First I want to emphasize that I adoped Richard's shorter definition believing that it would give the same answer as my definition, at least with all proposable methods, or maybe with all methods. So, when there's a case where the 2 definitions give different answers, it's obvious that my own definition is the one that appllies.
My own longer definition will be my definition of voting X over Y. But I'll still often, maybe usually, use the shorter definition, though I hereby state that my own definition is the one that applies when the two definitions differ.
Here's my improved short definition:
A voter votes X over Y if: If we count only his/her ballot, with all but X & Y deleted from it, then X wins and Y loses.
[end of short definition of voting X over Y]
That definition avoids the unintended loophole of its previous version, and therefore better carries out my intent for the definition. But I don't know that the unusual, implausible practice that it speaks of, counting only one ballot, couldn't lead to other problems. For instance, someone could speak of a method which explicitly requires more than one ballot, or whose results are unexpectedly affected by counting only one ballot.
Therefore my own longer definition is my actual definition of voting X over Y, though I'll often use my short definition, due to its brevity, with the understanding, stated in this messgage, that if they differ in their answers, my long definition is the one that applies.
Mike Ossipoff
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