Belief Merging versus Judgment Aggregation

Abstract

The problem of aggregating pieces of propositional information coming from several agents has given rise to an intense research activity. Two distinct theories have emerged. On the one hand, belief merging has been considered in AI as an extension of belief revision. On the other hand, judgment aggregation has been developed in political philosophy and social choice theory. Judgment aggregation focusses on some specific issues (represented as formulas and gathered into an agenda) on which each agent has a judgment, and aims at defining a collective judgment set (or a set of collective judgment sets). Belief merging considers each source of information (the belief base of each agent) as a whole, and aims at defining the beliefs of the group without considering an agenda. In this work the relationships between the two theories are investigated both in the general case and in the fully informed case when the agenda is complete (i.e. it contains all the possible interpretations). Though it cannot be ensured in the general case that the collective judgment computed using a rational belief merging operator is compatible with the collective judgment computed using a rational judgment aggregation operator, we show that some close correspondences between the rationality properties considered in the two theories exist when the agenda is complete.