Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/43798 
Year of Publication: 
2009
Series/Report no.: 
Working Papers No. 427
Publisher: 
Bielefeld University, Institute of Mathematical Economics (IMW), Bielefeld
Abstract: 
It is well known that the literature on judgment aggregation inherits the impossibility results from the aggregation of preferences that it generalises. This is due to the fact that the typical judgment aggregation problem induces an ultrafilter on the the set of individuals, as was shown in a model theoretic framework by Herzberg and Eckert (2009), generalising the Kirman-Sondermann correspondence and extending the methodology of Lauwers and Van Liedekerke (1995). In the finite case, dictatorship then immediately follows from the principality of an ultrafilter on a finite set. This is not the case for an infinite set of individuals, where there exist free ultrafilters, as Fishburn already stressed in 1970. The main problem associated with free ultrafilters in the literature on aggregation problems is however, the arbitrariness of their selection combined with the limited anonymity they guarantee (which already led Kirman and Sondermann (1972) to speak about invisible dictators). Following another line of Lauwers and Van Liedekerke's (1995) seminal paper, this note explores another source of impossibility results for free ultrafilters: The domain of an ultraproduct over a free ultrafilter extends the individual factor domains, such that the preservation of the truth value of some sentences by the aggregate model - if this is as usual to be restricted to the original domain - may again require the exclusion of free ultrafilters, leading to dictatorship once again.
Subjects: 
Arrow-type preference aggregation
judgment aggregation
model theory
first-order predicate logic
filter
ultrafilter
reduced product
ultraproduct
existential quantifier
JEL: 
D71
Document Type: 
Working Paper

Files in This Item:
File
Size
324.24 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.