A possibility theorem on aggregation over multiple interconnected propositions
AbstractDrawing on the so-called `doctrinal paradox`, List and Pettit (2002a) have shown that, given an unrestricted domain condition, there exists no procedure for aggregating individual sets of judgments over multiple interconnected propositions into corresponding collective ones, where the procedure satisfies some minimal conditions similar to the conditions of Arrow`s theorem. I prove that we can avoid the paradox and the associated impossibility result by introducing an appropriate domain restriction: a structure condition, called unidimensional alignment, is shown to open up a possibiity result, similar in spirit to Black`s median voter theorem (1948). Specifically, I prove that, given unidimensional alignment, propositionwise majority voting is the unique procedure for aggregating individul sets of judgments into collective ones in accordance with the above mentioned minimal conditions.
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Bibliographic InfoArticle provided by Elsevier in its journal Mathematical Social Sciences.
Volume (Year): 45 (2003)
Issue (Month): 1 (February)
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Web page: http://www.elsevier.com/locate/inca/505565
Other versions of this item:
- Christian List, 2002. "A Possibility Theorem on Aggregation Over Multiple Interconnected Propositions," Economics Series Working Papers 123, University of Oxford, Department of Economics.
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
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.:
- List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
- Brennan, Geoffrey, 2001. "Collective coherence?," International Review of Law and Economics, Elsevier, vol. 21(2), pages 197-211, June.
- Dietrich, Franz & List, Christian, 2007.
"Strategy-Proof Judgment Aggregation,"
Economics and Philosophy,
Cambridge University Press, vol. 23(03), pages 269-300, November.
- Franz Dietrich & Christian List, 2005. "Strategy-proof judgment aggregation," STICERD - Political Economy and Public Policy Paper Series 09, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Dietrich, Franz & List, Christian, 2007. "Strategy-proof judgment aggregation," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
- Franz Dietrich & Christian List, 2004. "Strategy-proof judgment aggregation," Public Economics 0404007, EconWPA, revised 25 Jul 2005.
- Dietrich, Franz & List, Christian, 2007. "Strategy-proof judgment aggregation," Open Access publications from Maastricht University urn:nbn:nl:ui:27-15412, Maastricht University.
- Saporiti, Alejandro, 2009.
"Strategy-proofness and single-crossing,"
Econometric Society, vol. 4(2), June.
- Alejandro Saporiti, 2007. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP48, University of Rochester - Wallis Institute of Political Economy.
- Alejandro Saporiti, 2008. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP55, University of Rochester - Wallis Institute of Political Economy.
- Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
- Franz Dietrich & Christian List, 2005. "Judgment aggregation by quota rules," Public Economics 0501005, EconWPA.
- Alejandro Saporiti & Fernando Tohmé, 2003.
"Single-Crossing, Strategic Voting and the Median Choice Rule,"
CEMA Working Papers: Serie Documentos de Trabajo.
237, Universidad del CEMA.
- Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer, vol. 26(2), pages 363-383, April.
- Christian List & Ben Polak, 2010.
"Introduction to Judgment Aggregation,"
Cowles Foundation Discussion Papers
1753, Cowles Foundation for Research in Economics, Yale University.
- 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, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," MPRA Paper 37752, University Library of Munich, Germany.
- Osherson, Daniel & Vardi, Moshe Y., 2006. "Aggregating disparate estimates of chance," Games and Economic Behavior, Elsevier, vol. 56(1), pages 148-173, July.
- Gilbert Laffond & Jean Lainé, 2008. "The Budget-Voting Paradox," Theory and Decision, Springer, vol. 64(4), pages 447-478, June.
- Christian List, 2007. "Group deliberation and the transformation ofjudgments: an impossibility result," STICERD - Political Economy and Public Policy Paper Series 26, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Pivato, Marcus, 2008. "The geometry of consistent majoritarian judgement aggregation," MPRA Paper 9608, University Library of Munich, Germany.
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