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A quantitative discursive dilemma

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Abstract

The typical judgment aggregation problem in economics and other fields is the following: A group of people has to judge (estimate) the value of an uncertain variable y which is a function of k other variables, i.e. y = D(x1,...xk) . We analyze when it is possible for the group to arrive at collective judgments on the variables that respect D. We consider aggregators that fulfill Arrow's IIA-condition and neutrality. We show how possibility and impossibility depend on the functional form of D, and generalize Pettit's (2001) binary discursive dilemma. (revised ed. 2008)

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File URL: http://www.norges-bank.no/en/Published/Papers/Working-Papers/2007/WP-20077/
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Paper provided by Norges Bank in its series Working Paper with number 2007/07.

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Length: 17 pages
Date of creation: 14 Dec 2007
Date of revision: 24 Nov 2008
Handle: RePEc:bno:worpap:2007_07

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Keywords: Judgment aggregation; Dependent variables; Impossibility;

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  1. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
  2. Carl Andreas Claussen & Øistein Røisland, 2005. "Collective economic decisions and the discursive dilemma," Working Paper 2005/3, Norges Bank.
  3. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
  4. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
  5. 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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