[EM] pairwise comparisons

[Curt]

Hi,

I’ve been chewing on some questions as part of exploring my views of ranked voting, and thought I would share here. For those of you who prefer not to think more philosophically about this, please excuse the missive. :-) But for the rest of you, I’m interested in your thoughts.

Imagine a set of ten candidates, and one voter. The voter is asked to determine their views of these candidates. But instead of just being asked to rank them in order, the voter is asked to judge them pairwise.

For ten candidates, this means 15 questions. Each question being a comparison of A and B, with the voter picking their favorite of the two.

First question, is it possible for a voter to generate a cycle? We know it is technically possible, trivially demonstrated. But is it possible that a voter, using some internal set of principles, would also generate a cycle? I would argue yes.

If the voter does generate a cycle via these pairwise comparisons, what does this mean? Does it mean the voter is confused? Does it mean the voter is inconsistent? Does it mean that this cycle or cycles are an accurate depiction of the voter’s actual views?

Say that we then ask the voter to create an actual ranked ballot out of these ten candidates, and the voter manages to do so. What happened in that process of the voter deciding the rankings? Was it a clarifying experience? Did the voter’s preferences change? Did the voter compromise? Did the voter lie?

And finally, say that a collection of these voters submit their ranked ballots (not just their pairwise comparisons), and the votes are tabulated, and the result is a three-candidate Smith Set, where each candidate defeats all other candidates outside the Smith Set.

What does that Smith Set mean? Is the electorate confused? Is the electorate inconsistent? Or is the Smith Set an accurate depiction of the electorate’s actual views?

Thanks,
Curt

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[Curt]

Errata: I forgot that my original mental model was six candidates, not ten. 6 candidates = 15 questions.

Post by Curt
Hi,
I’ve been chewing on some questions as part of exploring my views of ranked voting, and thought I would share here. For those of you who prefer not to think more philosophically about this, please excuse the missive. :-) But for the rest of you, I’m interested in your thoughts.
Imagine a set of ten candidates, and one voter. The voter is asked to determine their views of these candidates. But instead of just being asked to rank them in order, the voter is asked to judge them pairwise.
For ten candidates, this means 15 questions. Each question being a comparison of A and B, with the voter picking their favorite of the two.
First question, is it possible for a voter to generate a cycle? We know it is technically possible, trivially demonstrated. But is it possible that a voter, using some internal set of principles, would also generate a cycle? I would argue yes.
If the voter does generate a cycle via these pairwise comparisons, what does this mean? Does it mean the voter is confused? Does it mean the voter is inconsistent? Does it mean that this cycle or cycles are an accurate depiction of the voter’s actual views?
Say that we then ask the voter to create an actual ranked ballot out of these ten candidates, and the voter manages to do so. What happened in that process of the voter deciding the rankings? Was it a clarifying experience? Did the voter’s preferences change? Did the voter compromise? Did the voter lie?
And finally, say that a collection of these voters submit their ranked ballots (not just their pairwise comparisons), and the votes are tabulated, and the result is a three-candidate Smith Set, where each candidate defeats all other candidates outside the Smith Set.
What does that Smith Set mean? Is the electorate confused? Is the electorate inconsistent? Or is the Smith Set an accurate depiction of the electorate’s actual views?
Thanks,
Curt

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[Chris Benham]

Curt,

Yes, an individual voter with cyclic preferences is confused and
inconsistent.

Post by Curt
Or is the Smith Set an accurate depiction of the electorate’s actual views?

In answer to that  question I would say accurate but not necessarily
complete or fully adequate.

Voters should be allowed to truncate and probably a lot of them will and
the cycle examples produced
by them doing so are much more plausible-looking to me than those where
all the voters rank all the
candidates.

6: A
5: B>C
3: C

A>B 6-5    B>C 5-3    C>A 8-6

All the candidates are in the Smith set.

Say we infer rating from ranking by interpreting ranking below no other
candidate as Top Rating and ranked above
at least one candidate as Approval. (I think many would find that
reasonable and natural.)

Top Rating scores: A6 > B5 > C3.     Approval scores: C8 > A6 > B5

B is positionally dominated by A and has the lowest approval score.

