[Election-Methods] Elect the Compromise

[Jobst Heitzig]

Dear Rob!

> I tend to be in agreement with Forest that vote trading and randomness are the only solutions.   I have no clue what you are thinking of, but I suspect when I hear it I'm going to think its in the range of what I'd consider "cheating". :)

Think about Borda using scores 0, 1, and 2, without equal rankings allowed: The A voters can give A at most a score of 55*2=110 and have to give either B or C at least a score of 28. Hence whatever the A voters do, they cannot be sure to have A elected since the B voters could advance B or C to at least a score of 118 by giving it a score of 45*2=90. From this one can see easily that there is no group strategy equilibrium electing A or B. All group strategy equilibria elect C, for example the one in which everbody puts C first and her favourite second. The drawback is only that these equilibria are not globally attractive, since there are starting points (e.g. sincere rankings) from which the process of repeatedly replacing the strategies by optimal respond strategies to the current strategies will not eventually lead to an equilibrium but may get stuck in a cycle.

> Randomness is a weird one....it is great that it can get people to vote honestly, but then it can just pick the "wrong" one.

Well... In D2MAC, when you assume people to be rational, all of them will approve of C and so C will be the certain outcome. I consider this evidence for the fact that a randomized method could be designed which will make rational voters elect a good compromise with certainty.
  
> Vote trading generally means the ballots can't be secret, so elections would be inherently corruptible by anyone with money.  Not good.  

You are right. That was not the form of trading I was thinking of. Rather the used method can give the voters means to trade votes (or rather winning probabilities) automatically. D2MAC is such a method.

Yours, Jobst
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