Does VA Schulze violate SEC?

[Blake Cretney]

On Thu, 01 Oct 1998 17:17:19   Markus Schulze wrote:
>Blake Cretney wrote (29 Sep 1998):
>> All voters who know how Votes-Against works will use the
>> random-fill strategy instead of sincerely or insincerely
>> leaving candidates unranked.
>
>This is not true. Of course, if you use Condorcet[EM] or
>Smith//Condorcet[EM], then it will be a usefull strategy
>to rank the remaining candidates (sincerely or randomly),
>because if Condorcet[EM] or Smith//Condorcet[EM] is used,
>then the worst defeats of your less favourite candidates
>cannot decrease by ranking these candidates (sincerely or
>randomly).
It's important to remember that random-filling can back-fire,
but it is much more likely to get your candidates elected
than is leaving the lower candidates unranked.
>
>But if the Schulze method or the Tideman method is used,
>then this strategy won't work, because the strength of
>a pairwise defeat has only an influence on the question
>which beat-path is used or in which order the pairwise
>defeats are locked. Thus, the strength of the pairwise
>defeat of your less favourite candidates has no immediate
>influence on the scores of these candidates.

I'm glad to see that our difference of opinion is at least partly
based on a factual question that should be solveable, one way or
the other.
I think you're mistaken about Schulze and Tideman because both of
these methods are identical to Condorcet(EM) in the 3 candidate
case.  So, if you agree that Condorcet(EM) encourages random-fill
and violates SEC, then the same must be true of Schulze and Tideman
for three candidates.  Because your argument would seem to apply
to three candidates examples as well as any others, I have to
conclude that it includes an error.  Furthermore, I don't see
why adding additional candidates beyond three would fix these
problems where they exist.

Remember, that in Schulze increasing the pair-wise
victories against candidates is the most likely way to increasing 
the best beat path against them.
>
>For the Schulze method, the Tideman method and most other
>Condorcet methods, the random-fill strategy doesn't work,
>because it is not guaranteed that the scores of the less
>favourite candidates get worse by ranking them.
>Markus Schulze
>
Of course, there is no guarantee that random-fill will work.  But
there aren't a lot of guarantees in voting methods.  Consider the
violations of NoShow and IIAC.  We don't expect that voters will
consider these posibilities, and be paralysed with fear into not
voting a full preference list, so we can also expect that voters
will use random-fill if it works better on average than a sincere 
vote.

If you aren't convinced, we should probably try to swap more detailed
and rigorous proofs off the list.



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