Complexity of Judgment Aggregation
Ulle Endriss, Umberto Grandi, Daniele Porello

Abstract:
We analyse the computational complexity of three problems in judgment
aggregation: (1) computing a collective judgment from a profile of
individual judgments (the winner determination problem); (2) deciding
whether a given agent can influence the outcome of a judgment
aggregation procedure in her favour by reporting insincere judgments
(the strategic manipulation problem); and (3) deciding whether a given
judgment aggregation scenario is guaranteed to result in a logically
consistent outcome, independently from what the judgments supplied by
the individuals are (the problem of the safety of the agenda). We
provide results both for specific aggregation procedures (the quota
rules, the premise-based procedure, and a distance-based procedure)
and for classes of aggregation procedures characterised in terms of
fundamental axioms.