[EM] sincerity classification definitions

[MIKE OSSIPOFF]

Every nonfalsifying method that I know of has, in every situation,
an equilibrium that not only doesn't involve order-reversal, but
which also elects the sincere CW (The premise of these definitions
limits them to situations that have a sincere CW). For that reason,
and because an equilibrium that elects the CW is obviously more
important & desirable than other equilibria, I'd like to add that
to my definition of nonfalsifyingness. Here it all is, with the
revisions:

If voters have complete information about eachother's preferences,
and if there's a sincere CW, and there's no indifference between
that CW and the other candidates (though there could be indifference
among those others):

A method is falsifying if there's some situation in which it
doesn't have any equlibria in which there is no order-reversal and
in which the sincere CW wins.

A method is doubly falsifying if there's some situation in which
it doesn't have any equilibria at all in which there is no order-reversal.

A method is nonfalsifying if in every situation it has an equilibrium
in which there is no order-reversal and in which the sincere CW wins.

A method is strongly nonfalsifying if it is nonfalsifying without
the stipulation that there's no indifference between the CW and the
other candidates.

A method is expressive if in every situation there is an equilibrium
in which no one reverses a sincere preference or votes a less-liked
candidate equal to a candidate whom that voter has included in his/her
ranking, and in which the sincere CW wins.

A method is conditionally completely expressive if, in the event
that we rule order-reversal out as a strategy, that method has,
in every situation, an equilibrium in which everyone sincerely ranks
all of the candidates, and in which the sincere CW wins.

[end of definitions]

Approval is strongly nonfalsifying.

Condorcet(wv) is nonfalsifying, expressive, and conditionally
completely expressive.

Condorcet(margins), IRV, and Plurality are doubly falsifying.

(I've verified a few of these statements. I'll verify the rest over
the next few days).

Mike Ossipoff








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