From: Rob LeGrand <[EMAIL PROTECTED]> Subject: [EM] Re: simulating an Approval campaign/election
Russ wrote:
Rob responded:You seem to have confirmed my hypothesis that, in the idealized case (DSV batch mode), Approval voting almost always converges on the Cordorcet winner if one exists, but rarely (never?) converges if one does not exist.
Yes, that's true, if all voters use strategy A or something very much like it, which according to my investigations is in their best interest.
Forest responds:
Actually, DSV with Strategy A can sometimes converge to a stable equilibrium even when there is no Condorcet Winner:
4900 C 2400 B 2700 A>B
Here we have a three candidate cycle of A beats B beats C beats A.
But let's see how this plays out in ballot-by-ballot or cumulative batch DSV Approval (they give the same result on this one):
Candidates C and A start out in the lead. When it becomes apparent that C is beating A, the A faction voters start approving B. From here on the leaders are C and B, and in that case B gains approval at an average rate faster than either A or C, so eventually B gains and keeps the lead.
So even though there is no CW, there is convergence to a stable Approval equilibrium, even using Strategy A.
[In my opinion this is unfortunate, since it would be better to have B and C win with about equal probability in this example.]
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