An analytic logic of aggregation

Abstract

We present a modular approach to the logic of aggregated group preferences based on hybrid modal logic. The modularity of the system is twofold: 1) lifting preference relations between states to complex relations between propositions and 2) lifting individual preferences to group preferences. The preferences may be doxastic or proairetic, generating a logic of aggregated belief or aggregated desire, respectively, using a specific aggregation policy known as 'lexicographic re-ordering'. Each agent and each group of agents has an associated modal operator representing their preferences between states. The addition of the existential modality and nominals allows us to produce, first, a Hilbert-style axiomatization of the logic and then a more thorough analysis of inference using a Gentzen-style sequent calculus, in which the role of each operator is revealed. © 2009 Springer Berlin Heidelberg.