[EM] Hay voting bust, busted

[Peter de Blanc]

On Mon, 2007-02-05 at 10:47 -0500, Peter de Blanc wrote:
> are of how others will vote), because of the small amount of randomness
> in the method itself. This means that there should be a one-to-one
> correspondence between utility functions and voting strategies.

Sorry, I should have said injective mapping, not one-to-one
correspondence.

I'll add two more comments:

1. I'm worried that some people might be confused about which substances
are being purchased in Hay Voting. The substances are not votes; they're
transfers of votes between candidates. If you bought votes, then you
would not buy any votes for the candidates that you don't like. But if
you're buying transfers, then you would transfer votes from a greater
evil to a lesser evil. This is what allows us to discover your
preference between the two evils.

2. The more general criterion which Hay Voting satisfies is this: we
want a voting method such that, given a probability distribution for how
the other voters will vote, the mapping from utility functions to
optimal voting strategies is injective. In the original formulation of
Hay Voting, this mapping does not depend on the probability
distribution. In a deterministic (or "semi-deterministic") method, the
mapping would have to depend on this probability distribution. In either
case it has to be injective if we want to discover what the voters
really want.

Hay voting already satisfies this criterion, but we can play around with
it to try to make a variant that still satisfies the criterion and also
produces a sane outcome for the election (this is what Deterministic Hay
Voting was aiming at).