[EM] Condorcet - let's move ahead

[Steve Eppley]

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
>