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Scoring rules for judgment aggregation

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  • Franz Dietrich

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    Abstract

    This paper introduces a new class of judgment aggregation rules, to be called ‘scoring rules’ after their famous counterparts in preference aggregation theory. A scoring rule generates the collective judgment set which reaches the highest total ‘score’ across the individuals, subject to the judgment set having to be rational. Depending on how we define ‘scores’, we obtain several (old and new) solutions to the judgment aggregation problem, such as distance-based aggregation, premise- and conclusion-based aggregation, truth-tracking rules, and a generalization of the Borda rule to judgment aggregation theory. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory. Copyright The Author(s) 2014

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    Bibliographic Info

    Article provided by Springer in its journal Social Choice and Welfare.

    Volume (Year): 42 (2014)
    Issue (Month): 4 (April)
    Pages: 873-911

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    Handle: RePEc:spr:sochwe:v:42:y:2014:i:4:p:873-911

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    1. Pivato, Marcus, 2011. "Voting rules as statistical estimators," MPRA Paper 30292, University Library of Munich, Germany.
    2. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    3. Christian List, 2005. "The probability of inconsistencies in complex collective decisions," Social Choice and Welfare, Springer, vol. 24(1), pages 3-32, 05.
    4. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
    5. Franz Dietrich & Philippe Mongin, 2010. "The premiss-based approach to judgment aggregation," LSE Research Online Documents on Economics 27896, London School of Economics and Political Science, LSE Library.
    6. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
    7. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    8. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    9. Pivato, Marcus, 2013. "Variable-population voting rules," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 210-221.
    10. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2011. "Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions," MPRA Paper 32434, University Library of Munich, Germany.
    11. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
    12. Hartmann, Stephan & Pigozzi, Gabriella & Sprenger, Jan, 2010. "Reliable Methods of Judgement Aggregation," Economics Papers from University Paris Dauphine 123456789/6413, Paris Dauphine University.
    13. 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.
    14. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-41, November.
    15. 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.
    16. Franz Dietrich, 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.
    17. Franz Dietrich & Christian List, 2010. "Majority voting on restricted domains," LSE Research Online Documents on Economics 27902, London School of Economics and Political Science, LSE Library.
    18. Zwicker, William S., 1991. "The voters' paradox, spin, and the Borda count," Mathematical Social Sciences, Elsevier, vol. 22(3), pages 187-227, December.
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