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A Possibility Theorem on Aggregation Over Multiple Interconnected Propositions

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  • Christian List

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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Bibliographic Info

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: 01 Oct 2002
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Handle: RePEc:oxf:wpaper:123

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

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References

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  1. Brennan, Geoffrey, 2001. "Collective coherence?," International Review of Law and Economics, Elsevier, Elsevier, vol. 21(2), pages 197-211, June.
  2. 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.
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Cited by:
  1. Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer, Springer, vol. 26(2), pages 363-383, April.
  2. Franz Dietrich & Christian List, 2005. "Judgment aggregation by quota rules," Public Economics, EconWPA 0501005, EconWPA.
  3. Christian List, 2007. "Group deliberation and the transformation ofjudgments: an impossibility result," STICERD - Political Economy and Public Policy Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE 26, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  4. Christian List & Ben Polak, 2010. "Introduction to Judgment Aggregation," Levine's Working Paper Archive 661465000000000006, David K. Levine.
  5. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(2), pages 512-543, March.
  6. Alejandro Saporiti, 2007. "Strategy-Proofness and Single-Crossing," Wallis Working Papers, University of Rochester - Wallis Institute of Political Economy WP48, University of Rochester - Wallis Institute of Political Economy.
  7. Pivato, Marcus, 2008. "The geometry of consistent majoritarian judgement aggregation," MPRA Paper 9608, University Library of Munich, Germany.
  8. Franz Dietrich & Christian List, 2005. "Strategy-proof judgment aggregation," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 19299, London School of Economics and Political Science, LSE Library.
  9. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, Springer, vol. 73(3), pages 315-355, September.
  10. Gilbert Laffond & Jean Lainé, 2008. "The Budget-Voting Paradox," Theory and Decision, Springer, Springer, vol. 64(4), pages 447-478, June.
  11. Osherson, Daniel & Vardi, Moshe Y., 2006. "Aggregating disparate estimates of chance," Games and Economic Behavior, Elsevier, Elsevier, vol. 56(1), pages 148-173, July.

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