On the manipulability of proportional representation

Abstract

This paper presents a new model of voter behaviour under methods of proportional representation (PR). We assume that voters are concerned, first and foremost, with the distribution of power in the post-election parliament. We abstract away from rounding, and assume that a party securing k percent of the vote wins exactly k percent of the available seats. We show that, irrespective of which positional scoring rule is adopted, there will always exist circumstances where a voter would have an incentive to vote insincerely. We demonstrate that a voter's attitude toward uncertainty can influence his or her incentives to make an insincere vote. Finally, we show that the introduction of a threshold - a rule that a party must secure at least a certain percentage of the vote in order to reach parliament - creates new opportunities for strategic voting. We use the model to explain voter behaviour at the most recent New Zealand general election.