6: A
5: B
3: C

Assuming that we always elect A here (with all the voters truncating)
then electing B in the first example is a
failure of the Later-no-Help criterion, rewarding easy outrageous Burial
strategy.

Also electing B is a failure of the Plurality criterion, which says that
B isn't allowed to win because A has
more first-preference votes B has any sort of (above bottom) votes.

Although B is in the Smith set no method I consider good or acceptable
will elect B.

MinMax (Margins)  elects B.

(Ranked Pairs, Beatpath and River are all equivalent to MinMax when
there are only three candidates.)

Chris Benham

Post by Curt
Hi,
I’ve been chewing on some questions as part of exploring my views of ranked voting, and thought I would share here. For those of you who prefer not to think more philosophically about this, please excuse the missive. :-) But for the rest of you, I’m interested in your thoughts.
Imagine a set of ten candidates, and one voter. The voter is asked to determine their views of these candidates. But instead of just being asked to rank them in order, the voter is asked to judge them pairwise.
For six candidates, this means 15 questions. Each question being a comparison of A and B, with the voter picking their favorite of the two.
First question, is it possible for a voter to generate a cycle? We know it is technically possible, trivially demonstrated. But is it possible that a voter, using some internal set of principles, would also generate a cycle? I would argue yes.
If the voter does generate a cycle via these pairwise comparisons, what does this mean? Does it mean the voter is confused? Does it mean the voter is inconsistent? Does it mean that this cycle or cycles are an accurate depiction of the voter’s actual views?
Say that we then ask the voter to create an actual ranked ballot out of these ten candidates, and the voter manages to do so. What happened in that process of the voter deciding the rankings? Was it a clarifying experience? Did the voter’s preferences change? Did the voter compromise? Did the voter lie?
And finally, say that a collection of these voters submit their ranked ballots (not just their pairwise comparisons), and the votes are tabulated, and the result is a three-candidate Smith Set, where each candidate defeats all other candidates outside the Smith Set.
What does that Smith Set mean? Is the electorate confused? Is the electorate inconsistent? Or is the Smith Set an accurate depiction of the electorate’s actual views?
Thanks,
Curt
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[robert bristow-johnson]

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

Subject: [EM] pairwise comparisons

From: "Curt" <***@museworld.com>

Date: Wed, April 18, 2018 7:19 pm

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

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

... But for the rest of you, I&rsquo;m interested in your thoughts.

dunno if you'll like mine.

Imagine a set of six candidates, and one voter. The voter is asked to determine their views of these candidates. But instead of just being asked to rank them in order, the voter is asked to judge them pairwise.

that seems to be both a complicated ballot and a setup for possible
silliness.

For six candidates, this means 15 questions. Each question being a comparison of A and B, with the voter picking their favorite of the two.
First question, is it possible for a voter to generate a cycle?

of course it is.  but this voter is schitz.  maybe a little psychopharmocology or a little electricity in the brain might do that voter some good.

We know it is technically possible, trivially

demonstrated. But is it possible that a voter, using some internal set of principles, would also generate a cycle? I would argue yes.
only if the voter is jerking our chain or is schizoid.  (this, plus the fact of limited real-estate on the ballot, is why i would never offer pair-wise
binary choices, but just offer full ranking, which would require five levels for six candidates.)
here is what the voter should be thinking about for a single-winner race:  "Who do I like best?  Who do I think is the best person for this single seat office?"
Mark that
candidate #1.  The ask "If this person were taken out of the race and didn't exist at all, of the remaining candidates who do I think is the best person for this office?"
Mark that candidate #2.  Then take both #1 and #2 out of the race and ask oneself who is best in the
remaining field.
 
I just cannot see the psychology of if a voter thinks that Candidate A is better than Candidate B, and also thinks that Candidate B is better than Candidate C, there is no way that the same *sane* voter would decide that Candidate C is better than Candidate
A.
Now a voter can have tied preferences and rank Candidates A, B, and C all #1, but that is saying "I don't care which of those three are elected, but I sure as hell don't want the losers Candidates D or E or F to take this office.  but that is different than a circular preference
with A, B, and C.


