Binary Aggregation with Integrity Constraints
Umberto Grandi, Ulle Endriss
Abstract:
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 makes
available useful techniques both to prove theoretical results, such as
a new impossibility theorem in preference aggregation, and to analyse
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 the
class of aggregation procedures of generalised dictatorships.