Abstract
We study the relationships between two well-known social choice concepts, namely the principle of social acceptability introduced by Mahajne and Volij (Soc Choice Welf 51(2):223–233, 2018), and the majoritarian compromise rule introduced by Sertel (Lectures notes in microeconomics, Bogazici University, 1986) and studied in detail by Sertel and Yılmaz (Soc Choice Welf 16(4):615–627, 1999). The two concepts have been introduced separately in the literature in the spirit of selecting an alternative that satisfies most individuals in single-winner elections. Our results in this paper show that the two concepts are so closely related that the interaction between them cannot be ignored. We show that the majoritarian compromise rule always selects a socially acceptable alternative when the number of alternatives is even and we provide a necessary and sufficient condition so that the majoritarian compromise rule always selects a socially acceptable alternative when the number of alternatives is odd. Moreover, we show that when we restrict ourselves to the three well-studied classes of single-peaked, single-caved, and single-crossing preferences, the majoritarian compromise rule always picks a socially acceptable alternative whatever the number of alternatives and the number of voters.
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Notes
This rule is called the HAHR (Half Accepted Half Rejected) rule. Its formal definition will be presented in the next section.
It is worth noting that Diss and Mahajne (2020) extended the concept of social acceptability to multi-winner elections and in that setup studied the social acceptability of any q-Condorcet committee (Gehrlein 1985), that is a subset of alternatives where every member of that subset is head-to-head preferred by at least a proportion \(q\in ]\frac{1}{2},1]\) of voters than any non-member alternative. See also Diss and Doghmi (2016), Gehrlein (1983) and Gehrlein and Lepelley (2011, 2017).
A preference relation will also be denoted by \(\succ \) if the specification of the voter i is unnecessary.
As noted before, Mahajne and Volij (2018) provided an axiomatic characterization of the only scoring SCR that always follows the social acceptability principle, namely the HAHR rule. Consequently, they show that SA(p) is non-empty for any profile p.
See footnote 5.
Note that if \(m=3\), any Condorcet winner is socially acceptable according to Mahajne and Volij (2019).
Sometimes single-caved preferences are also called single-dipped (e.g., Klaus et al. 1997).
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Mostapha Diss would like to acknowledge financial support from Région Bourgogne Franche-Comté within the program ANER 2021–2024 (project DSG). This article was presented in various conferences and workshops: The 2022 Meeting of the Society for Social Choice and Welfare, Mexico City, Mexico; the 17th European Meeting on Game Theory (SING17), Padova, Italy; RISLAB, University Mohammed VI Polytechnic, Rabat, Morocco; CRESE, University of Franche-Comté, Besançon, France. We thank all the participants for their comments. We also would like to thank Remzi Sanver and Abdelmonaim Tlidi for their valuable comments and useful advice on our manuscript.
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Diss, M., Gassi, C.G. & Moyouwou, I. Social acceptability and the majoritarian compromise rule. Soc Choice Welf 61, 489–510 (2023). https://doi.org/10.1007/s00355-023-01464-4
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DOI: https://doi.org/10.1007/s00355-023-01464-4