Comparison of scoring rules in Poisson voting games
The main part of the paper considers voting systems where voters vote for three candidates in a normalized \((A,B)\) point-based system. That is, each voter gives 1 point to the most favored candidate, 0 points to the least favored candidate and either \(A\) or \(B\) points (where \(0\leq A\leq B \leq 1\)) to the remaining candidate. This scenario covers plurality, Borda, negative voting and approval voting, among other rules. The author is interested in the consequences of choosing different values for \(A\) and \(B\). The voters are divided into types and the number of voters is given by a Poisson distribution. The author considers limits of equilibria if the (mean) number of voters tends to infinity. The main assumption is that the voters act to maximize the expected utility, rather than voting sincerely, and so are most concerned about the impact of their points (and thus vote most strongly) on close, or serious, races. The author shows that, depending on the values of the parameters \(A\) and \(B\), various undesirable outcomes occur in the simple case where there are only two types of voters.
scientific article; zbMATH DE number 1751412