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 ---- Election-methods mailing list - see http://electorama.com/em for list info
