Hi,
I haven't confirmed the results in the articles by Jobst and Norm cited
by Markus, but clearly he has misrepresented their results, since Minmax
(aka Simpson-Kramer) was not one of the methods they simulated in those
articles. They simulated Smith//Minmax, which is a different method
that does NOT minimize the number of voters who prefer a different winner.
Markus also erred when he wrote that Minmax and Beatpath Winner always
pick the same winner when there are 4 candidates. Recall the classic
example that shows Minmax fails clone independence is a 4 candidate
scenario. In that scenario, Minmax elects the candidate outside the top
cycle because the 3 candidates in the top cycle are in a "vicious" cycle
of large majorities. Beatpath Winner elects within the top cycle (as
does MAM).
Minmax's best feature, I think, is its simplicity. Minmax+Withdrawal
would be a fine method, since any of the candidates in the vicious cycle
could withdraw to defeat the candidate outside the top cycle, and at
least one of them would be pressured to do so.
I don't see any validity in Markus' argument that Beatpath Winner is
better than MAM because BeatpathWinner elects the Smith//Minmax winner
more often than MAM does. Simulations support the conclusion that MAM
is better than both: More voters rank MAM winners over Beatpath winners
than vice versa, and more voters rank MAM winners over Smith//Minmax
winners than vice versa. Norm was one of the people whose simulations
corroborated these results.
By the way, http://m-schulze.webhop.net/schulze1.pdf didn't load
properly for me using either Firefox or Internet Explorer. It quickly
crashed Firefox and displayed nothing in IE.
Regards,
Steve
------------------------------------------------------------
On 1/18/2009 1:18 PM, Markus Schulze wrote:
Hallo,
Steve Eppley wrote (18 Jan 2009)
MAM satisfies all the desirable criteria satisfied
by Beatpath Winner (aka Cloneproof Schwartz Sequential
Dropping--CSSD for short--aka Schulze's method).
Many people consider the Simpson-Kramer MinMax method
to be the best single-winner election method because it
minimizes the number of overruled voters. The winner of
the Schulze method is almost always identical to the
winner of the MinMax method, while the winner of the
ranked pairs method differs needlessly frequently from
the winner of the MinMax method.
For example, Norman Petry made some simulations and
observed that the number of situations, where the
Schulze method and the MinMax method chose the same
candidate and the ranked pairs method chose a different
candidate, exceeded the number of situations, where the
ranked pairs method and the MinMax method chose the same
candidate and the Schulze method chose a different
candidate, by a factor of 100:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004540.html
Jobst Heitzig made a thorough investigation of the
4-candidate case. In no situation, the Schulze method
and the MinMax method chose different candidates.
("Beatpath and Plain Condorcet are unanimous in all
these examples!") But in 96 situations, the ranked
pairs method and the MinMax method chose different
candidates:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012801.html
There are even situations where the winner of the
ranked pairs method differs from the winner of the
MinMax winner without any plausible reason. See
section 9 of my paper:
http://m-schulze.webhop.net/schulze1.pdf
Markus Schulze
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