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

Listed author(s):
  • Herzberg, Frederik

    (Center for Mathematical Economics, Bielefeld University)

  • Eckert, Daniel

    (Center for Mathematical Economics, Bielefeld University)

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.

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File URL: https://pub.uni-bielefeld.de/download/1900253/2319751
File Function: First Version, 2009
Download Restriction: no

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

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Date of creation: 03 Nov 2010
Handle: RePEc:bie:wpaper:424
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