Statistical Robustness of Voting Rules

We introduce a notion of “statistical robustness” for voting rules. We say that a voting rule is statistically robust if the winner for a profile of ballots is most likely to be the winner of any random sample of the profile, for any positive sample size. We show that some voting rules, such as plurality, veto, and random ballot, are statistically robust, while others, such as approval, score voting, Borda, single transferable vote (STV), Copeland, and Maximin are not statistically robust. Furthermore, we show that any positional scoring rule whose scoring vector contains at least three different values (i.e., any positional scoring rule other than t-approval for some t) is not statistically robust.