[EM] Markus, 21 March, '05, 0603 GMT

[Markus Schulze]

Dear Mike,

you wrote (20 March 2005):
> In the _Journal of Economic Perspective_, for Winter
> '85, Simson-Kramer is defined as electing the candidate
> whose greatest votes for him in a pairwise comparison
> is greater than any other candidate's greatest votes
> for him in a pairwise comparison. (note that a
> candidate's pairwise comparisons aren't limited to his
> defeats). If you think that sounds like the definition
> of PC, or is equivalent to the definition of PC, then
> there's no way that I can reach you, and I won't try.
> By all means tell us that you prefer Simpson-Kramer to
> PC, but you're mis-using that term if you say that it's
> definition is the same as the definition of PC.

You wrote (21 March 2005):
> Simpson-Kramer is defined in the _Journal of Economic
> Perspective_, for Winter '85. That definition is of a
> method that elects the candidate whose greatest votes
> for him in a pairwise comparison is greater than any
> other candidate's greatest vote for him in a pairwise
> comparison. That isn't PC. The fact that you say that
> MinMax is Simpson-Kramer while also calling PC MinMax
> shows that you're very sloppy with terms, and it shows
> that MinMax doesn't mean anything, since it's applied
> to more than one method. List-members--Is there
> something familiar about this discusson? Yes. It took
> place a few days ago. This is what discussion with
> Markus is like. Continual repetition. We'll have a
> dozen copies of this discussion copied and recopied 
> in successive days of the EM archives. Markus has
> only begun.

Well, in that paper (Jonathan Levin, Barry Nalebuff, "An
Introduction to Vote-Counting Schemes", Journal of Economic
Perspectives, vol. 9, no. 1, pp. 3--26, Winter 1995) the
Simpson-Kramer method is described as follows:

> For our purposes, we assume that voters rank all the
> candidates on their ballots, and do not score candidates
> as ties. (...) The Simpson-Kramer min-max rule adheres to
> the principles offered by Condorcet in that it emphasizes
> large majorities over small majorities. A candidate's
> "max" score is the largest number of votes against that
> candidate across all head-to-head matchups. The rule
> selects the candidate with the minimum max score.
> A Condorcet winner will always be a min-max winner.
> When there is a cycle, we can think of the min-max
> winner as being the "least-objectionable" candidate.

Thus, this paper supports my claims (1) that Levin and
Nalebuff explicitly presume that each voter casts a
complete ranking of all candidates and (2) that the
Simpson-Kramer method _is_ the MinMax method.

Why do you believe that this paper supports your claims
about the Simpson-Kramer method?

Markus Schulze