking and truncation. Ranked Pairs could
be used to find the social ranking.

(The rest of your letter follows.)
Post by James Green-Armytage
Area (1) is not necessarily the most contentious; i.e. most people who
like beatpath like ranked pairs just about as much, and so on. However, I
would not feel especially good about a method that isn't Smith-efficient,
even to start out with. So that cuts out plain minimax as far as I'm
concerned.
I prefer winning votes for area (2), entirely for anti-strategic reasons.
This starts to bring us toward area (3), i.e. strategy. I agree that
winning votes has a better protection against the burying strategy than
margins, but I still suspect it to be somewhat unstable in certain
situations. If I am correct (which is debatable, of course), this brings
us into slightly uncomfortable terrain. CWO is the simplest anti-strategy
method, but some voters might be intuitively uncomfortable with the idea.
CWP has an intuitive interface, but one which requires very sophisticated
ballots, and the tally rule is complex. AWP, AERLO/ATLO, and similar
methods have a somewhat confusing interface, and while the tally rules are
not terribly complex, they are not brilliantly easy to explain, either.
I know that Mike Ossipoff has said that we should all come together
around a winning votes method without an additional anti-strategy measure.
But I'd like to hear what some other people think.
I'm not even sure what I would recommend, if I was in a position to
recommend something for public elections. I lean towards starting out with
a winning votes version of sequential dropping (or any one of ranked
pairs, beatpath, river, if there isn't an intense need for simplicity)
with a CWO. But that's subject to change, with further discussion.
my best,
James
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CF

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Fan de Condorcet
2005-03-14 21:05:08 UTC
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James,
Post by James Green-Armytage
Dear election methods fans,
In a recent message, I noted that there is no broad consensus among
Condorcet supporters as to which completion methods would be most
appropriate for a few key scenarios. I don't really expect to establish
such a consensus, but I would at least like to address some of the issues
involved, and hear where some of the other Condorcet supporters are coming
from.
1. The base method: Minimax (candidate whose worst loss is least bad),
sequential dropping (drop the weakest defeat that's in a cycle until a
candidate is unbeaten) ranked pairs, river, beatpath, Condorcet completed
by another method, approval hybrids, etc.
Like many others here, I'm a big fan of Ranked Pairs (RP), Schulze, and
River. To a great extent this is because I value approximations of IIA,
so I want a method that meets Smith-IIA and Independence of Clones.
Post by James Green-Armytage
2. Measures of defeat strength: margins, winning votes, or something else
(cardinal-weighted pairwise (CWP), approval-weighted pairwise (AWP), etc.)
I recently re-read your paper on CWP. I must confess that I didn't see
much justification for it at first, but I now find it to be well
justified and elegant. Unfortunately, there's the matter of the
complications this will create when it comes to creating and using
ballots. Perhaps over time I'll come to appreciate CWP more and think
it's worth the trouble, but for now I remain partial to margins.

To what I've said in regards to (1) and (2) so far I'd like to add that
for some time I've had difficulty deciding which of the aforementioned
three methods I prefer. Similarly I've had trouble finding any
criterion that makes either margins or winning votes the obvious choice.
However, I've recently become partial to RP(m). I'll post more about
this in the days to come.
Post by James Green-Armytage
3. Whether to use an anti-strategy measure (candidate withdrawal option
(CWO), CWP, AERLO/ATLO, iterative procedure, etc.)
I'm not about to advocate AERLO or ATLO, largely for the reasons you've
already mentioned. I also feel that CWO would give too much power to
candidates.

