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 InfoPaper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 123.
Date of creation: 01 Oct 2002
Date of revision:
aggregation; beliefs; propositional logic; domain restriction; unidimensional alignment;
Other versions of this item:
- List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
- 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
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Wallis Working Papers
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0404007, EconWPA, revised 25 Jul 2005.
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237, Universidad del CEMA.
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