François Durand, Antonin Macé* and Matías Núñez

This article was originally published in the May 2021 edition of the 5 papers…in 5 minutes.

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How can we organise elections so as to end up with a winner who represents most closely the voters’ preferences? While majority rule seems like the best way to decide between two candidates, the choice of voting rules becomes trickier when it comes to deciding between three or more candidates.

In this article, Durand, Macé and Núñez compare two main voting rules: the plurality system, in which each voter can vote for only one candidate, and the approval system, in which they can vote for as many candidates as they want (1). The plurality rule is the most widespread, used for example in the UK (in a first-past-the-post system) and in France (in the case of a three-way contest in the second round). But approval voting, invented 50 years ago, is beginning to be adopted in the US. The plurality rule creates incentives for “useful” or “tactical” voting, wherein electors have an interest in voting for a candidate they consider “serious” in order to make their vote carry more weight in the election, and are ready to give up on their favourite candidate. This results in self-fulfilling prophecies: if two candidates are considered serious, then each voter has a strategic interest in voting for their favourite candidate, and the original belief is validated. Thus, under the plurality system, the elected candidate does not depend simply on voters’ preferences but also, often, on voters’ beliefs about who are “serious” candidates. Approval voting creates different incentives: voters always have an interest in voting for the candidate they truly prefer, and they also vote for another candidate if their preferred choice is not considered serious, or if they like the other candidate enough. With these incentives, it is theoretically possible to elect the “Condorcet winner”, that is, the candidate who best represents the voters because he would beat any other candidate in a two-way race. To know whether this theoretical possibility occurs in practice, the authors ran a computer simulation of an electoral campaign: the voters reacted to a series of surveys, which recorded the changes. The results of these simulations speak clearly: in the approval voting system, it is always the Condorcet winner who ends up being elected, while with the plurality system, who is elected depends strongly on the initial surveys. In other words, the approval voting rule is better at translating voters’ preferences than the plurality rule. Moreover, the best performance of the approval voting rule is highly robust: it remains valid for other normative criteria and it is also maintained if only some electors vote tactically while others vote for their favourite candidate. These results confirm the findings of experimental studies that have revealed the interest and the simplicity of the approval voting system (2).

Finally, out of curiosity, the authors studied a third rule: what happens if the voters must vote against rather than for a candidate? This rule, called anti-plurality, seems very unstable: if two candidates are considered serious, then everyone has an interest in voting against the candidate they like the least among the two, and the belief is thus disproved. This instability means that every candidate, even the worst, has a non-negligible chance of being elected. There are, then, good reasons not to adopt this voting system in practice.

(1) The candidates are “approved” by voters and it is the one who receives the most approvals who is elected
(2) Jean-François Laslier (2019). Voter autrement. Éditions rue d’Ulm.



Original title of the article: Voter coordination in elections: a case for approval voting

Published in: PSE working paper n°2021-15

Available at

Credits (picture): Bibit Unggul – Shutterstock

* PSE Member