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The probability of inconsistencies in complex collective decisions

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  • Christian List

Abstract

Many groups make decisions over multiple interconnected propositions. The “doctrinal paradox” or “discursive dilemma” shows that propositionwise majority voting can generate inconsistent collective sets of judgments, even when individual sets of judgments are all consistent. I develop a simple model for determining the probability of the paradox, given various assumptions about the probability distribution of individual sets of judgments, including impartial culture and impartial anonymous culture assumptions. I prove several convergence results, identifying when the probability of the paradox converges to 1, and when it converges to 0, as the number of individuals increases. Drawing on the Condorcet jury theorem and work by Bovens and Rabinowicz (2001, 2003), I use the model to assess the “truth-tracking” performance of two decision procedures, the premise- and conclusion-based procedures. I compare the present results with existing results on the probability of Condorcet’s paradox. I suggest that the doctrinal paradox is likely to occur under plausible conditions. Copyright Springer-Verlag 2005

Suggested Citation

  • Christian List, 2005. "The probability of inconsistencies in complex collective decisions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 3-32, May.
    • Handle: RePEc:spr:sochwe:v:24:y:2005:i:1:p:3-32
    DOI: 10.1007/s00355-003-0253-7
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    Citations

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    Cited by:

    1. de Clippel, Geoffroy & Eliaz, Kfir, 2015. "Premise-based versus outcome-based information aggregation," Games and Economic Behavior, Elsevier, vol. 89(C), pages 34-42.
    2. Bozbay, Irem, 2012. "Truth-Seeking Judgment Aggregation over Interconnected Issues," Working Papers 2012:31, Lund University, Department of Economics.
    3. Masaki Miyashita, 2021. "Premise-based vs conclusion-based collective choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(2), pages 361-385, August.
    4. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, vol. 23(3), pages 269-300, November.
    5. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    6. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 873-911, April.
    7. Irem Bozbay, 2015. "Truth-Tracking Judgment Aggregation Over Interconnected Issues," School of Economics Discussion Papers 0916, School of Economics, University of Surrey.
    8. Takuya Sekiguchi, 2019. "Preferences over procedures and outcomes in judgment aggregation: an experimental study," Theory and Decision, Springer, vol. 86(2), pages 239-258, March.
    9. Dietrich, Franz & Spiekermann, Kai, 2010. "Epistemic democracy with defensible premises," MPRA Paper 40135, University Library of Munich, Germany, revised Jun 2012.
    10. Franz Dietrich & Kai Spiekermann, 2021. "Social Epistemology," Post-Print halshs-02431971, HAL.
    11. Mongin, Philippe & Dietrich, Franz, 2011. "An interpretive account of logical aggregation theory," HEC Research Papers Series 941, HEC Paris.
    12. Perote-Peña, Juan & Piggins, Ashley, 2015. "A Model Of Deliberative And Aggregative Democracy," Economics and Philosophy, Cambridge University Press, vol. 31(1), pages 93-121, March.
    13. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    14. Bozbay, İrem & Dietrich, Franz & Peters, Hans, 2014. "Judgment aggregation in search for the truth," Games and Economic Behavior, Elsevier, vol. 87(C), pages 571-590.
    15. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
    16. Baharad, Eyal & Neeman, Zvika & Rubinchik, Anna, 2020. "The rarity of consistent aggregators," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 146-149.
    17. Aureli Alabert & Mercè Farré & Rubén Montes, 2023. "Optimal Decision Rules for the Discursive Dilemma," Group Decision and Negotiation, Springer, vol. 32(4), pages 889-923, August.
    18. Takuya Sekiguchi & Hisashi Ohtsuki, 2023. "Aggregation of Correlated Judgments on Multiple Interconnected Issues," Group Decision and Negotiation, Springer, vol. 32(1), pages 233-256, February.
    19. Franz Dietrich, 2004. "Terrorism Prevention: A General Model," Others 0404001, University Library of Munich, Germany.
    20. Takuya Sekiguchi, 2016. "Optimal group composition for efficient division of labor," Theory and Decision, Springer, vol. 81(4), pages 601-618, November.
    21. Irem Bozbay, 2019. "Truth-tracking judgment aggregation over interconnected issues," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 337-370, August.
    22. Aureli Alabert & Mercè Farré, 2022. "The doctrinal paradox: comparison of decision rules in a probabilistic framework," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(4), pages 863-895, May.
    23. Osherson, Daniel & Vardi, Moshe Y., 2006. "Aggregating disparate estimates of chance," Games and Economic Behavior, Elsevier, vol. 56(1), pages 148-173, July.
    24. Takuya Sekiguchi, 2023. "Voting Records as Assessors of Premises Behind Collective Decisions," Group Decision and Negotiation, Springer, vol. 32(2), pages 257-275, April.
    25. Klaus Nehring, 2005. "The (Im)Possibility of a Paretian Rational," Economics Working Papers 0068, Institute for Advanced Study, School of Social Science.

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