We should do some Condorcet voting system for general elections in a multiparty and multi-candidate context.  but it should be a ranked ballot for each voter.  only let the voter express linear preferences.

If the voter does generate a cycle via these pairwise comparisons, what does this mean? Does it mean the voter is confused? Does it mean the voter is inconsistent?

yes and yes.

Does it mean that this cycle or cycles are an accurate depiction of the voter&rsquo;s actual

views?
only if he's wack.

Say that we then ask the voter to create an actual ranked ballot out of these six candidates, and the voter manages to do so. What happened in that process of the voter deciding the rankings? Was it a clarifying experience? Did the voter&rsquo;s preferences change? Did the voter compromise? Did

the voter lie?
we want a system where there is no incentive for the voter to have to vote tactically (i.e. compromise) or lie.
 

And finally, say that a collection of these voters submit their ranked ballots (not just their pairwise comparisons), and the votes are tabulated, and the result is a three-candidate Smith Set, where each candidate defeats all other candidates outside the Smith Set.
What does that Smith Set mean?

it means that there is a problem.  it means that these voters that voted for Nader in 2000 and preferred Bush over Gore have a much different way of thinking than the Nader voters who preferred Gore over Bush.
BTW, the Burlington 2009 IRV election
had 5 candidates, 3 of which any one could have credibly won the election, but one of the 3 was the Plurality (of 1st choice) winner, another was the IRV winner, and another was the Condorcet winner.  all three had some legit claim to being the "people's choice".  but, from a
Condorcet POV, it was perfectly ordered and there was no ambiguity of the voter preference.
i **really** think that if governments started using a Condorcet-compliant method regularly, a cycle would be very rare.  i think the possibility of a cycle as a reason not to go with Ranked-Choice
Voting and a Condorcet-compliant method, is a red herring.
 

Is the electorate confused? Is the electorate inconsistent? Or is the Smith Set an accurate depiction of the electorate&rsquo;s actual views?

it depicts a problem.  since a 3-candidate cycle is decided the
same way with MinMax or RankedPairs or Schulze, the defeat that is the weakest is the defeat that doesn't count and that will resolve the circular preference and the election.
but it won't stop the burning trash cans in the street.
ever since Nov 2016, we're all friggin' toast
anyway.
 
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r b-j                         ***@audioimagination.com



"Imagination is more important than knowledge."

 
 
 
 

[Juho Laatu]

Post by Curt
Hi,
I’ve been chewing on some questions as part of exploring my views of ranked voting, and thought I would share here. For those of you who prefer not to think more philosophically about this, please excuse the missive. :-) But for the rest of you, I’m interested in your thoughts.
Imagine a set of ten candidates, and one voter. The voter is asked to determine their views of these candidates. But instead of just being asked to rank them in order, the voter is asked to judge them pairwise.
For ten candidates, this means 15 questions. Each question being a comparison of A and B, with the voter picking their favorite of the two.
First question, is it possible for a voter to generate a cycle? We know it is technically possible, trivially demonstrated. But is it possible that a voter, using some internal set of principles, would also generate a cycle? I would argue yes.

Could be possible. There could be three candidates, A, B and C. The voter could have three areas of concern, a, b and c. The voter could rank the candidates in each area as (a: A>B>C), (b: B>C>A) and (c: C>A>B). A is better than B in two areas. B is better than C in two areas. C is better than A in two areas. The voter could form his pairwise preferences based on these (number of areas based) comparisons.

Post by Curt
If the voter does generate a cycle via these pairwise comparisons, what does this mean? Does it mean the voter is confused? Does it mean the voter is inconsistent? Does it mean that this cycle or cycles are an accurate depiction of the voter’s actual views?

You could say that the voter is somewhat confused in the sense that his thinking process has some problems. If someone would ask him if A or B should be elected, he would answer A. If he would be then asked about A and C, he would choose C. But then he might realize that he would however prefer B to C, and would be a bit confused. At this point he might realize that he should give some weights to the areas of concern, and to the pairwise preference strengths within those areas. If he does so, he would probably be able to give the candidates ratings (or personal total utility estimates) that would put them in some linear order. It is probably more common among human brains to give total preference weights (and thereby a linear order) to different candidates or other objects. But I would not rule out cyclic pairwise comparison based preferences either. Maybe you could say that probably cyclic preferences are based on limited information, and that it is usually possible to turn them to linear preferences, if one gives the thinking process some time.

