[EM] Markus, 22 March, '05, 0400 GMT

[MIKE OSSIPOFF]

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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