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

Authors Daniel Eckert, Frederik Herzberg



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Daniel Eckert
Frederik Herzberg

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Daniel Eckert and Frederik Herzberg. Systematic judgment aggregators: An algebraic connection between social and logical structure. In Information processing, rational belief change and social interaction. Dagstuhl Seminar Proceedings, Volume 9351, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DagSemProc.09351.9

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.
Keywords
  • Judgment aggregation; social structure; Boolean homorphism; ultraproduct

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