IRO & Margins Equilibria

Mike Ositoff ntk at
Wed Sep 30 00:34:00 PDT 1998

Netcom's garbage eruption problem is especially bad tonight,
so it's short messages again.

Though I'm not involved in the methods merit debates anymore,
there is something that I'd like to clarify.

I said that Weber & Myerson defined equilibrium as an outcome
that doesn't contradict the voter beliefs that resulted in that

Say it's Nader, Clinton, & Dole. You're a Nader voter. 
I've talked about how, in methods like FPP, IRO, & Margins, you
sometimes need to rank Clinton over Nader, abandoning your favorite
completely. In the above methods, and also in Approval, you
can need to vote for Clinton if you don't think Nader can beat
Dole. In Approval that's routine. In IRO & Margins it's true
under some conditions, more pervasive with IRO.

So say, as in Demorep's example, Nader has a majority, but kyou
don't know it, and the Nader voters do what it takes to protect
Clinton, defeat Dole. In all those methods but Approval, they
can have to vote Clinton alone in 1st place. Then, when the
election results are published, they say "Yeah, just as we thought,
Nader can't get any votes!"  Right, because they thought he couldn't
& voted for Clinton. That's an equilibrium. With Approval, if
they give it away, it isn't equilibrium, because Nader has their
votes too, and in this linear example, Clinton voters have no
reason to vote for Nader, and so his votes all come from Nader
voters, and their numbers are obvious. The outcome, then, contradicts
the voter beliefs that led to the outcome. The giveaway isn't
an equilibrium, unlike Margins & IRO.


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