Abstract
We say that an alternative is socially acceptable if the number of individuals who rank it among their most preferred half of the alternatives is at least as large as the number of individuals who rank it among the least preferred half. A Condorcet winner may not necessarily be socially acceptable. However, if preferences are single-peaked, single-dipped, or satisfy the single-crossing property, any Condorcet winner is socially acceptable. We identify maximal families of preferences that guarantee that Condorcet winners are socially acceptable.
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Notes
We adopt the convention of denoting the preference relation \(a \succ b \succ c\succ d\) by abcd.
Single-peaked preferences were introduced by Black (1948).
For any two alternatives, \(a,b\in A\), \(a<b\) means \(a\le b\) and not \(b\le a\).
For any two preferences, \(\succ ,\succ '\in \mathcal P\), \(\succ \sqsubset \succ 'b\) means \(\succ \sqsubseteq \succ '\) and not \(\succ '\sqsubseteq \succ \).
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We thank three anonymous referees for their helpful and generous comments. The first author acknowledges financial support from Université de Lyon (project INDEPTH Scientific Breakthrough Program of IDEX Lyon) within the program Investissement d’Avenir (ANR-16-IDEX-0005).
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Mahajne, M., Volij, O. Condorcet winners and social acceptability. Soc Choice Welf 53, 641–653 (2019). https://doi.org/10.1007/s00355-019-01204-7
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DOI: https://doi.org/10.1007/s00355-019-01204-7