General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence
AbstractThis 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 generalised Kirman-Sondermann correspondence as well as a dictatorial impossibility result follow.
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Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 424.
Length: 13 pages
Date of creation: Nov 2009
Date of revision:
Arrow-type preference aggregation; judgment aggregation; systematicity; model theory; first-order predicate logic; filter; ultrafilter; reduced product; ultraproduct;
Find related papers by JEL classification:
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-12-19 (All new papers)
- NEP-CDM-2009-12-19 (Collective Decision-Making)
- NEP-HPE-2009-12-19 (History & Philosophy of Economics)
- NEP-MIC-2009-12-19 (Microeconomics)
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