Judgment aggregators and Boolean algebra homomorphisms

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

Journal Article | Published | English

No fulltext has been uploaded

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. (C) 2009 Elsevier B.V. All rights reserved.
Publishing Year
ISSN
PUB-ID

Cite this

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.
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.
This data publication is cited in the following publications:
This publication cites the following data publications:

Export

0 Marked Publications

Open Data PUB

Web of Science

View record in Web of Science®

Search this title in

Google Scholar