[EM] Omission from equilibrium criteria. Renaming.

[MIKE OSSIPOFF]

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

_________________________________________________________________
Don’t just search. Find. Check out the new MSN Search! 
http://search.msn.click-url.com/go/onm00200636ave/direct/01/