Markus--
You said:
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?
I reply:
Is it possible that you don't appreciate the silliness of what you've just said?
Levin's & Nalebuff's definition of Simpson-Kramer, as you said, explicitly presumes that each voter casts a complete ranking of all the candidates. That makes Simpson-Kramer very differrent from PC, whose definition makes no such assumption.
If some voters don't rank all the candidates, then Simpson-Kramer doesn't have a result, because its definition doesn't apply to that ballot-set. But PC has a result. PC and Simpson-Kramer aren't the same method. Different definitions, different results, when Simpson-Kramer elects no one because a voter didn't rank all the candidates, or when Simpson-Kramer doesn't count a ballot because it doesn't rank all the candidates.
Of course if, in spite of that big difference, you wanted to claim that Simpson-Kramer is the same as PC, then it could also be claimed, with just as much justification or lack of justification, that the margins version of PC is also the same as Simpson-Kramer.
I want to emphasize that, in spite of what I've sometimes said here, I don't claim that Markus is a complete idiot: There are obviously a few parts missing.
Mike Ossipoff
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