Referendum Paradox for Party-List Proportional Representation
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Referendum Paradox for Party‑List Proportional Representation Hayrullah Dindar1 · Gilbert Laffond1 · Jean Lainé1,2 Accepted: 8 October 2020 © Springer Nature B.V. 2020
Abstract We consider two-tiers elections based on closed party-list proportional representation (PLPR), where party platforms involving multiple dichotomous issues are endogenously determined by their supporters’ preferences (via issue-wise simple majority voting). Assuming that voters compare platforms according to the criterion of the Hamming distance and provided a high enough number of voters and issues, we show that the outcome of PLPR may be Pareto dominated by the multiple referendum outcome defined as the issue-wise majority will in the whole electorate. We refer to this situation as the PLPR paradox. We characterize the set of party platforms for which the PLPR paradox is possible. We also investigate several restrictions upon voting situations that may be sufficient for avoiding the paradox. Keywords Proportional representation · Majority rule · Voting paradox JEL Classification D72
Authors are indebted to the editor and to a reviewer for valuable comments on an earlier draft. * Jean Lainé [email protected] Hayrullah Dindar [email protected] Gilbert Laffond [email protected] 1
Murat Sertel Center for Advanced Economic Studies, Istanbul Bilgi University, Istanbul, Turkey
2
Lirsa, Conservatoire National des Arts et Métiers, Paris, France
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1 Introduction Representative democracy combines two levels of choice, which respectively describe how citizens’ votes are transformed into assemblies, and how decisions are made within assemblies. A procedure widely used for electing assemblies is partylist proportional representation, where each political party makes a list involving as many candidates as positions to be filled, citizens vote for a single party, and each of the parties gets a proportion of seats consistent with its vote share. It is often claimed that party-list proportional representation (PLPR) is a voting procedure that is appropriate for a faithful accounting of the citizenry wills. Faithfulness can be given two meanings. The first is the ability of an assembly to embrace the full diversity of opinions within the country. The second is that assembly decisions can be regarded as the decisions of the country itself; that is, the assembly decisions should be identical (or at least close enough) to those which would emerge from direct democracy.1 It is often argued that PLPR is relevant according to the first meaning.2 By favoring the emergence of many parties, voters are more likely to find one that closely represents their political convictions. Supporters of a small party are likely to be represented by at least one member of parliament sharing their political views and convictions. This, in turn, may favor a significantly higher voter turnout. Other arguments in favor of PLPR are its ability to overcome the problem of gerrymandering and to complicate the pra
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