Protocols for Belief Merge: Reaching Agreement via Communication

We investigate the issue of reaching doxastic agreement among the agents of a group by ‘sharing’ information via successive acts of sincere, persuasive and public communication within the group. The topic relates to ‘preference aggregation’ in Social Choice theory, where the problem is to find a natural and fair merge operation for aggregating the agents' preferences into a single group preference. In this paper we study this topic within the setting of Dynamic Epistemic Logic (DEL) and its recent extensions to belief revision theory. First we interpret the agents' preference relations as ‘doxastic preferences’ or ‘doxastic plausibility orders’. Using these plausibility structures, we can express several types of relevant doxastic attitudes: ranging from an agent's simple beliefs and conditional beliefs to her defeasible knowledge and irrevocable knowledge. Next, we model communication via a series of doxastic/epistemic actions that affect the agent's plausibility structures. Because these structures can change in different ways, a group of agents has to adopt a specific communication protocol in order to aggregate their doxastic attitudes. We study the type of merges that are realizable via specific communication protocols and we highlight important factors which may influence the result, such as ‘the order of the speakers’, or the listeners' doxastic attitudes towards the speakers (i.e. their opinions concerning the reliability of the incoming information).