Post by Curt
Say that we then ask the voter to create an actual ranked ballot out of these ten candidates, and the voter manages to do so. What happened in that process of the voter deciding the rankings? Was it a clarifying experience? Did the voter’s preferences change? Did the voter compromise? Did the voter lie?

Based on the story I wrote above, this process was probably more clarifying than confusing. The initial voter preferences did not really change, but there were some changes in the weights (or better accuracy) of different preferences. The voter did not compromise and did not lie. If the linear preferences are now A>B>C, the voter abandoned the earlier idea that C>A. His thinking must be something like "C indeed was better than A in two areas, but the weights of those areas, and the strengths of pairwise beatings are such that C would be a worse choice than A or B".

Note that this kind of changes in thinking might take place also when we have only two candidates, A and C, and there is thus no cycle.

Post by Curt
And finally, say that a collection of these voters submit their ranked ballots (not just their pairwise comparisons), and the votes are tabulated, and the result is a three-candidate Smith Set, where each candidate defeats all other candidates outside the Smith Set.
What does that Smith Set mean? Is the electorate confused? Is the electorate inconsistent? Or is the Smith Set an accurate depiction of the electorate’s actual views?

The Smith set means about the same as the looped opinions of the voter above. If we use only pairwise preferences, preference loops are possible. The electorate is not confused nor inconsistent. All voters may have had linear preference opinions. The Smith set is an accurate depiction of actual views (as measured in this limited way, based of rankings only). This loop can not be "fixed" since rankings is all we have, and in typical (competitive) political elections it would be difficult to collect sincere ratings.

While we may assume that individual voters can usually form a well defined linear order of the candidates, benefits to the society are a more complex topic. There are many ways to measure that. One could for example measure the maximum sum of ratings (of individual voters), one could maximize the lowest rating, or one could base the method on majorities (as usual in political elections). If we must satisfy with rankings and majority decisions, the possibility of loops is unavoidable. In this situation we just need some additonal crierion on which one of the candidates (looped ones or others) is the best.

Juho

Post by Curt
Thanks,
Curt

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[Kristofer Munsterhjelm]

Post by Curt
Hi,
I’ve been chewing on some questions as part of exploring my views of ranked voting, and thought I would share here. For those of you who prefer not to think more philosophically about this, please excuse the missive. :-) But for the rest of you, I’m interested in your thoughts.
Imagine a set of [six] candidates, and one voter. The voter is asked to determine their views of these candidates. But instead of just being asked to rank them in order, the voter is asked to judge them pairwise.
For ten candidates, this means 15 questions. Each question being a comparison of A and B, with the voter picking their favorite of the two.
First question, is it possible for a voter to generate a cycle? W > know it is technically possible, trivially demonstrated. But is it
possible that a voter, using some internal set of principles, would also
generate a cycle? I would argue yes. >
If the voter does generate a cycle via these pairwise comparisons,
what does this mean? Does it mean the voter is confused? Does it mean
the voter is inconsistent? Does it mean that this cycle or cycles are an
accurate depiction of the voter’s actual views?

One way to look at voting is as a substitute for deliberation. The idea
is that you don't have a way to get a million people into a town hall
and discuss the issue; or that there's a deadlock in a small assembly
and you have to decide somehow.

Then the presence of cycles is an effect of the different parts of the
electorate prioritizing different things. E.g. if it's a presidential
election, one part may be prioritizing defense and rank the candidates
A>B>C, another part may be prioritizing not having been involved in
corruption and rank the candidates B>C>A, and yet another part may be
prioritizing domestic credibility and rank the candidates C>A>B.

(If the voters share the same 1D view of politics and prefer candidates
closer to their point on the line, then there will always be a Condorcet
winner.)

In the substitute-for-deliberation model, a single voter *could* have a
cyclical preference, but it would be very rare. Since a voter knows his
own mind very well (or so we would assume), he would "deliberate" with
it pretty easily and come up with a noncyclical ranking.

