Adam wrote: > It's not absolutely deterministic, although I admit it is close. Alex came > up with this example where Approval voting can settle in a rut: > > 25 A>B>C > 49 B>A>C > 26 C>A>B > > Now suppose the initial approval votes are > > 25 AB > 49 B > 26 C > > So B wins, 25-74-26, even though A is the Condorcet winner. No voter has a > clear incentive to change their vote; the vote combination is a Nash > equilibrium, when factions are considered players. Now this rut is very > tenuous, and one could certainly imagine the voters breaking out of > it. But they will not certainly break out of it.
That depends on the strategies the proxy approval "voters" use at each iteration. My CRAB simulations currently offer a voter four strategies: Strategy L: Approve all candidates I prefer to my least favorite of the current CRAB first-placer and second-placer. Strategy T: Approve all candidates I like at least as much as my favorite of the current CRAB first-placer and second-placer. Strategy M: Approve all candidates with a higher utility than the average of the current CRAB first-placer and second-placer. Strategy A: Approve all candidates I prefer to the current CRAB first-placer; also approve the first-placer if I prefer him to the second-placer. If the winning CRAB quota is calculated deterministically and the strategies the voters use are deterministic (like the above), then CRAB is completely deterministic. As for getting stuck in ruts, that's a valid concern. Of the four strategies listed above, only strategy A always homes in on the Condorcet winner when one exists and all voters use the same strategy. Strategy M does fairly well; it finds the CW about 96% of the time, but strategy T (by far the one most often recommended on this list) finds the CW only about 77% of the time. That's a lot of ruts. (Strategy L does even worse.) In Adam's above rut example, strategies A and L would get out of the rut and settle on 25 A 49 B 26 CA giving the victory to A, the Condorcet winner. Strategy M might get out of the rut, depending on the voters' reported utilities, but strategy T would stay stuck in the rut. Of course, the voters don't all have to use the same strategy. Presumably, each would choose the strategy thought to be most likely to lead to the best result for the individual voter. I'm currently working on a simluation to find how well each of the above strategies performs for its users in the long run. > Has anyone tried to simulate a repeated approval balloting election where > some voters use insincere strategy - that is, they approve a candidate who > they like less than a candidate they do not approve? Obviously, there is > no incentive to do so in a normal approval vote, but in a repeated approval > vote, such disinfestation may help you by convincing other voters to > approve your favorite as a compromise. The problem is that the approval "voters" in CRAB don't know when the balloting will stop, so insincere strategy almost always backfires in the end, even if it's effective at first. I've tried some tricky strategies in my simulations, but they never help the voters using them in the long run. If anyone has specific strategies for me to try, I'm taking suggestions. -- Rob LeGrand [EMAIL PROTECTED] http://www.aggies.org/honky98/ __________________________________________________ Do You Yahoo!? Yahoo! Health - your guide to health and wellness http://health.yahoo.com ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
