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Majority voting on restricted domains

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Author Info

  • Dietrich, Franz
  • List, Christian

Abstract

In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments sufficient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen's triplewise value-restriction, itself the most general classic condition. We also prove a new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results support the robustness of majority rule.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 2 (March)
Pages: 512-543

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:2:p:512-543

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Judgment aggregation Domain restriction Majority voting Consistency Value-restriction Analogues of single-peakedness May's theorem;

References

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  1. Philippe Mongin, 2005. "Factoring Out the Impossibility of Logical Aggregation," Working Papers hal-00243010, HAL.
  2. Franz Dietrich & Christian List, 2008. "Judgment aggregation without full rationality," Social Choice and Welfare, Springer, vol. 31(1), pages 15-39, June.
  3. Franz Dietrich & Christian List, 2005. "Strategy-proof judgment aggregation," STICERD - Political Economy and Public Policy Paper Series 09, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  4. Gaertner,Wulf, 2001. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521791021, October.
  5. Saporiti, Alejandro, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
  6. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  7. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
  8. Franz Dietrich & Christian List, 2005. "Judgment aggregation by quota rules," Public Economics 0501005, EconWPA.
  9. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
  10. Alejandro Saporiti & Fernando Tohmé, 2003. "Single-Crossing, Strategic Voting and the Median Choice Rule," CEMA Working Papers: Serie Documentos de Trabajo. 237, Universidad del CEMA.
  11. List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
  12. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
  13. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer, vol. 28(4), pages 649-666, June.
  14. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  15. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
  16. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
  17. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
  18. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
  19. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
  20. 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.
  21. 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.
  22. Rothstein, Paul, 1991. " Representative Voter Theorems," Public Choice, Springer, vol. 72(2-3), pages 193-212, December.
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Citations

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Cited by:
  1. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2013. "The Condorcet set: Majority voting over interconnected propositions," Working Paper Series in Economics 51, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  2. Nehring, Klaus & Pivato, Marcus, 2013. "Majority rule in the absence of a majority," MPRA Paper 46721, University Library of Munich, Germany.
  3. Christian List & Ben Polak, 2010. "Introduction to judgment aggregation," LSE Research Online Documents on Economics 27900, London School of Economics and Political Science, LSE Library.
  4. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
  5. Dietrich, Franz, 2013. "Judgment aggregation and agenda manipulation," MPRA Paper 51775, University Library of Munich, Germany.
  6. Dietrich, Franz, 2011. "Scoring rules for judgment aggregation," MPRA Paper 35657, University Library of Munich, Germany.
  7. Hervé Crès & Itzhak Gilboa, & Nicolas Vieille, 2012. "Bureaucracy in Quest for Feasibility," Sciences Po publications info:hdl:2441/dambferfb7d, Sciences Po.
  8. 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.
  9. Marcus Pivato, 2009. "Geometric models of consistent judgement aggregation," Social Choice and Welfare, Springer, vol. 33(4), pages 559-574, November.
  10. Herzberg, Frederik S., 2008. "Judgement aggregation functions and ultraproducts," MPRA Paper 10546, University Library of Munich, Germany, revised 10 Sep 2008.
  11. repec:spo:wpecon:info:hdl:2441/dambferfb7dfprc9m2e02cub3 is not listed on IDEAS
  12. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
  13. 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).
  14. García-Bermejo, Juan Carlos, 2012. "A Pooling Approach to Judgment Aggregation," Working Papers in Economic Theory 2012/01, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).

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