barnes99 said: > The Borda Count will punish an insincere vote in some cases, and that is > actually an incentive to vote sincerely. If too many people sincerely > put Nader between Bush and Gore, and voted either Bush>Nader>Gore or > Gore>Nader>Bush, Nader would have been elected. Therefore, you need > some information to successfully manipulate the BC,
True. It would be interesting to find out if there are any general results on Nash equilibria and the Borda Count. In that 3-candidate example, if we assume that most people rank Nader last, there is a disincentive for too many voters to falsely vote Nader in the middle. Here's the problem as I see it: In most ranked methods, reversing the rankings of #2 and #3 only hurts #2 (presumably to help #1 at #2's expense). In Borda, reversing the ranking of #2 and #3 hurts #2 but also hurts #1 to some extent. Granted, this isn't a quantitative statement. > As a start, maybe we could quantify the number of voters who could > successfully manipulate the outcome in a particular example. Here's a > simple example to kick off the game: > > 1 ABC > 1 ACB > 1 CAB > 1 CBA > 1 BCA > 1 BAC This case isn't really susceptible to analysis because ANY reasonable ranked method will give a 3-way tie, leaving the outcome in the hands of Justice Scalia ;) Even if we perturb the numbers a little to break the tie, so that each category has between 9 and 11 voters, say, any reasonable method will be very unstable: It will be very easy to change the outcome with a strategic adjustment because you're close to a 3-way tie. It's usually better to analyze strategic voting with specific criteria (e.g. montonicity, FBC, etc.). Individual criteria can usually be analyzed in cases that aren't near-ties. Maybe we need to invent more criteria to understand the manipulability of Borda, or maybe those commonly discussed on the list are sufficient. In any case, we need criteria to move this discussion forward. Alex ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
