Unanimity consistency in model-based belief merging∗

The problem of the aggregation of inputs coming from different sources arises in several contexts. Examples are the combination of individual preferences (studied in social choice theory), opinions (judgment aggregation), and data (artificial intelligence). While a number of results are available in each of these disciplines, a question that has been addressed only recently is how similar these aggregation problems are, despite the different types of inputs they try to combine. In this paper we consider aggregation problems that can be expressed in a Boolean-logic framework. The approaches developed so far are bounded to the combination of the individuals’ explicitly stated propositions into a collective one. We argue instead that the combination of information needs to be extended to the set of entailed sentences. We therefore introduce a new condition (called unanimity consistency condition), stating that all the unanimously entailed sentences at the individual level should be preserved at the collective level. Finally, it is shown that recent findings in judgment aggregation imply an impossibility result for an aggregation procedure that satisfies our unanimity consistency condition. ∗A preliminary version of this paper as “Pareto consistency in a model-based perspective on judgment aggregation” appeared in G. Bonanno, W. van der Hoek, M. Wooldridge (eds.), Proceedings of LOFT 06, University of Liverpool, UK, 169–176, 2006.