Even if he were to consider some candidates to be tied in a cycle, he'd
probably just rank them all equal. I think it's more realistic that a
voter would say "this candidate is better at defense, that candidate has
not been involvled in a corruption scandal, and that candidate has a
more convincing domestic program, but I can't decide which is more
important to me, so I'll rank them all equal" than "I'll switch my
mind's point of view in between each pairwise comparison and thus set up
a cycle".

On a side note, I've sometimes thought of having a pairwise-only ballot
for the purpose of discouraging strategy. When the voter is to vote, he
is given a "do you prefer X to Y" yes/no ballot where X and Y are given
at random. It's harder to coordinate strategy this way because not the
entire ballot is available to the voter. But in any case, under such a
protocol, I think it would be more likely to "see" cycles happening for
a single voter.

Imagine the universe splitting into three parallel universes at the time
the voter picks up one of these ballot cards at random. On one, the
ballot says "Do you prefer A to B?", on the other "Do you prefer B to
C?", and on the third, "Do you prefer C to A?". It's possible that the
voter would think of defense in the first universe, corruption in the
second, and domestic issues in the third, and so in all of these
universes, he would say yes. The difference between this and the usual
setup is that the voter isn't provided the whole question at once.

Post by Curt
Say that we then ask the voter to create an actual ranked ballot out of these ten candidates, and the voter manages to do so. What happened in that process of the voter deciding the rankings? Was it a clarifying experience? Did the voter’s preferences change? Did the voter compromise? Did the voter lie?
And finally, say that a collection of these voters submit their ranked ballots (not just their pairwise comparisons), and the votes are tabulated, and the result is a three-candidate Smith Set, where each candidate defeats all other candidates outside the Smith Set.
What does that Smith Set mean? Is the electorate confused? Is the electorate inconsistent? Or is the Smith Set an accurate depiction of the electorate’s actual views?

The model above would say that, assuming there's no strategy going on,
the electorate is inconsistent. They value different things. The Smith
set being a subset of the candidates would be analogous to the
outside-of-Smith set being judged worse on all three axes by a majority
of the voters (not necessarily the same majority for each).

Other possibilities are:

- Strategic cycle. A party judges that its candidate will win if it can
set up a particular cycle, and so it tells all its voters to vote in a
way that produces this cycle. This could even happen if the voting
method is runoff: the party could judge that its candidate is a
particularly good public speaker and so would have a better chance of
winning in a small runoff with increased attention on the few remaining
candidates.

- Strategic cycle backfire. As above, but with multiple parties and the
result is that someone neither party wants to win, wins.

- Noise: The voters aren't perfectly sure of what they want, e.g. each
voter has a "true ranking" of the candidates but it would take way too
long to come up with it, so the actual ranking a voter submits is
similar but not identical to the true ranking. If the perturbation from
this noise comes out just right, you could get an accidental cycle.
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Post by Kristofer Munsterhjelm
One way to look at voting is as a substitute for deliberation. The idea
is that you don't have a way to get a million people into a town hall
and discuss the issue; or that there's a deadlock in a small assembly
and you have to decide somehow.

Excellent perspective!

Post by Kristofer Munsterhjelm
Then the presence of cycles is an effect of the different parts of the
electorate prioritizing different things. E.g. if it's a presidential
election, one part may be prioritizing defense and rank the candidates
A>B>C, another part may be prioritizing not having been involved in
corruption and rank the candidates B>C>A, and yet another part may be
prioritizing domestic credibility and rank the candidates C>A>B.

Yes, and this fits my view that politics is multi-dimensional whereas
current voting methods -- including ranking -- regard politics as
one-dimensional.

Richard Fobes

Post by Kristofer Munsterhjelm

Post by Curt
Hi,
I’ve been chewing on some questions as part of exploring my views of
ranked voting, and thought I would share here. For those of you who
prefer not to think more philosophically about this, please excuse the
missive. :-) But for the rest of you, I’m interested in your thoughts.
Imagine a set of [six] candidates, and one voter. The voter is asked
to determine their views of these candidates. But instead of just
being asked to rank them in order, the voter is asked to judge them
pairwise.
For ten candidates, this means 15 questions. Each question being a
comparison of A and B, with the voter picking their favorite of the two.
First question, is it possible for a voter to generate a cycle? W >
know it is technically possible, trivially demonstrated. But is it
possible that a voter, using some internal set of principles, would also
generate a cycle? I would argue yes. >
If the voter does generate a cycle via these pairwise comparisons,
what does this mean? Does it mean the voter is confused? Does it mean
the voter is inconsistent? Does it mean that this cycle or cycles are an
accurate depiction of the voter’s actual views?

