[EM] Condorcet - let's move ahead

Markus Schulze markus.schulze at alumni.tu-berlin.de
Sun Jan 18 15:55:03 PST 2009


Steve Eppley wrote (18 Jan 2009):

> 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.

When the MinMax method chooses a candidate from outside
the Smith set, then the winners of both methods, the
Schulze method and the ranked pairs method, differ
from the winner of the MinMax method. Therefore, such
instances have no impact on the result of Norman Petry's

Steve Eppley wrote (18 Jan 2009):

> 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).

I didn't write that the MinMax method and the Schulze
method always pick the same candidate. I only wrote
that, in all of Heitzig's instances, the MinMax method
and the Schulze method chose the same candidate (Jobst
Heitzig: "Beatpath and Plain Condorcet are unanimous
in all these examples!") while, in 96 instances, the
ranked pairs method chose a different candidate.

Markus Schulze

More information about the Election-Methods mailing list