[EM] Simpson-Kramer Method

[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.

I wrote (21 March 2005):
> 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?

You wrote (22 March 2005):
> 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.

Well, when Levin and Nalebuff write that they "assume that
voters rank all the candidates on their ballots, and do not
score candidates as ties" then this doesn't mean that this
assumption is a part of the definition of the Simpson-Kramer
method; it simply means that Levin and Nalebuff don't discuss
partial individual rankings.

Markus Schulze