Judgment aggregators and Boolean algebra homomorphisms

Herzberg F (2009) Working Papers. Institute of Mathematical Economics; 414.
Bielefeld: Universität Bielefeld.

Diskussionspapier | Veröffentlicht | Englisch
 
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Herzberg, Frederik
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.
Stichworte
Systematicity; Judgment aggregation; Impossibility theorems; Filter; Boolean algebra homomorphism; Ultrafilter
Erscheinungsjahr
2009
Band
414
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/1900280

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Herzberg F. Judgment aggregators and Boolean algebra homomorphisms. Working Papers. Institute of Mathematical Economics. Vol 414. Bielefeld: Universität Bielefeld; 2009.
Herzberg, F. (2009). Judgment aggregators and Boolean algebra homomorphisms (Working Papers. Institute of Mathematical Economics, 414). Bielefeld: Universität Bielefeld.
Herzberg, F. (2009). Judgment aggregators and Boolean algebra homomorphisms. Working Papers. Institute of Mathematical Economics, 414, Bielefeld: Universität Bielefeld.
Herzberg, F., 2009. Judgment aggregators and Boolean algebra homomorphisms, Working Papers. Institute of Mathematical Economics, no.414, Bielefeld: Universität Bielefeld.
F. Herzberg, Judgment aggregators and Boolean algebra homomorphisms, Working Papers. Institute of Mathematical Economics, vol. 414, Bielefeld: Universität Bielefeld, 2009.
Herzberg, F.: Judgment aggregators and Boolean algebra homomorphisms. Working Papers. Institute of Mathematical Economics, 414. Universität Bielefeld, Bielefeld (2009).
Herzberg, Frederik. Judgment aggregators and Boolean algebra homomorphisms. Bielefeld: Universität Bielefeld, 2009. Working Papers. Institute of Mathematical Economics. 414.
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2019-09-06T08:57:10Z
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Judgment aggregators and Boolean algebra homomorphisms
Herzberg F (2010)
JOURNAL OF MATHEMATICAL ECONOMICS 46(1): 132-140.

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