I forgot to include all the wording that I intended for the equilibrium criteria:
And a different naming might be good too.
Falsifyingness:
A method is falsifying if, with that method, there are situations (configurations of candidates and voter preferences) in which there is a CW, and there are no Nash equilibria in which the CW wins and no one reverses a preference.
[end of falsifyingness definition]
Expressiveness:
A method is expressive if, with that method, every situation with a CW has at least one Nash equilibrium in which the CW wins and no one votes a less-liked candidate equal to or over a more-liked candidate (as I define that).
[end of expressiveness definition]
Also, instead of the name that I suggested for the criterion relating to James� co-operation/defection dilemma, let me instead just say that methods that have that dilemma are "defection-vulnerable" or "defection-prone".
So I�ve defined falsifyingness, expressiveness, and defection-proneness.
Of course any method that is expressive is nonfalsifying.
When a method is said to be falsifying, non-falsifying, expressive, or non-expressive, that term should be followed by "a", "s1", or "s2", depending on which voting extension of Nash equilibrium is being referred to. If those terms are used without that designation, then "a" is the default assumption. The "a" versions of nonfalsifyingness or expressiveness are the most demanding versions.
I defined "a", "s1", & "s2" in a posting yesterday.
But I�d like to replace "a" with "ac", so that it won�t need the quotation marks to disinguish it from the word "a".
I haven�t examined many methods for these properties, but Approval is nonfalsifying, so are the wv Condorcet versions. And BeatpathWinner/CSSD and RP are probably expressive. Maybe also Bucklin, and ERIRV and Kevin�s Approval elimination when they have AERLO.
Pluralitly, IRV, and Condorcet(margins) are falsifying, in all of that term�s versions ("a", "s1", & "s2").
I expect that methods that meet WDSC are nonfalsifying, and that methods that meet SDSC are expressive, but I�m not sure whether those properties always coincide.
Mike Ossipoff
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