Judgment aggregators and Boolean algebra homomorphisms

Herzberg F (2010)
JOURNAL OF MATHEMATICAL ECONOMICS 46(1): 132-140.

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Abstract / Bemerkung
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. (C) 2009 Elsevier B.V. All rights reserved.
Erscheinungsjahr
Zeitschriftentitel
JOURNAL OF MATHEMATICAL ECONOMICS
Band
46
Zeitschriftennummer
1
Seite
132-140
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Herzberg F. Judgment aggregators and Boolean algebra homomorphisms. JOURNAL OF MATHEMATICAL ECONOMICS. 2010;46(1):132-140.
Herzberg, F. (2010). Judgment aggregators and Boolean algebra homomorphisms. JOURNAL OF MATHEMATICAL ECONOMICS, 46(1), 132-140. doi:10.1016/j.jmateco.2009.06.002
Herzberg, F. (2010). Judgment aggregators and Boolean algebra homomorphisms. JOURNAL OF MATHEMATICAL ECONOMICS 46, 132-140.
Herzberg, F., 2010. Judgment aggregators and Boolean algebra homomorphisms. JOURNAL OF MATHEMATICAL ECONOMICS, 46(1), p 132-140.
F. Herzberg, “Judgment aggregators and Boolean algebra homomorphisms”, JOURNAL OF MATHEMATICAL ECONOMICS, vol. 46, 2010, pp. 132-140.
Herzberg, F.: Judgment aggregators and Boolean algebra homomorphisms. JOURNAL OF MATHEMATICAL ECONOMICS. 46, 132-140 (2010).
Herzberg, Frederik. “Judgment aggregators and Boolean algebra homomorphisms”. JOURNAL OF MATHEMATICAL ECONOMICS 46.1 (2010): 132-140.
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Judgment aggregators and Boolean algebra homomorphisms
Herzberg F (2009) Working Papers. Institute of Mathematical Economics; 414.
Bielefeld: Universität Bielefeld.