Judgment aggregators and Boolean algebra homomorphisms
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.
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| Date of creation: | 03 Nov 2010 |
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| Handle: | RePEc:bie:wpaper:414 |
| Contact details of provider: | Postal: Postfach 10 01 31, 33501 Bielefeld Phone: +49(0)521-106-4907 Web page: http://www.imw.uni-bielefeld.de/ More information through EDIRC
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References listed on IDEAS
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- Franz Dietrich & Christian List, 2008.
"Judgment aggregation without full rationality,"
Social Choice and Welfare,
Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 15-39, June.
- Dietrich Franz & List Christian, 2007. "Judgment aggregation without full rationality," Research Memorandum 023, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Dietrich Franz & List Christian, 2006. "Judgment aggregation without full rationality," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Franz Dietrich & Philippe Mongin, 2010.
"The premiss-based approach to judgment aggregation,"
LSE Research Online Documents on Economics
27896, London School of Economics and Political Science, LSE Library.
- Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
- Dietrich Franz & Mongin Philippe, 2008. "The Premiss-Based Approach to Judgment Aggregation," Research Memorandum 013, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Philippe Mongin & Franz Dietrich, 2010. "The Premiss-Based Approach to Judgment Aggregation," Post-Print hal-00528387, HAL.
- Philippe Mongin, 2011.
"Judgment Aggregation,"
Working Papers
hal-00625434, HAL.
- Philippe Mongin, 2011. "Judgment aggregation," Working Papers hal-00579346, HAL.
- Mongin, Philippe, 2011. "Judgment aggregation," Les Cahiers de Recherche 942, HEC Paris.
- Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
- Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, Oxford University Press, vol. 89(3), pages 456-469.
- Christian Klamler & Daniel Eckert, 2009. "A simple ultrafilter proof for an impossibility theorem in judgment aggregation," Economics Bulletin, AccessEcon, vol. 29(1), pages 319-327.
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