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An interpretive account of logical aggregation theory

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  • Mongin, Philippe

    ()
    (HEC Paris)

  • Dietrich, Franz

Abstract

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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Bibliographic Info

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

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Postal: HEC Paris, 78351 Jouy-en-Josas cedex, France
Web page: http://www.hec.fr/
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Related research

Keywords: Judgment Aggregation; Logical Aggregation; Doctrinal Paradox; Discursive Dilemma; General Logic; Premiss-Based vs Conclusion-Based Approach; Social Choice Theory;

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References

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  1. Heifetz, A. & Mongin, P., 1998. "Probability Logic for Type Spaces," Papers 9825, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  2. 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.
  3. 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).
  4. 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).
  5. Daniel Eckert & Bernard Monjardet, 2009. "Guilbaud's Theorem : an early contribution to judgment aggregation," Documents de travail du Centre d'Economie de la Sorbonne 09047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  6. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
  7. Frederik Herzberg, 2009. "Judgment aggregators and Boolean algebra homomorphisms," Working Papers 414, Bielefeld University, Center for Mathematical Economics.
  8. Brennan, Geoffrey, 2001. "Collective coherence?," International Review of Law and Economics, Elsevier, vol. 21(2), pages 197-211, June.
  9. Mongin, Philippe, 2006. "Factoring out the impossibility of logical aggregation," Les Cahiers de Recherche 854, HEC Paris.
  10. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer, vol. 28(4), pages 649-666, June.
  11. Frederik Herzberg & Daniel Eckert, 2010. "Impossibility results for infinite-electorate abstract aggregation rules," Working Papers 427, Bielefeld University, Center for Mathematical Economics.
  12. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
  13. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  14. 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.
  15. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
  16. Philippe Mongin, 2003. "L'axiomatisation et les théories économiques," Revue économique, Presses de Sciences-Po, vol. 54(1), pages 99-138.
  17. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
  18. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
  19. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
  20. 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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