Regretted Turnout. Insincere = ranking.

[David Marsay]

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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