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A Possibility Theorem on Aggregation Over Multiple Interconnected Propositions

  • Christian List

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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File URL: http://www.economics.ox.ac.uk/materials/working_papers/paper123.pdf
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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: 01 Oct 2002
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Handle: RePEc:oxf:wpaper:123
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Web page: http://www.economics.ox.ac.uk/
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  1. Brennan, Geoffrey, 2001. "Collective coherence?," International Review of Law and Economics, Elsevier, vol. 21(2), pages 197-211, June.
  2. 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.
  3. 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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