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A Possibility Theorem on Aggregation Over Multiple Interconnected Propositions

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Author Info
Christian List

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Abstract

Drawing 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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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 123.

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Date of creation: 2002
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Handle: RePEc:oxf:wpaper:123

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Related research
Keywords: aggregation; beliefs; propositional logic; domain restriction; unidimensional alignment;

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Find related papers by JEL classification:
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Models of Political Processes: Rent-seeking, Elections, Legislatures, and Voting Behavior

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  1. Brams, Steven J. & Kilgour, D. Marc & Zwicker, William, 1997. "Voting on Referenda: The Separability Problem and Possible Solutions," Working Papers 97-15, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  2. Brennan, Geoffrey, 2001. "Collective coherence?," International Review of Law and Economics, Elsevier, vol. 21(2), pages 197-211, June. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. 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. [Downloadable!]
  2. Alejandro Saporiti, 2007. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP48, University of Rochester - Wallis Institute of Political Economy. [Downloadable!]
  3. Pivato, Marcus, 2008. "The geometry of consistent majoritarian judgement aggregation," MPRA Paper 9608, University Library of Munich, Germany. [Downloadable!]
  4. Franz Dietrich & Christian List, 2005. "Judgment aggregation by quota rules," Public Economics 0501005, EconWPA. [Downloadable!]
  5. 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. [Downloadable!]
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  6. Gilbert Laffond & Jean Lainé, 2008. "The Budget-Voting Paradox," Theory and Decision, Springer, vol. 64(4), pages 447-478, June. [Downloadable!] (restricted)
  7. Alejandro Saporiti, 2008. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP55, University of Rochester - Wallis Institute of Political Economy. [Downloadable!]
    Other versions:
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