Does a least-preferred candidate win a seat? A comparison of three electoral systems

In this paper, the differences between two variations of proportional representation (PR), open-list PR and closed-list PR, are analyzed in terms of their ability to accurately reflect voter preference. The single nontransferable vote (SNTV) is also included in the comparison as a benchmark. We construct a model of voting equilibria with a candidate who is least preferred by voters in the sense that replacing the least-preferred candidate in the set of winners with any loser is Pareto improving, and our focus is on whether the least-preferred candidate wins under each electoral system. We demonstrate that the least-preferred candidate never wins under the SNTV, but can win under open-list PR, although this is less likely than winning under closed-list PR.