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The Premiss-Based Approach to Judgment Aggregation

Author

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  • Dietrich Franz
  • Mongin Philippe

    (METEOR)

Abstract

We investigate judgment aggregation by assuming that some formulas of the agenda are singled out as premises, and the Independence condition (formula-wise aggregation) holds for them, though perhaps not for others. Whether premise-based aggregation thus defined is non-degenerate depends on how premises 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

  • 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).
    • Handle: RePEc:unm:umamet:2008013
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    References listed on IDEAS

    as
    1. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 529-565, June.
    2. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    3. 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.
    4. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(1), pages 89-110, April.
    5. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, vol. 23(3), pages 269-300, November.
    6. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 19-33, July.
    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. Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April.
    9. Franz Dietrich & Christian List, 2008. "Judgment aggregation without full rationality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 15-39, June.
    10. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    11. Klaus Nehring, 2005. "The (Im)Possibility of a Paretian Rational," Economics Working Papers 0068, Institute for Advanced Study, School of Social Science.
    12. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
    13. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
    14. Elad Dokow & Ron Holzman, 2009. "Aggregation of binary evaluations for truth-functional agendas," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 221-241, February.
    15. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
    16. Kornhauser, Lewis A, 1992. "Modeling Collegial Courts. II. Legal Doctrine," Journal of Law, Economics, and Organization, Oxford University Press, vol. 8(3), pages 441-470, October.
    17. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
    18. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 41-57, June.
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    Citations

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    Cited by:

    1. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 855-867, October.
    2. Franz Dietrich & Christian List, 2017. "Probabilistic opinion pooling generalized. Part one: general agendas," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 747-786, April.
    3. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    4. Franz Dietrich & Christian List, 2017. "Probabilistic opinion pooling generalized. Part two: the premise-based approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 787-814, April.
    5. Bozbay, İrem & Dietrich, Franz & Peters, Hans, 2014. "Judgment aggregation in search for the truth," Games and Economic Behavior, Elsevier, vol. 87(C), pages 571-590.
    6. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    7. Dietrich, Franz, 2016. "Judgment aggregation and agenda manipulation," Games and Economic Behavior, Elsevier, vol. 95(C), pages 113-136.
    8. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
    9. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 873-911, April.
    10. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    11. repec:spr:grdene:v:28:y:2019:i:1:d:10.1007_s10726-018-9594-6 is not listed on IDEAS
    12. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
    13. repec:spo:wpecon:info:hdl:2441/dambferfb7dfprc9m2e02cub3 is not listed on IDEAS
    14. Dietrich, Franz & List, Christian, 2014. "From degrees of belief to beliefs: Lessons from judgment-aggregation theory," MPRA Paper 58257, University Library of Munich, Germany.
    15. Franz Dietrich & Christian List, 2013. "Propositionwise judgment aggregation: the general case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1067-1095, April.
    16. Cres, Herve & Gilboa, Itzhak & Vieille, Nicolas, 2012. "Bureaucracy in Quest for Feasibility," Foerder Institute for Economic Research Working Papers 275779, Tel-Aviv University > Foerder Institute for Economic Research.
    17. Jérôme Lang & Gabriella Pigozzi & Marija Slavkovik & Leendert Torre & Srdjan Vesic, 2017. "A partial taxonomy of judgment aggregation rules and their properties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 327-356, February.
    18. Herzberg, Frederik, 2010. "Judgment aggregators and Boolean algebra homomorphisms," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 132-140, January.
    19. Mongin, Philippe, 2011. "Judgment aggregation," HEC Research Papers Series 942, HEC Paris.
    20. Franz Dietrich, 2015. "Aggregation theory and the relevance of some issues to others," Post-Print halshs-01249513, HAL.
    21. Masaki Miyashita, 2017. "Binary Collective Choice with Multiple Premises," Discussion Paper Series DP2017-27, Research Institute for Economics & Business Administration, Kobe University.
    22. Franz Dietrich, 2015. "Aggregation theory and the relevance of some issues to others," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01249513, HAL.

    More about this item

    Keywords

    mathematical economics;

    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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