Update Monotone Preference Rules

Collective decisions are modeled by preference correspondences (rules). In particular, we focus on a new condition: “update monotonicity” for preference rules. Although many so-called impossibility theorems for the choice rules are based on -or related to- monotonicity conditions, this appealing condition is satisfied by several non-trivial preference rules. In fact, in case of pairwise, Pareto optimal, neutral, and consistent rules; the Kemeny-Young rule is singled out by this condition. In case of convex valued, Pareto optimal, neutral and replication invariant rules; strong update monotonicity implies that the rule equals the union of preferences which extend all preference pairs unanimously agreed upon by k agents, where k is related to the number of alternatives and agents. In both cases, it therewith provides a characterization of these rules.