Juho says:
I'd still appreciate the "no Nash equilibria problem" to be demonstrated as
a real life example. Well, maybe you think you already did this :-).
I reply:
As I said, my margins order-reversal example may be the example that you ask
for. It remains for me to check it, to find out if the B & C voters can save
B without defensive order-reversal. Maybe so, maybe not. If so, then Ill
post an example in which they cannot.
But your smiley suggests that my examples are not what you mean by real
life examples. Well, since margins isnt in use anywhere, it would be
difficult to find real life examples. All one can do is show what can
happen.
Now youre doubting that the voters will end up at a Nash equilibrium.What
can I say? Nash equilibria occur and are used in legal systems and
throughout the animal kingdom. By bees too? Maybe!
If, from a given voting configuration, its possible for a group of voters
to improve their outcome by voting differently, then why shouldnt they? You
know, the person who should be expected to defend his claim is the person
claiming that Nash equilibria wont matter.
Youre proposing a voting system that will often have situations in which
the only Nash equilibria, the only stable outcomes, are ones in which people
order-reverse. Do you realize how far youre going in order to forgive that
big fault of margins?
It isnt as if only a few methods meet Unreversed Nash Equilibrium Criterion
(URNEC). That criterion is met by wv, Approval, the various other
point-rating methods (collectively known as Cardinal Ratings, or CR), MDDA,
MAMPO, and Bucklin.
Methods that fail URNEC?: Plurality, IRV, margins, among others.
Methods that fail URNEC I refer to as reversed methods. You advocate a
reversed method, one in which voting configurations with order-reversal will
often be the only stable voting configurations.
Mike Ossipoff
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