[EM] Comparing CW with "write-in pairwise" CW

Kevin Venzke stepjak at yahoo.fr
Wed Oct 30 15:46:10 PDT 2013

Hi Kristofer,

----- Mail original -----
> De : Kristofer Munsterhjelm <km_elmet at t-online.de>
>>  To take a step back: Why regard pairwise contests at all? To my mind,
>>  what they can simulate is a test of whether supporters of one
>>  candidate feel cheated when the other candidate is elected. In the
>>  case of B vs. C we want to know whether we can elect one of those two
>>  without irritating the supporters of the other. The answer is: the
>>  election of one or the other gives neither side a strong reason to
>>  complain.
> Methods like River have another idea of what to do: they say that "okay, 
> there may be complaints, but our criteria state that there's always a 
> counter-argument that is stronger if you consider pairwise data and 
> paths alone". More specifically, that if A-supporters say that A should 
> have won instead of B, because X beats B and is beaten by A, then the 
> B-supporters can say that there also exists an Y that beats A and is 
> beaten by B, and Y beats A more strongly than X beats B.

Yes, in practice River etc. are good. But the actual logic or interpretation of the pairwise contests doesn't have a clear tie to the "big picture." In other words I fear we can have a long philosophical discussion on the methods and aesthetics of tracing beatpaths and thereby miss the forest for the trees, within a given scenario. Ultimately you have voters who regret the way they voted or would be happier had their candidate not run, and that's the key thing in my view.

> My own ideas about Condorcet is more that it is a good default balance 
> between strategy and honest results, if it is given that we only have 
> ranks to work with. The strategy resistance is related to a mean-median 
> link where Borda is to the mean rank as Condorcet is to the median rank. 
> The honesty aspect is related to that the CW is the one who can win any 
> runoff assuming that nobody changes his mind. In itself, it's an 
> intuitive generalization of majority rule, and one could also use 
> generalizations of the Condorcet Jury Theorem to more formally argue in 
> that direction -- or observations like Kemeny being a max-likelihood 
> estimator under certain models of noise on the ballots.

Yes, I think you can justify Condorcet via analogies like these or others. But I think it's frighteningly easy to find yourself discussing abstract fantasy at the very first step.

>>  The second type of disagreement, the other 30%, is the case where
>>  Condorcet picks a single winner while WICW picks *two* possible
>>  winners: 42 A 30 B>C 28 C>B
>>  Here we have a mutual majority and a CW, but WICW is indecisive. The
>>  B>C pairwise win isn't counted, because once the majority splits up
>>  between B and C camps, neither can contend with the A>{B,C} voters.
>>  This is quite an oddity and I'm not sure what to make of it.
>>  Does it suggest any actual insights? I kind of think it does: While B
>>  is unambiguously the superior candidate, it isn't by much. It's 
> quite
>>  possible that if we forcibly extracted second preferences from the A
>>  voters, that they would prefer C. It's unknown, it may matter, and
>>  WICW says as much.
>>  Furthermore, there should be no shame in being indecisive,
>>  considering that Condorcet is often indecisive as well.
> Couldn't this be fixed by a Smith intersect WICW method? I guess that 
> would feel a bit like a hack, though, and may induce what I call 
> discontinuities, thus breaking certain types of criterion compliance.

Yes to all that. I suspect the WICW method itself would have some discontinuities already.

> Or if you think there's real indecision here in the people, and the 
> methods are just mirroring that, you could hold a runoff among the 
> candidates in the more indecisive set (WICW and Smith respectively).

You could. It's not that I think there is actually indecision (or rather: it's not that I think it would actually be helpful to judge this as indecision) but that I'm trying to insist on a specific principle (that the winner should be somebody who might win if all voters were maximally informed and strategic), and I don't think that principle has a single selection here. I suspect it can't.

>>  On the other hand, I could easily believe that this result is
>>  indicative of a need for a "second draft" of the concept, that
>>  wouldn't suffer from this problem. One thing you could easily do is
>>  remove non-winners and then refigure WICW's result. But that takes it
>>  further from the original idea and the justification becomes cloudy.
> That's also possible, yes, but I do agree with you that elimination 
> feels kludgy.
>>  I should say, my point isn't really to define a new criterion (and
>>  less still, a method). It's more that I want to define a model that
>>  matches the logic or aesthetic that I tend to use when evaluating
>>  scenarios.
> I see that point. It is good to quantify what one thinks is aesthetic or 
> right... although at this point, we may be getting to kind of the 
> opposite problem - that we have so many criteria, aesthetics, and models 
> to choose between that it's hard to know which one models how people 
> act, or which one is most appropriate for an accurate election method.

I would describe the situation differently. For myself, I use three different criteria (SDSC, SFC, and Plurality) that I view as facets of this exact paradigm that I'm trying to put words to. It's an effort to consolidate, not just add to the pile. There are a lot of criteria out there but I'm not sure there are so many underlying paradigms to aid in picking from them.

Kevin Venzke

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