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The impossibility of unbiased judgment aggregation


  • Franz Dietrich
  • Christian List



Standard impossibility theorems on judgment aggregation over logically connected propositions either use a controversial systematicity condition or apply only to agendas of propositions with rich logical connections. Are there any serious impossibilities without these restrictions? We prove an impossibility theorem without systematicity that applies to most standard agendas: Every judgment aggregation function (with rational inputs and outputs) satisfying a condition called unbiasedness is dictatorial (or effectively dictatorial if we remove one of the agenda conditions). Our agenda conditions are tight. Applied illustratively to (strict) preference aggregation represented in our model, the result implies that every unbiased social welfare function with universal domain is effectively dictatorial.
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Suggested Citation

  • Franz Dietrich & Christian List, 2010. "The impossibility of unbiased judgment aggregation," Theory and Decision, Springer, vol. 68(3), pages 281-299, March.
  • Handle: RePEc:kap:theord:v:68:y:2010:i:3:p:281-299
    DOI: 10.1007/s11238-009-9186-7

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    References listed on IDEAS

    1. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    2. 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.
    3. Dietrich Franz & List Christian, 2006. "Judgment aggregation on restricted domains," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. 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.
    5. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 529-565, June.
    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, 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.
    8. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
    9. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    10. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
    11. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
    12. 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.
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    Cited by:

    1. 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).
    2. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.


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