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The aggregation of propositional attitudes: towards a general theory

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Author Info
Dietrich, Franz
List, Christian (METEOR)

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Abstract

How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove two new theorems. Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation.

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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 047.

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Date of creation: 2008
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Handle: RePEc:dgr:umamet:2008047

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Keywords: mathematical economics;

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  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. Franz Dietrich & Christian List, 2005. "Strategy-proof judgment aggregation," STICERD - Political Economy and Public Policy Paper Series 09, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  3. Saran Rene, 2009. "How Communication Improves Efficiency in Bargaining: Reconciling Theory with Evidence," Research Memoranda 022, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  4. Dietrich, Franz & List, Christian, 2007. "Opinion pooling on general agendas," Research Memoranda 038, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  5. dÕASPREMONT, Claude & GEVERS, Louis, 2001. "Social welfare functionals and interpersonal comparability," CORE Discussion Papers 2001040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  6. Franz Dietrich & Christian List, 2005. "Arrow's Theorem in Judgement Aggregation," Public Economics 0504007, EconWPA, revised 10 Sep 2005. [Downloadable!]
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  7. Dietrich, Franz, 2008. "Bayesian Group Belief," Research Memoranda 046, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  8. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August. [Downloadable!] (restricted)
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  9. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January. [Downloadable!] (restricted)
  10. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer, vol. 28(4), pages 529-565, June. [Downloadable!] (restricted)
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  11. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June. [Downloadable!] (restricted)
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