Logics for modelling collective attitudes

TL;DR

This paper introduces new logics based on substructural propositional logic to model collective attitudes like beliefs and desires, addressing issues of irrationality in majority rule aggregation.

Contribution

It presents novel logical frameworks that enable consistent modeling of collective attitudes by circumventing known irrational outcomes of majority-based aggregation.

Findings

The proposed logics can model collective attitudes consistently.

They avoid irrational outcomes associated with majority rule.

The framework supports basic principles of collective propositional attitudes.

Abstract

We introduce a number of logics to reason about collective propositional attitudes 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 proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal modalities to ensure a number of basic principles. In this way, a viable consistent modelling of collective attitudes is obtained.