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General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence

Author

Listed:
  • Herzberg, Frederik

    (Center for Mathematical Economics, Bielefeld University)

  • Eckert, Daniel

    (Center for Mathematical Economics, Bielefeld University)

Abstract

This article proves a very general version of the Kirman-Sondermann [Journal of Economic Theory, 5(2):267-277, 1972] correspondence by extending the methodology of Lauwers and Van Liedekerke [Journal of Mathematical Economics, 24(3):217-237, 1995]. The paper first proposes a unified framework for the analysis of the relation between various aggregation problems and the social structure they induce, based on first-order predicate logic and model theory. Thereafter, aggregators satisfying Arrow-type rationality axioms are shown to be restricted reduced product constructions with respect to the filter of decisive coalitions; an oligarchic impossibility result follows. Under stronger assumptions, aggregators are restricted ultraproduct constructions, whence a generalized Kirman-Sondermann correspondence as well as a dictatorial impossiblity result follow.

Suggested Citation

  • Herzberg, Frederik & Eckert, Daniel, 2010. "General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence," Center for Mathematical Economics Working Papers 424, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:424
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    File URL: https://pub.uni-bielefeld.de/download/1900253/2319751
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    Keywords

    Systematicity; Arrow-type preference aggregation; Judgment aggregation; Ultrafilter; First-order predicate logic; Model theory; Filter;
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