Belief Update as Social Choice

Abstract

Dynamic epistemic-doxastic logics describe the new knowledge or new beliefs indexBelief of agents after some informational event has happened. Technically, this requires an update rule that turns a doxastic-epistemic modelM(recording the current information state of the agents) and a dynamic `event model' E (modeling the relevant, possibly complex event taking place right now) into a new model M{\texttimes}E, with in particular new epistemic accessibility and new doxastic plausibility relations. Concrete rules have been proposed for this purpose, and they work well in examples, and generate complete logics. But can such rules be justified in a deeper sense by appealing to underlying considerations? This technical Note proposes a way of thinking about this, by making a connection between belief revision and social choice theory, broadly construed. Our analysis mixes the updates proposed by Baltag {\&} Smets Baltag and Smets (2008) in dynamic epistemic logic with the framework of Andr'eka, Ryan {\.A} Schobbens Andr{\&}eka et al (2002) for merging of binary relations. Reasonable social choice-like postulates turn out to leave very few candidates for update rules. In particular, we show how `Priority Update' for new plausibility relations can be viewed as a process of social choice between the various signals that make up an agent over time. We also discuss how our style of analysis might be extended.