Abstract
We analyze single binary-choice voting rules and identify the presence of the No-Show paradox in this simple setting, as a consequence of specific turnout or quorum conditions that are included in actual rules. Since these conditions are meant to ensure a representative outcome, we formalize this concern and reach our main result: no voting rule can ensure representation if abstention is possible, unless restrictive assumptions are made on the preference domain of abstainers. We then focus on the main referendum systems and show that appropriate restrictions do make them compatible with representation. The main purpose of our paper is, however, to provide a tool for referendum design: rather than imposing arbitrary restrictions on the preference domain of non-voters, we recommend instead that a conscious choice be made on how abstention is to be interpreted and that this choice be used to derive the corresponding referendum rule.
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The idea for this paper started with some jocose but insightful notes written by José João Marques da Silva at the time of the first referendum held in Portugal (1998). When José João passed away in August 2000, ISEG lost a bright, interested and friendly scholar. May we dedicate this paper to his memory. This paper was presented at the 2002 Annual Meeting of the Public Choice Society and Economic Science Association, San Diego, CA and a preliminary version was presented at the 2001 Annual Meeting of the European Public Choice Society, Paris. We would like to thank Mathew Braham, Moshé Machover, Eric Maskin, Vincent Merlin, Hannu Nurmi, Katri Sieberg, Frank Steffen, and two anonymous referees for helpful comments. The usual proviso applies.
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Côrte-Real, P., Pereira, P. The voter who wasn’t there: Referenda, representation and abstention. Soc Choice Welfare 22, 349–369 (2004). https://doi.org/10.1007/s00355-003-0219-9
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DOI: https://doi.org/10.1007/s00355-003-0219-9