[EM] Condorcet and the Muller-Satterthwaite Theorem
Alex Small
asmall at physics.ucsb.edu
Tue Oct 22 15:42:19 PDT 2002
Forest Simmons said:
> I know that the name Pareto is associated with various related but
> distinct concepts in game theory because the referee of a paper that I
> co-authored on the subject of "consensus halving" and related fair
> division problems asked if we could show that the method was Pareto
> Efficient, by which he meant that no participant in the consensus
> division procedure would have an incentive to lie about any of her
> preferences.
That definition sounds like either Nash equilibrium (no incentive to be
insincere if every other participant is sincere) or non-manipulability, as
I've understood the terms.
Below I've included instructions for finding the paper, if you're
interested. The author defines Pareto efficient in an even more lenient
manner than I used in my post: If candidate A is at the top of each
voter's preference list then A is elected. To my knowledge all ranked
methods satisfy that criterion. The assumption wasn't treated as anything
profound, but it was necessary for technical purposes.
Since I've had problems attaching files to posts, just do the following to
find the paper:
Go to www.google.com
Enter the search terms "Gibbard-Satterthwaite" and "arrow"
The first document displayed will be a link to a .pdf file. The paper is
called "Arrow's Theorem and the Gibbard Satterthwaite Theorem: A Unified
Approach."
Alex
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