Judgment aggregators and Boolean algebra homomorphisms

Frederik Herzberg

No 414, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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.

Keywords: Systematicity; Judgment aggregation; Impossibility theorems; Filter; Boolean algebra homomorphism; Ultrafilter (search for similar items in EconPapers)
Date: 2010-11-03
New Economics Papers: this item is included in nep-cdm
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Citations: View citations in EconPapers (3)

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https://pub.uni-bielefeld.de/download/1900280/2319752 First Version, 2009 (application/pdf)

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Journal Article: Judgment aggregators and Boolean algebra homomorphisms (2010)
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