[EM] MELLS (min expected lack of log satisfaction)

fsimmons at pcc.edu fsimmons at pcc.edu
Wed Dec 31 17:09:38 PST 2008

Here's a variation that I like better:

As before each range ballot b is assigned to a candidate c(b) by a method to be specified presently, and the 
winner is c(b) on a randomly drawn ballot b.

First some more notation: b(X) is the rating of candidate X by ballot b, and n(X) is the number of ballots in 
the pre-image of X under choice function c.

A choice function c (from a set of range ballots to the set of candidates) is in "cooperative equilibrium" iff for 
each ballot b, the value n(X) times b(X) is maximal when X = c(b).


Determine the winner by the lottery based on the choice function c in cooperative equilibrium that has the 
highest expected log of the product n(c(b)) and b(c(b)).

This is just MELLS (in disguise) restricted to the "cooperative equilibrium" lotteries.


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