[EM] Example of participation/no-show paradox with Condorcet?

Kevin Venzke stepjak at yahoo.fr
Sat Nov 5 11:08:24 PST 2005

```Allen,

--- Allen Smith <easmith at beatrice.rutgers.edu> a écrit :
> >It's not possible that if X is the CW, and some ballots are added which favor
> >X over Y, then the new CW is Y. Y will still have a pairwise loss to X.
>
> That's about what I was thinking, but the articles I have been able to
> locate regarding the No Show Paradox did not make that at all clear, so I
> was wondering if my logic was screwy someplace; thank you.
>
> >But this doesn't matter, since there's no such thing as a Condorcet method
> >which isn't a Condorcet completion method.
>
> I agree that in most cases some method of solving (top) cycles is
> necessary. (But not in all - there are some purposes for which a full-scale
> Condorcet winner is what is desirable, and if there isn't one, no winner
> should be selected; for instance, election to a collegium with life
> terms.)

But as far as Participation is concerned, you don't obtain compliance by
specifying that no one wins when there's no CW. Suppose that nobody wants
a cycle, and everyone prefers any winner to no winner. Suppose X is the CW.
Then it's possible that adding ballots will change the winner from X to
nobody, unless these ballots don't rank X below anyone.

Suppose the additional voters *want* to create a cycle. Then it could be
that their sincere vote actually eliminates a cycle that already existed.

> >There are very few methods which satisfy Participation: FPP, Approval,
> >range, Borda, and Woodall's DAC/DSC methods. These methods all assign
> >points in a very simple way to candidates (or sets of candidates) and then
> >use a very simple method of interpreting the ranking of candidates (or
> >sets).
>
> True. I suspect what is more practical is to try to make occurences of the
> paradox both rare and risky (by which I mean maximizing the potential of, if
> one decided that one's vote was likely to result in one's first-place candidate
> losing and therefore failed to vote, one would get an even worse candidate
> winning than the candidate that would _actually_ win if one failed to vote -
> make the amount of information needed to plan a successful no-show strategy
> as high as possible), by using an appropriate completion system.

I think you overestimate the problem. For one thing, a voter is not likely
to have information to determine that a sincere vote is more harmful for him
than abstaining. But even if he does have this information, he can probably
also come up with an insincere vote that is at least as effective.

> (I am
> currently contemplating a Schwartz/Approval combo.)

The most obvious ones are to eliminate the approval loser until one candidate
beats everyone left, or to explicitly reduce to Schwartz and take the approval
winner of those candidates.

I still favor my "improved Condorcet//Approval" method, which nearly satisfies
Condorcet, and also avoids "favorite betrayal" incentive. That is, you can
never cause one of your first-place candidates to win by lowering another of
them in your ranking.

Kevin Venzke

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