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The probability of inconsistencies in complex collective decisions

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  • Christian List

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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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    File URL: http://hdl.handle.net/10.1007/s00355-003-0253-7
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    Cited by:

    1. Dietrich, Franz & Spiekermann, Kai, 2013. "Epistemic Democracy With Defensible Premises," Economics and Philosophy, Cambridge University Press, vol. 29(01), pages 87-120, March.
    2. de Clippel, Geoffroy & Eliaz, Kfir, 2015. "Premise-based versus outcome-based information aggregation," Games and Economic Behavior, Elsevier, vol. 89(C), pages 34-42.
    3. 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.
    4. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, vol. 23(03), 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. Franz Dietrich, 2004. "Terrorism Prevention: A General Model," Others 0404001, EconWPA.
    8. Takuya Sekiguchi, 2016. "Optimal group composition for efficient division of labor," Theory and Decision, Springer, vol. 81(4), pages 601-618, November.
    9. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    10. Osherson, Daniel & Vardi, Moshe Y., 2006. "Aggregating disparate estimates of chance," Games and Economic Behavior, Elsevier, vol. 56(1), pages 148-173, July.
    11. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
    12. 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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