What do I propose? I'll briefly reiterate an idea I presented to this
list some time ago: Make runners-up matter. One modest example would be
that the bylaws of an organization could state that when an officer
becomes incapacitated, the runner-up will assume the role until
re-election or the officer is able to serve again. This might dissuade
people from (some) insincere ranking and truncation. Ranked Pairs could
be used to find the social ranking.
Post by James Green-Armytage
Area (1) is not necessarily the most contentious; i.e. most people who
like beatpath like ranked pairs just about as much, and so on. However, I
would not feel especially good about a method that isn't Smith-efficient,
even to start out with. So that cuts out plain minimax as far as I'm
concerned.
I prefer winning votes for area (2), entirely for anti-strategic reasons.
This starts to bring us toward area (3), i.e. strategy. I agree that
winning votes has a better protection against the burying strategy than
margins, but I still suspect it to be somewhat unstable in certain
situations. If I am correct (which is debatable, of course), this brings
us into slightly uncomfortable terrain. CWO is the simplest anti-strategy
method, but some voters might be intuitively uncomfortable with the idea.
CWP has an intuitive interface, but one which requires very sophisticated
ballots, and the tally rule is complex. AWP, AERLO/ATLO, and similar
methods have a somewhat confusing interface, and while the tally rules are
not terribly complex, they are not brilliantly easy to explain, either.
I know that Mike Ossipoff has said that we should all come together
around a winning votes method without an additional anti-strategy measure.
But I'd like to hear what some other people think.
I'm not even sure what I would recommend, if I was in a position to
recommend something for public elections. I lean towards starting out with
a winning votes version of sequential dropping (or any one of ranked
pairs, beatpath, river, if there isn't an intense need for simplicity)
with a CWO. But that's subject to change, with further discussion.
my best,
James
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Sincerely,
CF


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James Green-Armytage
2005-03-15 07:51:07 UTC
Permalink
Dear CF,
I appreciate your feedback. Some replies follow.
Post by Fan de Condorcet
I recently re-read your paper on CWP. I must confess that I didn't see
much justification for it at first, but I now find it to be well
justified and elegant.
Thank you; I'm glad to hear that.
Post by Fan de Condorcet
Unfortunately, there's the matter of the
complications this will create when it comes to creating and using
ballots.
Yes. Again, I don't consider it to be a "first wave" Condorcet method.
The ballot interface should be electronic, e.g. a touch screen. When you
get right down to it, it is not necessary to input rankings and rating
separately. If it is easier, one can just have the voters input ratings,
and infer the rankings from the ratings. Getting voters to rate candidates
on a scale from 0 to 100 shouldn't be terribly hard... about as hard as
using an ATM, perhaps.
Post by Fan de Condorcet
Perhaps over time I'll come to appreciate CWP more and think
it's worth the trouble, but for now I remain partial to margins.
Okay... Let me try to make the case that margins has a significant
strategy problem. Actually, it's a big topic, so I'll do it in a separate
post.
Post by Fan de Condorcet
Post by James Green-Armytage
3. Whether to use an anti-strategy measure (candidate withdrawal option
(CWO), CWP, AERLO/ATLO, iterative procedure, etc.)
I'm not about to advocate AERLO or ATLO, largely for the reasons you've
already mentioned. I also feel that CWO would give too much power to
candidates.
What do I propose? I'll briefly reiterate an idea I presented to this
list some time ago: Make runners-up matter. One modest example would be
that the bylaws of an organization could state that when an officer
becomes incapacitated, the runner-up will assume the role until
re-election or the officer is able to serve again. This might dissuade
people from (some) insincere ranking and truncation. Ranked Pairs could
be used to find the social ranking.
I'm not sure that this would have a strong anti-strategic effect. Also, I
worry that it may increase the incentive for political assassination.
my best,
James
http://fc.antioch.edu/~james_green-armytage/voting.htm

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James Green-Armytage
2005-03-15 07:53:51 UTC
Permalink
Here is my argument that "margins" methods have a critical strategy
problem. Some of this is a repeat from earlier posts, but there are subtle
and important differences in the argument, especially in my understanding
of how winning votes will work in this example.
Let me introduce example 1, variations of which will be used throughout
this post.

Ex. 1: Sincere preferences:
46: A>B>C
44: B>A>C
5: C>A>B
5: C>B>A
Ex. 1: Pairwise comparisons:
A>B 51-49
A>C 90-10
B>C 90-10

C is an extremely unpopular candidate who loses both pairwise comparisons
by 90 votes to 10. A is a Condorcet winner, but the A:B comparison is
quite close. Really, the only legitimate contest in the election is the
A:B comparison, and the fact that A wins it should rightfully seal the
result. However, if the B voters are very determined, they can vote B>C>A,
and stand a good chance of stealing the election by so doing.

