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

[Árpád Magosányi]

Hi!

Sorry for top posting, But I believe I have found something nearing a
suitable simple-word definition for Schulze. As this is what I desperately
need, I offer it for scrutiny here:

""""
- 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.


2009/6/7 Markus Schulze <markus.schulze at alumni.tu-berlin.de>

> Dear Árpád Magosányi,
>
> here are the proposed statutory rules for the
> Schulze method:
>
> http://m-schulze.webhop.net/propstat.pdf
>
> If I understand you correctly, then you want
> to define the Schulze method in an axiomatic
> manner in your proposal. I don't think that
> this is a good idea.
>

I'm afraid you haven't yet understood the Hungarian situation ([?]). There is
no hope to push real changes through the Parliament. The only way to achieve
any democratic change is referendum. The rules for the questions eligible
for referendum are very strict. Nothing remotely as complex as your
statutory proposal would go through. Of course when time comes for changing
the text of law, we will push this text.
What I need is a small set of simply worded criteria, and to be able to show
that these criteria are not just wishes with a broad meaning, but can be
matched with exact mathematical definitions.

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)."

Sorry for thinking loudly, this boils down to:
-Condorcet and majority for solid coalitions can be described with ISDA
"whenever you can partition the candidates into group *A* and group *B* such
that each candidate in group *A* is preferred over each candidate in group *
B*, you can eliminate all candidates of group *B* without changing the
outcome of the election."
-Monotonicity
"*A candidate* x *should not be harmed* [i.e., change from being a winner to
a loser] *if* x *is raised on some ballots without changing the orders of
the other candidates."
-*Clone immunity
"the addition of a candidate identical to one already present in an election
will not cause the winner of the election to change."
- reversal symmetry
 "If a candidate A is the unique winner, and the individual preferences of
each voter are inverted, then candidate A must not be elected."
- "tends to produce winners with weak worst pairwise defeats"
prefers candidates who are cooperative

Now there are 3 methods I know of (
http://en.wikipedia.org/wiki/Schulze_method#Comparison_with_other_preferential_single-winner_election_methods)
complying with ISDA. Of them only Schulze "tends to produce winners with
weak worst pairwise defeats". But this does not imply clone independency,
and it is overly important, so we should add this as well.

So my definition is the above.
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