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The impossibility of unbiased judgment aggregation

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  • Dietrich, F.K.

    (Quantitative Economics)

  • List, C.

    (Externe publicaties SBE)

Abstract

All existing impossibility theorems on judgment aggregation over logically connected propositions have one of two restrictions: they either use a controversial systematicity condition or apply only to special agendas of propositions with rich logical connections. An important open question is whether judgment aggregation faces any serious impossibilities without these restrictions. Here we prove the first impossibility theorem without systematicity that applies to all standard agendas: there exists no judgment aggregation rule satisfying universal domain, collective rationality, anonymity and a new condition called unbiasedness. For many agendas, anonymity can be weakened. Applied illustratively to (strict) preference aggregation represented in the judgment aggregation model, our result implies that every unbiased social welfare function with universal domain depends only on a single individual.
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Suggested Citation

  • Dietrich, F.K. & List, C., 2007. "The impossibility of unbiased judgment aggregation," Research Memorandum 022, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2007022
    DOI: 10.26481/umamet.2007022
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    References listed on IDEAS

    as
    1. 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.
    2. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    3. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(1), pages 89-110, April.
    4. Dietrich, F.K. & List, C., 2006. "Judgment aggregation on restricted domains," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    5. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    6. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    7. 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.
    8. 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.
    9. Zhi-Long Chen, 2004. "Simultaneous Job Scheduling and Resource Allocation on Parallel Machines," Annals of Operations Research, Springer, vol. 129(1), pages 135-153, July.
    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.
    13. 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.
    14. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
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    Cited by:

    1. Iida, Hiroshi, 2008. "Partition のある風景," ビジネス創造センターディスカッション・ペーパー (Discussion papers of the Center for Business Creation) 10252/918, Otaru University of Commerce.
    2. Maarten Vendrik & Christiane Schwieren, 2010. "Identification, screening and stereotyping in labour market discrimination," Journal of Economics, Springer, vol. 99(2), pages 141-171, March.
    3. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    4. Zoi Terzopoulou & Ulle Endriss, 2020. "Neutrality and relative acceptability in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 25-49, June.
    5. 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).
    6. Nicole Megow & Rolf H. Möhring & Jens Schulz, 2011. "Decision Support and Optimization in Shutdown and Turnaround Scheduling," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 189-204, May.

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