Axiomatizing collective judgment sets in a minimal logical language

Marc Pauly

pp. 233-250

in: Knowledge, rationality & action, Synthese 158 (2), 2007.

Abstract

We investigate under what conditions a given set of collective judgments can arise from a specific voting procedure. In order to answer this question, we introduce a language similar to modal logic for reasoning about judgment aggregation procedures. In this language, the formula (square varphi) expresses that(varphi) is collectively accepted, or that(varphi) is a group judgment based on voting. Different judgment aggregation procedures may be underlying the group decision making. Here we investigate majority voting, where(square varphi) holds if a majority of individuals accepts(varphi), consensus voting, where(square varphi) holds if all individuals accept(varphi), and dictatorship. We provide complete axiomatizations for judgment sets arising from all three aggregation procedures.