One way to look at voting is as a substitute for deliberation. The idea
is that you don't have a way to get a million people into a town hall
and discuss the issue; or that there's a deadlock in a small assembly
and you have to decide somehow.
Then the presence of cycles is an effect of the different parts of the
electorate prioritizing different things. E.g. if it's a presidential
election, one part may be prioritizing defense and rank the candidates
A>B>C, another part may be prioritizing not having been involved in
corruption and rank the candidates B>C>A, and yet another part may be
prioritizing domestic credibility and rank the candidates C>A>B.
(If the voters share the same 1D view of politics and prefer candidates
closer to their point on the line, then there will always be a Condorcet
winner.)
In the substitute-for-deliberation model, a single voter *could* have a
cyclical preference, but it would be very rare. Since a voter knows his
own mind very well (or so we would assume), he would "deliberate" with
it pretty easily and come up with a noncyclical ranking.
Even if he were to consider some candidates to be tied in a cycle, he'd
probably just rank them all equal. I think it's more realistic that a
voter would say "this candidate is better at defense, that candidate has
not been involvled in a corruption scandal, and that candidate has a
more convincing domestic program, but I can't decide which is more
important to me, so I'll rank them all equal" than "I'll switch my
mind's point of view in between each pairwise comparison and thus set up
a cycle".
On a side note, I've sometimes thought of having a pairwise-only ballot
for the purpose of discouraging strategy. When the voter is to vote, he
is given a "do you prefer X to Y" yes/no ballot where X and Y are given
at random. It's harder to coordinate strategy this way because not the
entire ballot is available to the voter. But in any case, under such a
protocol, I think it would be more likely to "see" cycles happening for
a single voter.
Imagine the universe splitting into three parallel universes at the time
the voter picks up one of these ballot cards at random. On one, the
ballot says "Do you prefer A to B?", on the other "Do you prefer B to
C?", and on the third, "Do you prefer C to A?". It's possible that the
voter would think of defense in the first universe, corruption in the
second, and domestic issues in the third, and so in all of these
universes, he would say yes. The difference between this and the usual
setup is that the voter isn't provided the whole question at once.

Post by Curt
Say that we then ask the voter to create an actual ranked ballot out
of these ten candidates, and the voter manages to do so. What happened
in that process of the voter deciding the rankings? Was it a
clarifying experience? Did the voter’s preferences change? Did the
voter compromise? Did the voter lie?
And finally, say that a collection of these voters submit their ranked
ballots (not just their pairwise comparisons), and the votes are
tabulated, and the result is a three-candidate Smith Set, where each
candidate defeats all other candidates outside the Smith Set.
What does that Smith Set mean? Is the electorate confused? Is the
electorate inconsistent? Or is the Smith Set an accurate depiction of
the electorate’s actual views?

The model above would say that, assuming there's no strategy going on,
the electorate is inconsistent. They value different things. The Smith
set being a subset of the candidates would be analogous to the
outside-of-Smith set being judged worse on all three axes by a majority
of the voters (not necessarily the same majority for each).
- Strategic cycle. A party judges that its candidate will win if it can
set up a particular cycle, and so it tells all its voters to vote in a
way that produces this cycle. This could even happen if the voting
method is runoff: the party could judge that its candidate is a
particularly good public speaker and so would have a better chance of
winning in a small runoff with increased attention on the few remaining
candidates.
- Strategic cycle backfire. As above, but with multiple parties and the
result is that someone neither party wants to win, wins.
- Noise: The voters aren't perfectly sure of what they want, e.g. each
voter has a "true ranking" of the candidates but it would take way too
long to come up with it, so the actual ranking a voter submits is
similar but not identical to the true ranking. If the perturbation from
this noise comes out just right, you could get an accidental cycle.
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