Tideman vs. Schulze

[Norman Petry]

Dear Markus,

On 5 Aug 1998, you wrote:

>That some participants of the Election Methods Mailing List
>believe that Tideman's Method is identical to Condorcet's Method
>or that Schulze's Method is identical to Condorcet's Method seems
>to me to be caused by the fact that the translator of their copies
>of Condorcet's Essai has already interpreted Condorcet's
>method in this direction. Condorcet explicitly wrote,
>that the weakest pairwise comparisons should be eliminated
>successively. He didn't write, that the largest pairwise
>comparisons should be locked successively.

It appears that Condorcet may have actually written _both_ things in the
same essay.  The quotation I provided:

>"...The preceding reflections suggest this general rule: that whenever it
is
>essential to make the election, it is necessary to take successively all
the
>propositions that have a majority, beginning with those possessing the
>largest.  As soon as these first propositions produce a result, it should
be
>taken as the decision, without regard for the less probable decisions that
>follow." -- Condorcet, Essay on the Application of Mathematics to the
Theory
>of Decision-Making

 came from the English translation (Keith Baker, ed.) of the Condorcet's
_introduction_ to his essay, rather than the Essai proper.  I can't say for
certain (since I only have portions of the introduction, and that is in
English) but I suspect that your quotation is taken from the body of the
work (considering it's on p.126).  It's no wonder Condorcet's method has so
many interpretations, if he contradicts himself in the same paper!  We
should probably assume, however, that your extraction:

>> Create an opinion of those n*(n-1)/2 propositions, which
>> win most of the votes. If this opinion is one of the n*(n-1)*...*2
>> possible, then consider as elected that subject, with which this
>> opinion agrees with its preference. If this opinion is one of the
>> (2^(n*(n-1)/2))-n*(n-1)*...*2 impossible opinions, then eliminate
>> of this impossible opinion successively those propositions, that
>> have a smaller plurality, & accept the resulting opinion of the
>> remaining propositions.

is a more definitive statement of what he intended than what he wrote in the
introduction.  This description of his method seems a lot more like the
"Reverse-Tideman" method I described than Tideman's original "ranked pairs"
rule.  As Reverse-Tideman goes about creating it's final "opinion", it
successively eliminates propositions having a smaller plurality in cases
where they would create an "impossible opinion" (i.e.: a cycle).


Norm Petry