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

Herzberg F, Eckert D (2009) Working Papers. Institute of Mathematical Economics; 424.
Bielefeld: Universität Bielefeld.

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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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Herzberg F, Eckert D. General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence. Working Papers. Institute of Mathematical Economics. Vol 424. Bielefeld: Universität Bielefeld; 2009.
Herzberg, F., & Eckert, D. (2009). General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence (Working Papers. Institute of Mathematical Economics, 424). Bielefeld: Universität Bielefeld.
Herzberg, F., and Eckert, D. (2009). General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence. Working Papers. Institute of Mathematical Economics, 424, Bielefeld: Universität Bielefeld.
Herzberg, F., & Eckert, D., 2009. General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence, Working Papers. Institute of Mathematical Economics, no.424, Bielefeld: Universität Bielefeld.
F. Herzberg and D. Eckert, General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence, Working Papers. Institute of Mathematical Economics, vol. 424, Bielefeld: Universität Bielefeld, 2009.
Herzberg, F., Eckert, D.: General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence. Working Papers. Institute of Mathematical Economics, 424. Universität Bielefeld, Bielefeld (2009).
Herzberg, Frederik, and Eckert, Daniel. General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence. Bielefeld: Universität Bielefeld, 2009. Working Papers. Institute of Mathematical Economics. 424.
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