Abstract
Proponents of proportional electoral rules often argue that majority rule depresses turnout and may lower welfare due to the ‘tyranny of the majority’ problem. The present paper studies the impact of electoral rules on turnout and social welfare. We analyze a model of instrumental voting where citizens have private information over their individual cost of voting and over the alternative they prefer. The electoral rule used to select the winning alternative is a combination of majority rule and proportional rule. Results show that the above arguments against majority rule do not hold in this set up. Social welfare and turnout increase with the weight that the electoral rule gives to majority rule in a close election, while they are independent of the electoral rule when the expected size of the minority tends to zero. However, more proportional rules can increase turnout within the minority group; this effect is stronger the smaller the minority group. We provide a general version of the competition effect, i.e. that turnout in close elections is higher than in biased elections, independently of the systems adopted in the two cases.
Highlights
In May 2011, the UK held a referendum on its electoral rule
We show that in biased elections, that is, when the expected size of the minority group tends to zero, proportional rule is not welfare enhancing either, because social welfare is independent of the electoral rule that is adopted
We have studied how di¤erent electoral rules a¤ect turnout and social welfare
Summary
In May 2011, the UK held a referendum on its electoral rule. The Liberal Democrat party and the civic initiative “Make My Vote Count”campaigned in favor of abandoning the ...rst-past-the-post (FPTP) system, with the long run goal of shifting to a proportional representation (PR) system. The wasted votes phenomenon is worrisome in multi-party systems and was especially acute in the UK 2005 national election, when more than half of the votes were cast in favor of losing candidates This concern relates to the tyranny of the majority problem (Madison et al, 1788; Mill, 1861), that is, the fact that under majority rule just above half of the electorate might impose its preferred alternative on the other half.. The magnitude of that impact is relatively small As it turns out, when the minority group is expected to be large, magnitude is a much stronger force than frequency, resulting in majority providing stronger incentives to vote than proportional rule. The collective action problem faced by the majority group in this type of elections is so severe that, for any electoral rule, minority supporters vote more often than majority supporters We refer to this result as the generalized underdog e¤ect. We chose to maintain in the text only those proofs that help to understand the main results by providing their intuitions, while we relegated the more technical proofs to the Appendix
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