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