General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence - Frederik Herzberg; Daniel Eckert (Bielefeld University, Institute of Mathematical Economics (IMW), 2009)
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.
urn:nbn:de:hbz:361-15937
Keywords: D71; 330; Arrow-type preference aggregation; Judgment aggregation; Systematicity; Model theory; First-order predicate logic; Filter; Ultrafilter; Nutzenfunktion; Präferenztheorie; Aggregation; Soziale Wohlfahrtsfunktion; Unmöglichkeitstheorem; Theorie