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

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Author Info

  • Frederik Herzberg

    ()
    (Institute of Mathematical Economics, Bielefeld University)

  • Daniel Eckert

    (Institute of Public Economics, Graz 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 generalised Kirman-Sondermann correspondence as well as a dictatorial impossibility result follow.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-424.pdf
File Function: First version, 2009
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 424.

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Length: 13 pages
Date of creation: Nov 2009
Date of revision:
Publication status: Published in Mathematical Social Sciences, volume 64, issue 1, July 2012, pages 41–47
Handle: RePEc:bie:wpaper:424

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Related research

Keywords: Arrow-type preference aggregation; judgment aggregation; systematicity; model theory; first-order predicate logic; filter; ultrafilter; reduced product; ultraproduct;

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