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 majori- tarian 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 mod- elling 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.