[EM] equilibrium definitions revised

[MIKE OSSIPOFF]

I'd like to slightly revise my definition of falisifyingness,
nonfalsifyingness, etc.

The change is: Where I stipulated some conditions at the beginning,
I now add the condition that there be no indifference between the CW
and the other candidates (though there can be indifference among
the others).

So let me start over:

A method is falsifying if there are situations (configurations
of candidates, voters, & voters' utilities & preferences) where
all of the method's equilibria involve order-reversal.

A method is nonfalsifying if it isn't falsifying. To reword it:

A method is nonfalsifying if in every situation it has an equilibrium
that doens't involve order-reversal.

A method is strongly nonfalsifying if it's nonfalsifying without
the stipulation about no indifference between the CW & the other
candidates.

[end of definitions]

My definitions of expressiveness and conditional complete
expressiveness remain the same as before, but of course with the
stipulation about no indifference between the CW & the other
candidates.

Approval is strongly nonfalsifying. Condorcet(wv) is nonfalsifying.

Condorcet(margins) is falsifying, as are IRV & Plurality.

Over the next few days I'll be posting demonstrations of the
facts that I've just stated about methods' falsifyingness &
nonfalsifyingness. Maybe I'll get a chance to post some of that
tonight, but if not, it will be posted within the next few days.

Mike Ossipoff


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