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Scoring rules for judgment aggregation

  • Franz Dietrich

    ()

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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File URL: http://hdl.handle.net/10.1007/s00355-013-0757-8
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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. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
  2. Pivato, Marcus, 2013. "Variable-population voting rules," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 210-221.
  3. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-41, November.
  4. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
  5. 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).
  6. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer, vol. 39(4), pages 855-867, October.
  7. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
  8. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  9. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
  10. 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.
  11. Christian List, 2005. "The probability of inconsistencies in complex collective decisions," Social Choice and Welfare, Springer, vol. 24(1), pages 3-32, 05.
  12. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
  13. 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.
  14. Franz Dietrich, 2006. "General Representation of Epistemically Optimal Procedures," Social Choice and Welfare, Springer, vol. 26(2), pages 263-283, April.
  15. 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).
  16. Zwicker, William S., 1991. "The voters' paradox, spin, and the Borda count," Mathematical Social Sciences, Elsevier, vol. 22(3), pages 187-227, December.
  17. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
  18. Hartmann, Stephan & Pigozzi, Gabriella & Sprenger, Jan, 2010. "Reliable Methods of Judgement Aggregation," Economics Papers from University Paris Dauphine 123456789/6413, Paris Dauphine University.
  19. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer, vol. 40(2), pages 581-630, February.
  20. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
  21. 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.
  22. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
  23. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
  24. 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.
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