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Majority voting on restricted domains

  • Dietrich, Franz
  • List, Christian

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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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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  1. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 19-33, July.
  2. Franz Dietrich & Christian List, 2008. "Judgment aggregation without full rationality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 15-39, June.
  3. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
  4. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, November.
  5. Franz Dietrich & Christian List, 2007. "Strategy-proof judgment aggregation," LSE Research Online Documents on Economics 5812, London School of Economics and Political Science, LSE Library.
  6. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
  7. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
  8. Christian List, 2002. "A Possibility Theorem on Aggregation Over Multiple Interconnected Propositions," Economics Series Working Papers 123, University of Oxford, Department of Economics.
  9. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
  10. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, SAGE Publishing, vol. 19(4), pages 391-424, October.
  11. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
  12. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  13. Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 363-383, April.
  14. 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.
  15. Alejandro Saporiti, 2008. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP55, University of Rochester - Wallis Institute of Political Economy.
  16. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 649-666, June.
  17. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
  18. Rothstein, Paul, 1991. "Representative Voter Theorems," Public Choice, Springer, vol. 72(2-3), pages 193-212, December.
  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. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 41-57, June.
  21. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
  22. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  23. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
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