Judgment aggregators and Boolean algebra homomorphisms
AbstractThe 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 the Pareto principle.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 414.
Length: 12 pages
Date of creation: Feb 2009
Date of revision:
judgment aggregation; systematicity; impossibility theorems; filter; ultrafilter; Boolean algebra; homomorphism;
Other versions of this item:
- Herzberg, Frederik, 2010. "Judgment aggregators and Boolean algebra homomorphisms," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 132-140, January.
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Franz Dietrich & Christian List, 2008.
"Judgment aggregation without full rationality,"
Social Choice and Welfare,
Springer, vol. 31(1), pages 15-39, June.
- 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).
- 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).
- 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.
- Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
- Brown, Donald J, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, MIT Press, vol. 89(3), pages 456-69, August.
- Mongin, Philippe, 2012.
"The doctrinal paradox, the discursive dilemma, and logical aggregation theory,"
37752, University Library of Munich, Germany.
- Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
- Mongin, Philippe & Dietrich, Franz, 2011. "An interpretive account of logical aggregation theory," Les Cahiers de Recherche 941, HEC Paris.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dr. Frederik Herzberg).
If references are entirely missing, you can add them using this form.