[EM] Strategy free method proposal

[rob brown]

On 12/17/05, Simmons, Forest <simmonfo at up.edu > wrote:
>
> Rob, in my experience typically when there is a Condorcet Cycle there is
> no Approval Strategy A style equilibrium of the kind you posit in your
> second message on this topic.


It had been under the understanding that there will always be at least one
equilibrium, but that iterative limit-seeking programs don't always find
it.  Maybe I misinterpreted something someone else said.  I haven't yet
written a program to test it.

However, the method you propose in your earlier message might indeed
> approach an approval strategy A configuration as a limit without this limit
> configuration itself being an equilibrium configuration.


If it does converge on a limit that is not an actual nash equilibrium, I
assume it would be creating Range ballots in the end, not having converged
all the ballots to be Approval ballots.  That is not ideal, but not so bad
either.  The problem I have with Range ballots is they are not stratigically
optimal in the last round of voting (from the point of view of each voter),
and having the "agent" vote in a way that is not strategically optimal for
the voter it represents makes this a bit less pure.

This is analogous to the fact that a function with a jump discontinuity will
> approach a different value then the value of the function. *


Got it.  Your example, of course, converges toward a "jump discontinuity"
(what I was calling a "cusp").  Now certainly there will be conditions like
this if there are true ties, which should be less and less common as the
number of voters gets larger.  If these cases happen that rarely, I don't
see it as a problem.  However, if they are relatively common (like Condorcet
cycles), then this technique is nowhere near as interesting.

I have no way of knowing which is the case, without writing something to
test it.

Anyway, I think your first approach is worth exploring further.  I'm sure
> there is something valuable there to be learned.


Thanks....
-rob
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