Ex. 2: Expressed preferences (some insincere):
46: A>B>C
44: B>C>A
5: C>A>B
5: C>B>A
Ex. 2: Pairwise comparisons:
A>B 51-49
C>A 54-46
B>C 90-10

Now, A>B is the weakest defeat, and so B wins. This is a hideous result
that would shower Condorcet methods in shame for generations to come.
We should NOT assume that any other voters knew ahead of time whether the
B voters would execute this strategy or not. We should NOT assume that the
B voters' strategy relies on central coordination. These assumptions are
too optimistic, and thus by making them, we would fail to be appropriately
cautious. The question is: what could A>B voters have done to avoid this
bad result, without messing things up in case the strategic incursion did
not occur?
For one, the C>A>B voters could have voted C=A>B to begin with, but this
means abandoning their favorite to some extent, which is a lot to ask if
the B>A>C voters' strategy is not clearly known. Furthermore, the C voters
may have a lot to gain from leaving their votes as is and letting A and B
voters get involved in a strategy fight, as we will see later.
Since the B voters are happy with the result as is, this leaves us with
the A>B>C voters. They want A to win, but they cannot get that result from
example 2. So, instead, they would have liked the B>A>C voters to know
ahead of time that their strategy could yield no benefit. We'll call this
a deterrent strategy. But how to do it?
Here's the punch line: Using margins, the deterrent strategy can't be
done without a very good chance of severely messing things up. Using
winning votes, it can be done without messing things up (at least in THIS
EXAMPLE... not necessarily in all examples!).
How does a margins deterrent strategy mess things up? Well, first, we
need to figure out how the A>B>C voters can provide a genuine deterrent in
margins. Let's say that the A voters try to deter through mere truncation,
the B voters execute their burying strategy, and we get something like
this:

Ex. 2: Expressed preferences:
46: A>B=C
44: B>C>A
5: C>A>B
5: C>B>A
Ex. 2: Pairwise comparisons:
A>B 51-49
C>A 54-46
B>C 44-10

A>B is still the weakest defeat in margins, but B>C is now the weakest
defeat in winning votes. Therein lies the key difference between the
methods. The consequence is that truncation tends to be an effective
deterrent in winning votes, but it tends not to be an effective deterrent
in margins.
So how can the A>B>C voters deter in margins? Only by voting A>C>B. Now
we have hit our problem. The only way that A voters can prevent their
hard-won A>B defeat from being overruled by a false C>A defeat is to rank
C in second place (and to vote this way in polls before the election,
announcing their intention), in the hopes of deterring the incursion
before it happens.
However, what if the B voters weren't intending to bury A after all?
Since the A:B race is so close, we should not assume that the voters know
who will actually win it, before the election. Therefore we should not
assume that B voters will accept that A is the "rightful" winner and step
aside. Meanwhile, we have polls saying that most of the A voters are
listing this strange candidate C in second place, which means that a C>B
defeat could potentially overrule a genuine B>A defeat. The B voters will
not be happy about this; they will suspect it to be strategic, and they
will be sorely tempted to provide a deterrent of their own. If the B>A>C
voters respond by voting B>C>A, then candidate C becomes a Condorcet
winner! This brings us to a terribly complex game of chicken, played by
millions of voters simultaneously. At this point, any of the three
candidates could be elected with roughly equal probability, depending not
on voters' actual preferences, but rather on their predilections for
swerving rather than staying the course. This is a horrible result, which
would shower Condorcet methods in shame for generations to come.

This is why margin methods are unusable. Now, let's go back to winning
votes. In this example, using winning votes, the A>B>C voters should vote
A>B=C, and the B>A>C voters should vote B>A=C. Then we get something like
this:

Ex. 3: semi-sincere truncated votes:
46: A>B=C
44: B>A=C
5: C>A>B
5: C>B>A
Ex. 3: Pairwise comparisons:
A>B 51-49
A>C 46-10
B>C 44-10

This is a stable result, even though the voters don't know the result of
the A:B contest. If A wins it, as above, and the B voters bury A under C,
the B>C defeat will be the weakest of the A>B>C>A cycle. If B wins it (not
shown), and the A voters bury B under C, the result is similarly
counter-productive.
**IMPORTANT: This deterrent strategy does NOT require the A voters to
DISCOVER that the B voters INTEND to commit a strategic incursion, and to
COORDINATE a response. Rather, this example is stable insofar as it is
intuitive from the beginning that the A and B voters ranking their primary
rivals is an unnecessary source of trouble. They do not truncate because
of any particular information that the 'enemy camp' is hatching a plan.
Rather they truncate because reporting a full ranking creates a liability
without creating a benefit.
This particular example treats winning votes kindly, in that these two
primary rivals do not rely on each other's second preferences to be
viable. Winning votes may well exhibit a strategy problem when this is not
the case, but let me leave that issue for another time.
So, I am not arguing that winning votes does not have significant
strategic vulnerability. Indeed, I have argued that it does, and I will
probably continue to argue this at a later time. However, I would first
like to work towards a broad understanding that margins Condorcet has a
very severe strategy problem, and that it should not be used for
contentious public elections.
Sincerely,
James Green-Armytage
http://fc.antioch.edu/~james_green-armytage/voting.htm


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Juho Laatu
2005-03-23 17:59:30 UTC
Permalink
Hi,

This is a response to James Green-Armytage's mail
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015125.html

You asked me to read the mail after I had defended the margin based methods. Now I did - or actually I had read the mail ealier but only now find some good time to reply.

