Social acceptability of Condorcet committees

Abstract

We define and examine the concept of social acceptability of committees, in multi-winner elections context. We say that a committee is socially acceptable if each member in this committee is socially acceptable, i.e., the number of voters who rank her in their top half of the candidates is at least as large as the number of voters who rank her in the least preferred half, otherwise she is unacceptable. We focus on the social acceptability of Condorcet committees, where each committee member beats every nonmember by a majority, and we show that a Condorcet committee may be completely unacceptable, i.e., all its members are unacceptable. However, if the preferences of the voters are single-peaked or singlecaved and the committee size is not "too large" then a Condorcet committee must be socially acceptable, but if the preferences are single-crossing or group-separable, then a Condorcet committee may be socially acceptable but may not. Furthermore, we evaluate the probability for a Condorcet committee, when it exists, to be socially (un)acceptable under Impartial Anonymous Culture (IAC) assumption. It turns to be that, in general, Condorcet committees are significantly exposed to social unacceptability.. AbstractWe define and examine the concept of social acceptability of committees, in multi-winner elections context. We say that a committee is socially acceptable if each member in this committee is socially acceptable, i.e., the number of voters who rank her in their top half of the candidates is at least as large as the number of voters who rank her in the least preferred half, otherwise she is unacceptable.We focus on the social acceptability of Condorcet committees, where each committee member beats every non-member by a majority, and we show that a Condorcet committee may be completely unacceptable, i.e., all its members are unacceptable. However, if the preferences of the voters are single-peaked or single-caved and the committee size is not "too large" then a Condorcet committee must be socially acceptable, but if the preferences are single-crossing or group-separable, then a Condorcet committee may be socially acceptable but may not. Furthermore, we evaluate the probability for a Condorcet committee, when it exists, to be socially (un)acceptable under Impartial Anonymous Culture (IAC) assumption. It turns to be that, in general, Condorcet committees are significantly exposed to social unacceptability.

Social acceptability and the majoritarian compromise rule

“…The following results from Diss and Mahajne (2020) are useful properties of singlecaved preference relations that we will use later. Proof.…”

“…Diss and Mahajne, 2020) Let ≤ be a linear order on A and assume without loss of generality that a1 < • • • < a m .Let a, b, and c be any three alternatives such that a < b < c and let be a single-caved preference with respect to ≤. Then it holds that b a ⇒ c b and b c ⇒ a b.…”

Social Unacceptability for Simple Voting Procedures

“…Furthermore, Mahajne and Volij (2019) show that a socially acceptable candidate may not be a −Condorcet winner and they identify some restricted preference domains that guarantee that any −Condorcet winner is socially acceptable as a function of the threshold . Diss and Mahajne (2020) extend the concept of social acceptability to multi-winner elections, i.e., when the goal is to select a given group of candidates, and perform the same analysis as Mahajne and Volij (2019) in that context.…”

Combining Diversity and Excellence in Multiwinner Elections

“…A committee selection rule is stable if it always picks a weak Condorcet committee when such a committee exists. A weak Condorcet committee is a committee such that no member of that committee is defeated in pairwise majority comparisons by a candidate that does not belong to it (see, for instance,Bubboloni et al, 2020;Diss and Doghmi, 2016;Diss and Mahajne, 2020;Gehrlein, 1985).…”