Belief merging, judgment aggregation and some links with social choice theory

Abstract

In this paper we explore the relation between three areas: judgment aggregation, belief merging and social choice theory. Judgment aggregation studies how to aggregate individual judgments on logically interconnected propositions into a collective decision on the same propositions. When majority voting is applied to some propositions (the premises) it may however give a different outcome than majority voting applied to another set of propositions (the conclusion). Starting from this so-called doctrinal paradox, the paper surveys the literature on judgment aggregation (and its relation to preference aggregation), and shows that the application of a well known belief merging operator can dissolve the paradox. Finally, the use of distances is shown to establish a link between belief merging and preference aggregation in social choice theory.