Some Consistency Results for Many-Valued Judgment Aggregation

Abstract

Judgment aggregation (JA) poses the problem of finding a consistent collective judgment for a set of logically related propositions based on judgments of individuals. There are well-known impossibility results for classical JA, which have recently been extended to non-classical logics, including many-valued logics. We complement these negative results with some positive results. We first study average aggregation, which is arguably the most natural rule in a many-valued setting, and show how to generate consistent aggregated judgments in either Kleene-Zadeh or Łukasiewicz logic for certain types of agendas. We then generalize these results to a wider class of aggregation rules applied to judgments using Kleene-Zadeh and Gödel logic by imposing a restricted systematicity condition. Finally, we introduce median aggregation and show a possibility result that applies to arbitrary many-valued logics by generalizing List’s profile condition of unidimensional alignment to a many-valued setting.