Superset-robust collective choice rules

A new property of collective choice rules that we refer to as superset robustness is introduced, and we employ it in several characterization results. The axiom requires that if all individual preference orderings expand weakly (in the sense of set inclusion), then the corresponding social preference relation must also expand weakly. In other words, if a given profile is changed by adding instances of weak preference to some individual relations, then the social weak preference relation for the expanded profile must contain the social weak preference relation for the original—that is, the social relation cannot contract in response to the addition of pairs to the individual relations. We begin by examining social welfare functions (that is, collective choice rules such that the resulting social preferences are orderings) and then move on to rules that generate transitive (but not necessarily complete) social rankings. The remaining results of the paper focus on Suzumura-consistent collective choice rules. In all of these cases, it turns out that the property of superset robustness is closely related to classes of agreement-based collective choice rules. These are rules such that the social relation is determined by collecting the pairs on whose relative rankings the members of the decisive sets agree.