[EM] Re: simulating an Approval campaign/election

[Forest Simmons]

> From: Rob LeGrand <honky1998 at yahoo.com>
> Subject: [EM] Re: simulating an Approval campaign/election

Russ wrote:
>> 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.
>
Rob responded:
> 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.]

Forest