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

Frederik Herzberg and Daniel Eckert ()

No 424, Center for Mathematical Economics Working Papers from 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.

Keywords: Systematicity; Arrow-type preference aggregation; Judgment aggregation; Ultrafilter; First-order predicate logic; Model theory; Filter (search for similar items in EconPapers)
Date: 2010-11-03
New Economics Papers: this item is included in nep-cdm, nep-hpe and nep-mic
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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:424

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