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The Premiss-Based Approach to Logical Aggregation

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

    (ASE - Amsterdam School of Economics - UvA - University of Amsterdam [Amsterdam] = Universiteit van Amsterdam)

Abstract

We investigate judgment aggregation by assuming that some formulas of the agenda are singled out as premisses, and the Independence condition (formula-wise aggregation) holds for them, though perhaps not for others. Whether premiss-based aggregation thus defined is non-degenerate depends on how premisses are logically connected, both among themselves and with other formulas. We identify necessary and sufficient conditions for dictatorship or oligarchy on the premisses, and investigate when these results extend to the whole agenda. Our theorems recover or strengthen several existing ones and are formulated for infinite populations, an innovation of this paper.

Suggested Citation

  • Philippe Mongin & Franz Dietrich, 2007. "The Premiss-Based Approach to Logical Aggregation," Working Papers hal-00578986, HAL.
    • Handle: RePEc:hal:wpaper:hal-00578986
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    Cited by:

    1. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    2. Mongin, Philippe & Dietrich, Franz, 2011. "An interpretive account of logical aggregation theory," HEC Research Papers Series 941, HEC Paris.
    3. Daniel Eckert & Bernard Monjardet, 2009. "Guilbaud's Theorem : An early contribution to judgment aggregation," Post-Print halshs-00404185, HAL.
    4. Frederik S. Herzberg, 2013. "The (im)possibility of collective risk measurement: Arrovian aggregation of variational preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 69-92, May.

    More about this item

    Keywords

    Judgment Aggregation; Premiss-Based Approach; Doctrinal Para- dox; Discursive Dilemma; Independence; Impossibility Theorems; In.nite Populations;
    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

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