I think strategies in voting methods are quite different in large public elections and in small elections. To keep the answer simple and because public elections are the default case (and because this is easier :-) ) I'll cover the large public election case only.

In general I think one should always evaluate the seriousness of each strategy problem before deciding to defend against it by modifying the voting method. I drafted a quick list of possible classifications in http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015172.html.

But now to the mail itself.

I think this vulnerability is one of the worst I have seen. I however do not want to jump to the conclusion that margin based methods are all bad. I'll try to analyse where and how likely the problems are.

First I try to list some reasons why this strategy would not be used in real life:
- bad reputation to the party that (publicly) proposes it voters to use the strategy
- impossibility to co-ordinate party votes without the plot leaking out
- lack of understanding of the voters (it is difficult enough to give a sincere vote)
- common knowledge that this strategy exists, which means that all parties could try the same trick
- or same percentage of voters from each party would do the trick
- risk of electing C
- unwillingness of voters to participate in this kind of plotting
- it may be that there are more cases where strategical voting attempts bring harm than it brings benefits => people think that it is better to be sincere
- government and parties may do propaganda to emphasize that sincere voting brings best results (in Condorcet methods) and strategies typically harm the voter
- exact number of votes of each party is not known (gallups may give some info)
- rankings of those voters are known even less

In summary, the risks of recommending this strategy may well lead to not recommending its use. If there is a threat that members of different parties want to apply the strategy themselves, it may be better for the parties to recommend not to use this (nor any other) strategy. Otherwise the results couls be a mess and the party could lose the election instead of winning it. Parties that defend sincere and honest voting might also get more support from the voters.


Some more detailed notes follow.

In example 2 the B voters voted strategically B>C>A.

Let's assume that a margins based method was used as the voting method because it was considered to be the sincere method (one that brings the intended results with sincere votes).

What if the voter preferences were sincere and B>C>A was the true opinion of the B voters. In this case it would not be a good idea to modify the voting method (e.g. to use winning votes) since then it would give wrong results with these sincere votes. And it is impossible to tell how many of the B>C>A voters were sincere and how many did that for strategic reasons.

What I mean is that every deviation from the sincere method makes the voting method worse so that it no more gives correct results with sincere votes. If the voting method is changed, then we may have to recommend all voters to vote strategically. But of course that is not a nice idea. All such steps may lead us away from the target of electing the best candidate. This is the reason for my interest to try to live with the sincere method as long as I can.


In the last example (numbered as 3) I noted one interesting thing. If both A and B supporters would truncate their votes, then it doesn't change the situation much is also voters of C do the same thing. And if all truncate their votes, then we are close to recommending a plurality based method to be used. (A vores vote A, B voters vote B, and C voters vote C)

I guess the good part of Condorcet is allows people to give their full rankings. Therefore strategies that involve such heavy truncation may reduce ranking based methods to something less.


Summary:
I hope that in large public elections most of the stratecic voting cases would be too problematic, general opinion would be in favour of voting sincerely and there would be no efficient strategies that would force everyone to voting stretegically. I was not yet convinced that this strategy, although a very threatening one, would be probable in large public elections. If that would be the truth and margins would be the chosen sincere method, then margins could be still used despite of this vulnerability. Making changes to the sincere voting method may bring other kind of problems. Of course this is a problem situation that just must be balanced right.

Best Regards,
Juho

Send instant messages to your online friends http://uk.messenger.yahoo.com
c***@delphiforums.com
2005-03-17 01:19:21 UTC
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James,

Thanks for posting your "margins" example.

While I don't want to commit myself to saying that "winning votes" is better for public elections (there could be examples I haven't thought of yet), I won't be recommending "margins" for public elections any time soon.

CF

P.S. I'm sorry I've violated EM ettiquette by failing to quote from your message, but I'm currently answering e-mail remotely.

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