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Majority voting on restricted domains

  • Franz Dietrich
  • Christian List

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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File URL: http://eprints.lse.ac.uk/27902/
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Paper provided by London School of Economics and Political Science, LSE Library in its series LSE Research Online Documents on Economics with number 27902.

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Date of creation: Mar 2010
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Publication status: Published in Journal of Economic Theory, March, 2010, 145(2), pp. 512-543. ISSN: 1095-7235
Handle: RePEc:ehl:lserod:27902
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Web page: http://www.lse.ac.uk/

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  1. Saporiti, Alejandro, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
  2. Dietrich Franz & List Christian, 2007. "Judgment aggregation without full rationality," Research Memorandum 023, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Mongin, Philippe, 2006. "Factoring out the impossibility of logical aggregation," Les Cahiers de Recherche 854, HEC Paris.
  4. Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer, vol. 26(2), pages 363-383, April.
  5. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, vol. 23(03), pages 269-300, November.
  6. 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.
  7. Franz Dietrich & Christian List, 2005. "Judgment aggregation by quota rules," Public Economics 0501005, EconWPA.
  8. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
  9. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
  10. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
  11. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
  12. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  13. List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
  14. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
  15. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
  16. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer, vol. 29(1), pages 19-33, July.
  17. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer, vol. 28(4), pages 529-565, June.
  18. repec:cup:cbooks:9780521791021 is not listed on IDEAS
  19. 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.
  20. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
  21. Rothstein, Paul, 1991. " Representative Voter Theorems," Public Choice, Springer, vol. 72(2-3), pages 193-212, December.
  22. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  23. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer, vol. 28(4), pages 649-666, June.
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