Regretted Turnout. Insincere = ranking.
David Marsay
djmarsay at dera.gov.uk
Mon Sep 21 05:30:52 PDT 1998
In response to:
> From: Markus Schulze <schulze at sol.physik.tu-berlin.de>
> Subject: Re: Regretted Turnout. Insincere = ranking.
> Unfortunately, I have just found an article that proves, that
> the Condorcet Criterion and the No Punishment Criterion are
> incompatible.
This seems horrific. Like Arrow's theorem, but worse. But is it so?
I'm trying to get a copy. Meanwhile ..
Is it the Condorcet Criterion that's the problem, or some other
hidden assumption?
Consider the method in:
> From: "Norman Petry" <npetry at sk.sympatico.ca>
> Subject: Re: Schulze Method - Simpler Definition
It is quite true, and unavoidable, that adding ballots can sometime
have the opposite effect to that intended.
If a candidate pair-wise beats all others, there is no problem. The
problem arises with cycles.
Consider 3 candidates, with X winning due to Condorcet's tie-breaker.
Let #XY,#YZ,#ZX denote positive majorities (e.g., X over Y). Thus #ZX
< #XY, #YZ. Suppose we add a vote with X first. Then #ZX decreases by
1, and so remains the smallest, and so the result is unchanged.
An important special case is spatial voting (see my other post of
today Subject: 'Re: Margins Example Continued'.)
If everyone votes spatially then there are no cycles and no weird
outcomes.
Thus we at least have sensible behaviour for 3 candidates or spatial
voting. The general problem is where one has a cycle of 4 or more
candidates and the added votes change which tie is broken. But even
here we can regard the Condorcet tie-break as a tie break, and so
perhaps forgive its behaviour.
Alternatively, perhaps here is a good reason for minimizing 'votes
against' as a variant on Condorcet, noting that for 3 candidates and
spatial voting it amounts to the same thing.
Markus's reference is:
>The article is "Condorcet's Principle Implies
> the No Show Paradox" by Herve Moulin (Journal of Economic
> Theory, vol. 45, p. 53-64, 1988). The author uses the name
> "No Show Paradox" but he means the No Punishment Paradox.
>
> No Show Paradox:
>
> Suppose, candidate X does _not_ win the election.
> Then it can happen that a set of additional voters, who vote
> identically and who strictly prefer every other candidate to
> candidate X, change the winner from another candidate to
> candidate X.
>
> No Punishment Paradox:
>
> Suppose, candidate X does _not_ win the election.
> Then it can happen that a set of additional voters, who vote
> identically and who strictly prefer candidate Y to
> candidate X, change the winner from candidate Y to
> candidate X.
>
> Markus Schulze
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Sorry folks, but apparently I have to do this. :-(
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