[EM] Puzzle: Vote A. Better yet...

[MIKE OSSIPOFF]

If you want to do it the easy way, and just let the other voters
flip a coin, as they were going to, then vote only for A.

But you improve on that. Speak privately to voter #1, to arrange a
conversation in front of voters # 2 & 3, where you'll "convince" him
that it's better to vote for B, to be on the safe side. He agrees,
and that conversation convinces the other 2 voters that you're both
going to vote for A & B.

Voter #3 knows that he can't possibly win, since A will get 2 votes,
B will get 3 votes, and C can't get more than 2 votes, at the most.
So C will vote for A, and it will be a tie between A & B. Your expectation 
in that tie is .85, which is just slightly lower than your
expectation if you'd just let them all flip a coin, and voted only for
A.  So why do it that way if it will lower your expectation slightly?

Because then you suggest voting by Condorcet. A is sincere CW, and
the only member of the sincere Schwartz set. A wins under sincere voting
in Cloneproof SSD, SSD, & PC.

Ask for a vote on changing the voting system to Condorcet. You & voter
#1 both benefit from a sure win for A. Voter #3 would rather elect A
than have a lottery between A & B. Condorcet wins 3 to 1. A wins the
Condorcet vote.

Mike Ossipoff



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