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Title:General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence PDF Logo
Authors:Herzberg, Frederik
Eckert, Daniel
Issue Date:2009
Series/Report no.:Working papers // Institute of Mathematical Economics 424
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.
Subjects:Arrow-type preference aggregation
Judgment aggregation
Systematicity
Model theory
First-order predicate logic
Filter
Ultrafilter
JEL:D71
Persistent Identifier of the first edition:urn:nbn:de:hbz:361-15937
Document Type:Working Paper
Appears in Collections:Working Papers, Institute of Mathematical Economics, Universität Bielefeld

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