Minority Representation in Multimember Districts

Abstract

Given the recent court rulings against racial gerrymandering, the effect of multimember district elections on minority representation is an important issue. We present a model of voting in double-member district elections with two majority candidates and one minority candidate and consider the voting equilibria under straight and cumulative voting. In straight voting, while an equilibrium always exists in which the two majority candidates are expected to win the two seats, minority candidates may be elected. In cumulative voting, minority candidate wins are also possible in equilibrium but are less likely when minority voters prefer one majority candidate over another. We then present experimental evidence showing that minority candidates win significantly more seats in cumulative than in straight voting elections. When minority voters perceive a substantial difference between the majority candidates, however, they are more likely to split their votes between the minority and majority candidates, winning fewer seats.

Does a Least-Preferred Candidate Win a Seat? A Comparison of Three Electoral Systems

“…Later, we examine what types of equilibria exist for each set of parameter values. Following Cox [10] and Gerber, Morton and Rietz [13], we assume additivity of utility. For example, if candidates 1 and 2 win seats, type-c voters receive a utility of c 1 + c 2 .…”

“…Their results are in contrast to the view of Duverger, who suggested that strategic voting would not appear under PR. Second, the model-building strategy proposed herein is based on the research of Myerson and Weber [7] and Gerber, Morton and Rietz [13]. Myerson and Weber [7] introduced voter perception of the probability of close races between each pair of candidates and required consistency between the perception and the electoral outcome.…”

“…They compared electoral outcomes under the plurality rule, approval voting, and the Borda rule, and showed that no minority candidate wins a seat with certainty only under approval voting. As Cox [10] did, Gerber, Morton and Rietz [13] assumed additive utility and extended Myerson and Weber's [7] model to a two-member district with two majority candidates and one minority candidate. They focused on whether the minority candidate wins a seat under straight voting and cumulative voting.…”

“…Under both rules, casting only one vote is also allowed. Gerber, Morton and Rietz [13] also conducted laboratory experiments to test the theoretical predictions.…”

“…Under closed-list PR, a stage of party decision making regarding the order of their candidates is introduced before voting. Our model is related to the models proposed by Myerson and Weber [7] and Gerber, Morton and Rietz [13], but we use a different equilibrium criterion, as explained in Section 2. We focus on whether the least-preferred candidate wins a seat.…”