<html><head></head><body>A couple of weeks ago I described my idea for "majority potential" as a better-calibrated<br>
standard than SU for evaluating methods by way of simulation.<br>
<br>
I've started writing a program to try out this concept. I'd like some suggestions on a few<br>
things.<br>
<br>
1. I have one statement that eliminates clones during random selection of the candidates.<br>
I can take this statement out and the sims would have occasional clones. Would it be<br>
better to simulate with or without clones?<br>
<br>
2. Most of the methods will only be simulated with sincere strategies. For a few<br>
methods such as Approval it might be possible to simulate some (non-statistical)<br>
strategy variations. To do this, I need to designate two front runners in each race.<br>
Two ways of doing this come to mind, but neither seems satisfactory:<br>
<br>
a. Randomly select two candidates as front runners. In this method, a candidate from<br>
the lunatic fringe is as likely to be a front runner as the most boring centrist.<br>
b. Select the two candidates with the highest majority potential rating as the front<br>
runners. But if it were always true that the front runners are also the most<br>
democratic choices, then there would be no reason to change the current Plurality<br>
system. Certainly, factors other than policy, such as charisma, party loyalty, and<br>
(would you believe?) money play a role in determining a candidate's popularity.<br>
<br>
I suspect the truth lies somewhere in between these options. Any ideas? (Initially, I<br>
will use option "a" since it is easier to program.)<br>
<br>
3. The strategies I have in mind for Approval are (a) above-the-mean, (b) pick your<br>
favorite of the two front runners plus everybody you like better, and (c) insurance.<br>
The insurance strategy works like this: For each candidate that a voter rates higher<br>
than his favorite of the two front runners, set that candidate's utility the same as<br>
the favorite of the two front runners. For each candidate that a voter rates lower<br>
than his least favorite of the two front runners, set that candidate's utility the same<br>
as the least favorite front runner. After these steps have been taken, apply the<br>
above-the-mean strategy. This strategy has the advantage of allowing extra<br>
candidates rated between the two front runners to be selected as insurance over<br>
just drawing the line at the favorite front runner. Any comments?<br>
<br>
4. I am going to use a 2-dimensional policy space. I am going to calculate utilities<br>
based on the L1 (Hamming) distance between the voter and the candidate. The<br>
rationale for L1 is that if policy X has a cost to the voter and policy Y has a cost<br>
to the voter (not necessarily monetary costs but such can be used as a tangible<br>
example), then the combined costs of both policies is a simple sum. If there are<br>
any arguments for using L2 distance please let me hear them.<br>
<br>
5. I need an algorithm for populating the policy space with voters and candidates<br>
having a non-uniform distribution. Currently I am writing this with a uniform<br>
distribution (easy!) but that will be very unrealistic. Any suggestions?<br>
<br>
Richard<br>
<br>
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