Binary Aggregation with Integrity Constraints
Umberto Grandi and Ulle Endriss
Binary aggregation studies problems in which individuals express yes/no choices over a number of possibly correlated issues, and these individual choices need to be aggregated into a collective choice. We show how several classical frameworks of Social Choice Theory, particularly preference and judgment aggregation, can be viewed as binary aggregation problems by designing an appropriate set of integrity constraints for each specific setting. We explore the generality of this framework, showing that it provides a useful technique both for proving theoretical results, such as a new impossibility theorem in preference aggregation, and for the analysis of practical problems, such as the characterisation of safe agendas in judgment aggregation in a syntactic way. The framework also allows us to formulate a general definition of paradox that is independent of the domain under consideration, which gives rise to the study of a new class of aggregation procedures of generalised dictatorships.