[EM] pairwise comparisons

[VoteFair]

On 4/23/2018 1:40 AM, Kristofer Munsterhjelm wrote:
 > 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!

 > 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


On 4/23/2018 1:40 AM, Kristofer Munsterhjelm wrote:
> On 2018-04-19 01:19, Curt wrote:
>> 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.
>
>> 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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