Collective Belief Revision

Abstract

In this article, we study the dynamics of collective beliefs. As a first step, we formulate David Westlund’s Principle of Collective Change (PCC) —a criterion that characterizes the evolution of collective knowledge— in the realm of belief revision. Thereafter, we establish a number of unsatisfiability results pointing out that the widely-accepted revision operators of Alchourrón, Gärdenfors and Makinson, combined with fundamental types of merging operations —including the ones proposed by Konieczny and Pino Pérez as well as Baral et al.— collide with the PCC. These impossibility results essentially extend in the context of belief revision the negative results established by Westlund for the operations of contraction and expansion. At the opposite of the impossibility results, we also establish a number of satisfiability results, proving that, under certain (rather strict) requirements, the PCC is indeed respected for specific merging operators. Overall, it is argued that the PCC is a rather unsuitable property for characterizing the process of collective change. Last but not least, mainly in response to the unsatisfactory situation related to the PCC, we explore some alternative criteria of collective change, and evaluate their compliance with belief revision and belief merging.