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Scoring rules for judgment aggregation

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  • Dietrich, Franz

Abstract

This paper studies a class of judgment aggregation rules, to be called `scoring rules' after their famous counterpart in preference aggregation theory. A scoring rule delivers the collective judgments which reach the highest total `score' across the individuals, subject to the judgments 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 Borda-type rule. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory.

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File URL: http://mpra.ub.uni-muenchen.de/35657/
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File URL: http://mpra.ub.uni-muenchen.de/36892/
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File URL: http://mpra.ub.uni-muenchen.de/42431/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 35657.

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Date of creation: 26 Dec 2011
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Handle: RePEc:pra:mprapa:35657

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Related research

Keywords: judgment aggregation; social choice; scoring rules; Hamming rule; Borda rule; premise- and conclusion-based rules;

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References

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  1. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  2. Franz Dietrich & Christian List, 2005. "Judgment aggregation by quota rules," Public Economics 0501005, EconWPA.
  3. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer, vol. 39(4), pages 855-867, October.
  4. Christian List, 2002. "A Model of Path-Dependence in Decisions over Multiple Propositions," Economics Series Working Papers 2002-W15, University of Oxford, Department of Economics.
  5. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer, vol. 40(2), pages 581-630, February.
  6. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
  7. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
  8. 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.
  9. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
  10. Christian List, 2005. "The probability of inconsistencies in complex collective decisions," Social Choice and Welfare, Springer, vol. 24(1), pages 3-32, 05.
  11. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
  12. 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.
  13. Franz Dietrich, 2006. "General Representation of Epistemically Optimal Procedures," Social Choice and Welfare, Springer, vol. 26(2), pages 263-283, April.
  14. Bozbay Irem & Dietrich Franz & Peters Hans, 2011. "Judgment aggregation in search for the truth," Research Memorandum 040, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  15. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
  16. 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.
  17. 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.
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Cited by:
  1. García-Bermejo, Juan Carlos, 2013. "A Non-Proposition-Wise Variant of Majority Voting for Aggregating Judgments," Working Papers in Economic Theory 2013/02, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).

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