[EM] thoughts on majority potential simulations

[Richard Moore]

A couple of weeks ago I described my idea for "majority potential" as a better-calibrated
standard than SU for evaluating methods by way of simulation.

I've started writing a program to try out this concept. I'd like some suggestions on a few
things.

1. I have one statement that eliminates clones during random selection of the candidates.
I can take this statement out and the sims would have occasional clones. Would it be
better to simulate with or without clones?

2. Most of the methods will only be simulated with sincere strategies. For a few
methods such as Approval it might be possible to simulate some (non-statistical)
strategy variations. To do this, I need to designate two front runners in each race.
Two ways of doing this come to mind, but neither seems satisfactory:

   a. Randomly select two candidates as front runners. In this method, a candidate from
       the lunatic fringe is as likely to be a front runner as the most boring centrist.
   b. Select the two candidates with the highest majority potential rating as the front
       runners. But if it were always true that the front runners are also the most
       democratic choices, then there would be no reason to change the current Plurality
       system. Certainly, factors other than policy, such as charisma, party loyalty, and
       (would you believe?) money play a role in determining a candidate's popularity.

I suspect the truth lies somewhere in between these options. Any ideas? (Initially, I
will use option "a" since it is easier to program.)

3. The strategies I have in mind for Approval are (a) above-the-mean, (b) pick your
favorite of the two front runners plus everybody you like better, and (c) insurance.
The insurance strategy works like this: For each candidate that a voter rates higher
than his favorite of the two front runners, set that candidate's utility the same as
the favorite of the two front runners. For each candidate that a voter rates lower
than his least favorite of the two front runners, set that candidate's utility the same
as the least favorite front runner. After these steps have been taken, apply the
above-the-mean strategy. This strategy has the advantage of allowing extra
candidates rated between the two front runners to be selected as insurance over
just drawing the line at the favorite front runner. Any comments?

4. I am going to use a 2-dimensional policy space. I am going to calculate utilities
based on the L1 (Hamming) distance between the voter and the candidate. The
rationale for L1 is that if policy X has a cost to the voter and policy Y has a cost
to the voter (not necessarily monetary costs but such can be used as a tangible
example), then the combined costs of both policies is a simple sum. If there are
any arguments for using L2 distance please let me hear them.

5. I need an algorithm for populating the policy space with voters and candidates
having a non-uniform distribution. Currently I am writing this with a uniform
distribution (easy!) but that will be very unrealistic. Any suggestions?

Richard