Majoritarian Group Actions

In this paper, we introduce a logic to reason about group actions for groups that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The logic of action that we use here for modelling group actions is based on a substructural propositional logic that allows for preventing inconsistent outcome. Agency is modeled by means of a "bringing-it-about" modal logic with coalitions. We show that, in this way, it is possible to obtain a consistent model of agency of groups that are defined in an aggregative manner.