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An Interpretive Account of Logical Aggregation Theory

Author

Listed:
  • Philippe Mongin

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Franz Dietrich

    (LSE - London School of Economics and Political Science)

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.

Suggested Citation

  • Philippe Mongin & Franz Dietrich, 2011. "An Interpretive Account of Logical Aggregation Theory," Working Papers hal-00579343, HAL.
  • Handle: RePEc:hal:wpaper:hal-00579343
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00579343
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    References listed on IDEAS

    as
    1. Le Breton, Michel & Weymark, John A., 2002. "Arrovian Social Choice Theory on Economic Domains," IDEI Working Papers 143, Institut d'Économie Industrielle (IDEI), Toulouse, revised Sep 2003.
    2. Philippe Mongin, 2011. "Judgment aggregation," Working Papers hal-00579346, HAL.
    3. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    4. 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.
    5. Herzberg, Frederik, 2010. "Judgment aggregators and Boolean algebra homomorphisms," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 132-140, January.
    6. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 649-666, June.
    7. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
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    11. Daniel Eckert & Bernard Monjardet, 2009. "Guilbaud's Theorem : An early contribution to judgment aggregation," Post-Print halshs-00404185, HAL.
    12. Philippe Mongin, 2003. "L'axiomatisation et les théories économiques," Revue économique, Presses de Sciences-Po, vol. 54(1), pages 99-138.
    13. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
    14. Herzberg, Frederik & Eckert, Daniel, 2017. "Impossibility results for infinite-electorate abstract aggregation rules," Center for Mathematical Economics Working Papers 427, Center for Mathematical Economics, Bielefeld University.
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    More about this item

    Keywords

    General Logic; Discursive Dilemma; Doctrinal Paradox; Logical Aggregation; Judgment Aggregation; Social Choice Theory; Premiss-Based vs Conclusion-Based Approach; Social Choice Theory.;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D79 - Microeconomics - - Analysis of Collective Decision-Making - - - Other

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