Social acceptability and the majoritarian compromise rule

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.