Aggregation of binary evaluations for truth-functional agendas

• Published in: Social choice and welfare Vol. 32; no. 2; pp. 221 - 241
• Main Authors: Dokow, Elad, Holzman, Ron
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Science + Business Media 01.02.2009; Springer-Verlag; Springer Nature B.V
• Subjects: Aggregation; Classification; Coordinate systems; Decision making; Dictators; Dictatorship; Economic analysis; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Game Theory; Grammatical clauses; International Political Economy; Judgement; Judges; Logic; Logical impossibility; Logical theorems; Original Paper; Pareto optimum; Public Finance; Search services; Social and Behav. Sciences; Social Policy; Studies; Subjectivity; Truth value; Vertices; Welfare economics; Working papers; Atomic Proposition; Consistent Evaluation; Logical Consistency; Agenda Condition; Impossibility Theorem
• ISSN: 0176-1714; 1432-217X
• DOI: 10.1007/s00355-008-0320-1

In the problem of judgment aggregation, a panel of judges has to evaluate each proposition in a given agenda as true or false, based on their individual evaluations and subject to the constraint of logical consistency. We elaborate on the relation between this and the problem of aggregating abstract binary evaluations. For the special case of truth-functional agendas we have the following main contributions: (1) a syntactical characterization of agendas for which the analogs of Arrow's aggregation conditions force dictatorship; (2) a complete classification of all aggregators that satisfy those conditions; (3) an analysis of the effect of weakening the Pareto condition to surjectivity.