[EM] Problem solved (for pure ranked ballot)
Forest W Simmons
fsimmons at pcc.edu
Mon Jan 29 18:44:14 PST 2007
As Kevin pointed out in one of his posts I have been using a overly
difficult standard of Favorite Betrayal.
Here's a simpler proof based on the following definition of FBC:
Raising favorite to top rank must not decrease expected utility.
Given three voters with utilities consistent with the ranked preferences
1 A>B>>C
1 B>>C>A
1 C>>A>B
Sincere pure ordinal ballots would be
1 A>B>C
1 B>C>A
1 C>A>B
Neutrality and anonimity require that A, B, and C win with equal
probability, so the expected utility for the A voter is below the
utility of B.
Swapping B and A on that ballot yields
1 B>A>C
1 B>C>A
1 C>A>B
Clone immunity together with Majority Rule in the two candidate case
implies that B wins with this ballot set.
Moving favorite back up to top rank displaces B down a rank because we
are still assuming pure rankings. This puts us back where we started
with less utility than B.
That's it.
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