In this paper we study several monotonicity axioms in approval-based multi-winner voting rules. We consider monotonicity with respect to the support received by the winners and also monotonicity in the size of the committee. Monotonicity with respect to the support is studied when the set of voters does not change and when new voters enter the election. For each of these two cases we consider a...

The concept of a monotone operator — which covers both linear positive semi-definite operators and subdifferentials of convex functions — is fundamental in various branches of mathematics. Over the last few decades, several stronger notions of monotonicity have been introduced: Gossez’s maximal monotonicity of dense type, Fitzpatrick and Phelps’s local maximal monotonicity, and Simons’s monoton...