Systematic judgment aggregators: An algebraic connection between social and logical structure

2009/01/01 by Daniel Eckert, Eckert, Daniel, Frederik Herzberg +1
Computer Science · Economics, Econometrics and Finance · #Bayesian Modeling and Causal Inference #Boolean homorphism #Game Theory and Voting Systems #Judgment aggregation #Logic, Reasoning, and Knowledge #social structure #ultraproduct

paper · doi:10.4230/dagsemproc.09351.9

openalex publication_date 2009/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present several results that show that systematic (complete) judgment aggregators can be viewed as both (2-valued) Boolean homomorphisms and as syntatic versions of reduced (ultra)products. Thereby, Arrovian judgment aggregators link the Boolean algebraic structures of (i) the set of coalitions (ii) the agenda, and (iii) the set of truth values of collective judgments. Since filters arise naturally in the context of Boolean algebras, these findings provide an explanation for the extraordinary effectiveness of the filter method in abstract aggregation theory.

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