[EM] Schulze definition (was: information content, game theory, cooperation)

Raph Frank raphfrk at gmail.com
Sun Jun 7 12:27:01 PDT 2009


On Sun, Jun 7, 2009 at 7:35 PM, Árpád Magosányi <magwas at rabic.org> wrote:

> """"
> - The electors rank the candidates according to their preferences.
> - If there is a group of candidates all preferred over all candidates
> outside the group, then ignoring the candidates outside the group should not
> change the outcome of the election.
> - The winner should be choosen from the above group in a way that
> guarantees that if a candidate similar to an already running candidate is
> introduced, the outcome of the election is not changed, and the less
> controversial candidates are preferred.
> """
> Reasoning below. Please point out possible mistakes and ways to better
> phrase it between the boundary conditions given (simple words, no expert
> terms like "Schulze" or "beatpath", and should be matchable to correct
> mathematical definitions.



Ok, so you are basically saying (in simple terms)

A) the method is a ranked method
B) All candidates outside the Smith set can be ignored without changing the
result
C) The method should be clone independent.

That is a pretty good idea.  You are in effect defining the characteristics
that Schulze meets and the others don't.

Wikipedia has a table at:

http://en.wikipedia.org/wiki/Schulze_method

Schulze and ranked pairs are the only methods that meet clone independence
and the condorcet rule.

Does ranked pairs fail the Smith criterion?

I would change B to "If there is a group of candidates all preferred over
all candidates outside the group, then only those candidates may win and the
candidates outside the group may have no effect on the result".

If you don't restrict the winner to the Smith set (which your rules don't
necessarily), then you could end up with a non-condorcet method.

Also, just because the popular/proposed condorcet methods are excluded by
your definition doesn't mean that some other weird method can't be found
that also meets the rule.

It might be better to just include the reasons that you like Sculze and use
those rules rather than trying to select Sculze by a process of elimination.


> BTW it would be nice if the wikipedia page would actually contain something
> describing Schulze method, not just the heuristics.
> The best I have found so far is:
> http://rangevoting.org/SchulzeExplan.html
> "Therefore, my aim was to find a method that satisfies Condorcet,
> monotonicity, clone-immunity, majority for solid coalitions, and reversal
> symmetry, *and* that tends to produce winners with weak worst pairwise
> defeats (compared to the worst pairwise defeat of the winner of Tideman's
> Ranked Pairs method)."



Yeah.  Though, ofc, Schulze isn't allow to edit the article.

Could someone on this list give a brief outline or the formal rule (actually
his statutory rules are probably it)?
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