Dear Markus--
Levin & Nalebuff said:
For our purposes, we assume that voters rank all the candidates on their ballots, and do not score candidates as ties
I reply:
Here are two possibilities: for what "For our purposes..."
1. "For our purposes..." means that Levin & Nalebuff are telling what Simpson-Kramer (and other methods) would be if all the rankings were complete. But if rankins aren't all complete, Simpson-Kramer could mean something else, some unknown, unstated meaning.
2. "For our purposes..." means "For the purposes of defining the methods defined in this paper", in which case Simpson-Kramer is not defined for sets of rankings that include some incomplete rankings.
Then Simposn-Kramer is undefined when there's truncation.
If one of the above is what "For our purposes..." means, then, for _our_ purposes, for public elections in which truncation is allowed, Levin & Nalebuff haven't defined Simpson-kramer. Either Simpson-Kramer is undefind for elections with truncation, or it has an unknown meaning under those conditions.
Either the definition that they give applies when truncationt takes place, or it doesn't.
If their definition doesn't apply when there's truncation:
Then they haven't given a definition of Simpson-Kramer that applies in the public elections that we discuss. As I said above, then, either Simpson-Kramer is undefined for elections with truncation, or Simpson-Kramer's defiinition is unknown under those conditions. PC is defined for elections with truncation, and any method that is not defined in such elections is not PC. And if the definition of Simpson-Kramer is unknown for elections with truncation, then you don't know if Simpson-Kramer is PC.
If their definition applies when there is truncation:
Then Siimpson-Kramer elects the candidate whose greatest vote against him in a pairwise defeat is the least--even if, due to truncation, the greatest vote against him in a pairwise comparison is in one of his pairwise victories. That is very different from PC.
Markus, don't reply to this unless you can justify, by what you say, a denial of something that I've said in this posting. In other words, don't just keep repeating something that you've already said, as you usually do.
Mike Ossipoff
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