[Séminaire Caen] Simple Monotonicity: A Microscopic Analysis

Abstract:
Monotonicity is one of the basic and critical axioms in the literature. Suppose that x is chosen by a voting rule F at some preference profile and x is improved with respect to other alternatives by some voter, while all other things remain as the same. In a broad sense, the monotonicity axiom requires that the alternative x is chosen after this improvement. In this study, we address the monotonicity axiom in more details. First, we define three versions of monotonicity M1, M2, M3, based whether x is uniquely chosen (M1), whether the set of alternatives chosen is a subset of previous choice set (M2) or not (M3). Next, we specify a rate  indicating how much an alternative is improved. For each version, we propose a more refined definition of these monotonicities based on this rate, denoting - monotonicity. For instance, the plurality rule satisfies M2 monotonicity for any  , but M1 monotonicity if and only if =1. Our aim is to study and classify several voting rules employing - monotonicity.
(joint with Ali Özkes and Remzi Sanver)