Some Consistency Criteria for Many-Valued Judgment Aggregation

Abstract

Classical judgment aggregation has produced several well-known impossibility results that extend to a variety of logics, including many-valued logics. In this paper, we aim to complement these negative results by providing some positive ones, which we develop in response to an analysis of the discursive dilemma. Specifically, we investigate the use of the averaging operator, which is arguably the most natural operator in a many-valued setting, to generate consistent aggregated judgments in either Kleene-Zadeh or Łukasiewicz logic. Our results show that under certain conditions, the averaging operator can yield consistent aggregated judgments for specific types of agendas and judgment profiles.