The Optimal Ballot Structure for Double-Member Districts

The Anglo-American double-member districts employing plurality-at-large are frequently criticized for giving a large majority premium to a winning party. In this paper, we demonstrate that the premium stems from a limited degree of voters' discrimination associated with only two positive votes on the ballot. To enhance voters' ability to discriminate, we consider rules that give voters more positive and negative votes. We identify voting equilibria of alternative scoring rules in a situation where candidates differ in binary ideology and binary quality; strategic voters are of two ideology types; and a candidate's ideology is more salient than quality. The most generous rules such as approval voting and combined approvaldisapproval voting only replicate the outcomes of plurality-at-large. The highest minority representation and the highest quality is achieved by a rule that assigns two positive votes and one negative vote to each voter.