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The possibility of judgment aggregation on agendas with subjunctive implications

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  • Dietrich, Franz

Abstract

The new field of judgment aggregation aims to find collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely as subjunctive implications rather than material implications. For these agendas, consistent and complete collective judgments can be reached through appropriate quota rules (which decide propositions using acceptance thresholds). I characterise the class of these quota rules. I also prove an abstract result that characterises consistent aggregation for arbitrary agendas in a general logic.

Suggested Citation

  • Dietrich, Franz, 2010. "The possibility of judgment aggregation on agendas with subjunctive implications," LSE Research Online Documents on Economics 27899, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:27899
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    File URL: http://eprints.lse.ac.uk/27899/
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    References listed on IDEAS

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    1. List, Christian, 2004. "A Model of Path-Dependence in Decisions over Multiple Propositions," American Political Science Review, Cambridge University Press, vol. 98(3), pages 495-513, August.
    2. 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.
    3. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    4. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, vol. 23(3), pages 269-300, November.
    5. 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.
    6. 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.
    7. Dietrich, F.K. & List, C., 2006. "Judgment aggregation on restricted domains," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
    9. Christian List, 2002. "A Model of Path-Dependence in Decisions over Multiple Propositions," Economics Papers 2002-W15, Economics Group, Nuffield College, University of Oxford.
    10. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. repec:hal:spmain:info:hdl:2441/dambferfb7dfprc9m2e02cub3 is not listed on IDEAS
    2. Bozbay, Irem, 2012. "Truth-Seeking Judgment Aggregation over Interconnected Issues," Working Papers 2012:31, Lund University, Department of Economics.
    3. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    4. 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.
    5. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    6. 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.
    7. Ruth Ben-Yashar & Leif Danziger, 2015. "When is voting optimal?," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 341-356, October.
    8. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
    9. Crès, Hervé & Gilboa, Itzhak & Vieille, Nicolas, 2024. "Bureaucracy in quest of feasibility," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    10. Mongin, Philippe & Dietrich, Franz, 2011. "An interpretive account of logical aggregation theory," HEC Research Papers Series 941, HEC Paris.
    11. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    12. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    13. repec:spo:wpecon:info:hdl:2441/dambferfb7dfprc9m2e02cub3 is not listed on IDEAS
    14. Franz Dietrich & Christian List, 2010. "The impossibility of unbiased judgment aggregation," Theory and Decision, Springer, vol. 68(3), pages 281-299, March.
    15. 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.
    16. repec:hal:wpspec:info:hdl:2441/dambferfb7dfprc9m2e02cub3 is not listed on IDEAS

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    More about this item

    Keywords

    ISI; Judgment aggregation; Subjunctive implication; Material implication; Characterisation of possibility agendas;
    All these keywords.

    JEL classification:

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

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