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An interpretive account of logical aggregation theory

  • Mongin, Philippe


    (HEC Paris)

  • Dietrich, Franz

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager’s doctrinal paradox and Pettit’s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final aim of the paper is to give the latter its own theoretical development, along the lines of Dietrich and Mongin’s recent technical work. However, the paper also aims at reviewing the main existing results, starting from the first impossibility theorem proved by List and Pettit. It provides a uniform logical framework in which the whole of theory can be stated and its theorems can be compared with each other. The account goes through three historical steps: the scattered early results on the independence axiom, the collective achievement of the canonical theorem which provided the theory with its specific method of analysis; and finally the recent extension mentioned above to the doctrinal paradox.

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Paper provided by HEC Paris in its series Les Cahiers de Recherche with number 941.

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Length: 48 pages
Date of creation: 01 Feb 2011
Date of revision:
Handle: RePEc:ebg:heccah:0941
Contact details of provider: Postal: HEC Paris, 78351 Jouy-en-Josas cedex, France
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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. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
  3. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
  4. Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April.
  5. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
  6. Frederik Herzberg, 2009. "Judgment aggregators and Boolean algebra homomorphisms," Center for Mathematical Economics Working Papers 414, Center for Mathematical Economics, Bielefeld University.
  7. Michel Le Breton & John A. Weymark, 2002. "Arrovian Social Choice Theory on Economic Domains," Vanderbilt University Department of Economics Working Papers 0206, Vanderbilt University Department of Economics, revised Sep 2003.
  8. P. Mongin, 1999. "L'axiomatisation et les théories économiques," THEMA Working Papers 99-45, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  9. Philippe Mongin & Franz Dietrich, 2007. "The Premiss-Based Approach to Logical Aggregation," Working Papers hal-00578986, HAL.
  10. Frederik Herzberg & Daniel Eckert, 2010. "Impossibility results for infinite-electorate abstract aggregation rules," Center for Mathematical Economics Working Papers 427, Center for Mathematical Economics, Bielefeld University.
  11. Conal Duddy & Ashley Piggins, 2009. "Many-valued judgment aggregation: characteriing the possibility/impossibility boundary for an important class of agendas," Working Papers 0154, National University of Ireland Galway, Department of Economics, revised 2009.
  12. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer, vol. 28(4), pages 649-666, June.
  13. Mongin, P., . "Consistent Bayesian aggregation," CORE Discussion Papers RP 1176, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. KIRMAN, Alan P. & SONDERMANN, Dieter, . "Arrow's theorem, many agents, and indivisible dictators," CORE Discussion Papers RP 118, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Philippe Mongin, 2011. "Judgment Aggregation," Working Papers hal-00625434, HAL.
  16. Dietrich Franz & List Christian, 2006. "Judgment aggregation without full rationality," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  17. Daniel Eckert & Bernard Monjardet, 2009. "Guilbaud's Theorem : An early contribution to judgment aggregation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00404185, HAL.
  18. 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.
  19. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
  20. 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.
  21. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
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  23. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
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