Dear Russ,
I interpret Mike Ossipoff's "Strategy-Free Criterion" (SFC) and "Generalized Strategy-Free Criterion" (GSFC) as follows:
"X >> Y" means that a majority of the voters strictly prefers candidate X to candidate Y.
SFC: Suppose (1) A >> B and (2) the partial individual rankings can be completed in such a manner that candidate A is a Condorcet candidate. Then candidate B must be elected with zero probability.
I think you are trying to convert what I call a "Mike-style" criterion into a "normal" criterion. Let me repeat a portion of what I wrote yesterday:
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What we have here, it seems to me, is confusion cause by a failure to distinguish between two fundamentally different classes of criteria. Consider the basic voting process. It starts with the voters' true preferences, then the votes are cast, then the votes are tallied and the winner is determined:
true preferences --> votes cast --> winner determined
Let's call the process represented by the first arrow the "voting strategy" and the process represented by the second the "tally rules."
All voting system criteria that I have ever seen, excluding those that originated with Mike, involve the tally rules only. They consider only the votes cast and make no reference whatsoever to the true preferences of the voters.
At some point Mike came along and changed the paradigm fundamentally, probably without ever explaining that he was doing so. Naturally, this causes confusion. To minimize the confusion, I suggest we distinguish between "normal" criteria and "Mike-style" criteria.
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You seem to be trying to interpret SFC in terms of the tally rules only, but you can't do that because, unlike "normal" criteria, it involves the voting strategy too.
In your interpretation of SFC above, I think your supposition 2 should actually be part of the result. Here is my attempt at it:
SFC: Suppose A >> B. Then partial individual rankings can be completed in such a manner that no preferences are reversed and candidate B must be elected with zero probability.
--Russ ---- Election-methods mailing list - see http://electorama.com/em for list info
