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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
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:
Publication status: Published in Mathematical Social Sciences, volume 64, issue 1, July 2012, pages 41–47
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)
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dr. Frederik Herzberg).
If references are entirely missing, you can add them using this form.