Stable Rules for Electing Committees and Divergence on Outcomes

For three-candidate elections, this paper focuses on the relationships that exist between three stable rules for committee elections and the classical rules from which each of these stable rules are adapted. When selecting committees, a voting rule is said to be stable if it always elects a fixed-size subset of candidates such that there is no candidate in this set that is majority dominated by a candidate outside (Barberà and Coelho in Soc Choice Welfare 31:79–96, 2008; Coelho in Understanding, evaluating and selecting voting rules through games and axioms, 2004). There are some cases where a committee selected by a stable rule may differ from the committee made by the best candidates of the corresponding classical rule from which this stable rule is adapted. We call this the divergence on outcomes. We characterize all the voting situations under which this event is likely to occur. We also evaluate the likelihood of this event using the impartial anonymous culture assumption. As a consequence of our analysis, we highlight a strong connection between three Condorcet consistent rules: the Dodgson rule, the Maximin rule and the Young rule.