 Judgment aggregators and Boolean algebra homomorphismsJournal of Mathematical Economics, 2010, vol. 46, issue 1, 132-140 Abstract: The theory of Boolean algebras can be fruitfully applied to judgment aggregation: assuming universality, systematicity and a sufficiently rich agenda, there is a correspondence between (i) non-trivial deductively closed judgment aggregators and (ii) Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Furthermore, there is a correspondence between (i) consistent complete judgment aggregators and (ii) 2-valued Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Since the shell of such a homomorphism equals the set of winning coalitions and since (ultra)filters are shells of (2-valued) Boolean algebra homomorphisms, we suggest an explanation for the effectiveness of the (ultra)filter method in social choice theory. From the (ultra)filter property of the set of winning coalitions, one obtains two general impossibility theorems for judgment aggregation on finite electorates, even without assuming the Pareto principle. Keywords: Judgment; aggregation; Systematicity; Impossibility; theorems; Filter; Ultrafilter; Boolean; algebra; homomorphism (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:46:y:2010:i:1:p:132-140 Access Statistics for this article Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii More articles in Journal of Mathematical Economics from Elsevier |
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