Impossibility results for infinite-electorate abstract aggregation rules
| Autor: | Daniel Eckert, Frederik Herzberg |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Model theory
Arrow-type preference aggregation Existential quantification Ultrafilter Unmöglichkeitstheorem D71 Aggregation ultraproduct ddc:330 Nutzenfunktion Impossibility Filter (mathematics) Mathematics Discrete mathematics filter Reduced product first-order predicate logic Soziale Wohlfahrtsfunktion Ultraproduct First-order logic Präferenztheorie judgment aggregation existential quantifier Philosophy model theory reduced product Mathematical economics Theorie ultrafilter |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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