@techreport{Herzberg2009General,
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.},
address = {Bielefeld},
author = {Frederik Herzberg and Daniel Eckert},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {D71; 330; Arrow-type preference aggregation; Judgment aggregation; Systematicity; Model theory; First-order predicate logic; Filter; Ultrafilter; Nutzenfunktion; Pr\"{a}ferenztheorie; Aggregation; Soziale Wohlfahrtsfunktion; Unm\"{o}glichkeitstheorem; Theorie},
language = {eng},
note = {urn:nbn:de:hbz:361-15937},
number = {424},
publisher = {Inst. of Mathematical Economics, IMW},
title = {General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence},
type = {Working papers // Institute of Mathematical Economics},
url = {http://hdl.handle.net/10419/43824},
year = {2009}
}
