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Introduction to Judgment Aggregation

This introduces the symposium on judgment aggregation. The theory of judgment ag­gregation asks how several individuals' judgments on some logically connected propo­sitions can be aggregated into consistent collective judgments. The aim of this intro­duction is to show how ideas from the familiar theory of preference aggregation can be extended to this more general case. We first translate a proof of Arrow's impos­sibility theorem into the new setting, so as to motivate some of the central concepts and conditions leading to analogous impossibilities, as discussed in the symposium. We then consider each of four possible escape-routes explored in the symposium.

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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1753.

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Length: 29 pages
Date of creation: Feb 2010
Date of revision:
Publication status: Published in Journal of Economic Theory (March 2010), 145(2): 441-466
Handle: RePEc:cwl:cwldpp:1753
Note: CFP 1297
Contact details of provider: Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/

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  1. Dietrich, Franz, 2006. "Aggregation theory and the relevance of some issues to others," MPRA Paper 58870, University Library of Munich, Germany, revised Sep 2014.
  2. Dietrich Franz & List Christian, 2007. "Judgment aggregation without full rationality," Research Memorandum 023, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Christian List, 2002. "A Model of Path-Dependence in Decisions over Multiple Propositions," Economics Series Working Papers 2002-W15, University of Oxford, Department of Economics.
  4. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer, vol. 28(4), pages 649-666, June.
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  6. Alejandro Saporiti, 2007. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP48, University of Rochester - Wallis Institute of Political Economy.
  7. Dietrich, Franz, 2010. "The possibility of judgment aggregation on agendas with subjunctive implications," Journal of Economic Theory, Elsevier, vol. 145(2), pages 603-638, March.
  8. Franz Dietrich & Christian List, 2005. "Arrow’s theorem in judgment aggregation," STICERD - Political Economy and Public Policy Paper Series 13, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  9. Dietrich, Franz, 2007. "Aggregation and the relevance of some issues for others," Research Memorandum 002, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  10. Dietrich Franz & Mongin Philippe, 2008. "The Premiss-Based Approach to Judgment Aggregation," Research Memorandum 013, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  11. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
  12. Brennan, Geoffrey, 2001. "Collective coherence?," International Review of Law and Economics, Elsevier, vol. 21(2), pages 197-211, June.
  13. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, vol. 23(03), pages 269-300, November.
  14. Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, vol. 148(2), pages 793-805.
  15. Michael Miller & Daniel Osherson, 2009. "Methods for distance-based judgment aggregation," Social Choice and Welfare, Springer, vol. 32(4), pages 575-601, May.
  16. Franz Dietrich & Christian List, 2005. "Judgment aggregation by quota rules," Public Economics 0501005, EconWPA.
  17. List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
  18. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
  19. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer, vol. 28(4), pages 529-565, June.
  20. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
  21. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
  22. Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
  23. Christian List, 2005. "The probability of inconsistencies in complex collective decisions," Social Choice and Welfare, Springer, vol. 24(1), pages 3-32, 05.
  24. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
  25. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
  26. Philippe Mongin, 2005. "Factoring Out the Impossibility of Logical Aggregation," Working Papers hal-00243010, HAL.
  27. Nehring, Klaus, 2007. "The impossibility of a Paretian rational: A Bayesian perspective," Economics Letters, Elsevier, vol. 96(1), pages 45-50, July.
  28. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
  29. Kornhauser, Lewis A, 1992. "Modeling Collegial Courts. II. Legal Doctrine," Journal of Law, Economics and Organization, Oxford University Press, vol. 8(3), pages 441-70, October.
  30. Franz Dietrich, 2005. "The possibility of judgment aggregation for network agendas," Public Economics 0504002, EconWPA.
  31. Franz Dietrich & Christian List, 2010. "Majority voting on restricted domains," LSE Research Online Documents on Economics 27902, London School of Economics and Political Science, LSE Library.
  32. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
  33. 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.
  34. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
  35. Franz Dietrich & Christian List, 2008. "A liberal paradox for judgment aggregation," Social Choice and Welfare, Springer, vol. 31(1), pages 59-78, June.
  36. Campbell, Donald E. & Kelly, Jerry S., 2002. "Impossibility theorems in the arrovian framework," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 1, pages 35-94 Elsevier.
  37. Osherson, Daniel & Vardi, Moshe Y., 2006. "Aggregating disparate estimates of chance," Games and Economic Behavior, Elsevier, vol. 56(1), pages 148-173, July.
  38. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  39. Elad Dokow & Ron Holzman, 2009. "Aggregation of binary evaluations for truth-functional agendas," Social Choice and Welfare, Springer, vol. 32(2), pages 221-241, February.
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