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The doctrinal paradox: comparison of decision rules in a probabilistic framework

Author

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  • Aureli Alabert

    (Universitat Autònoma de Barcelona)

  • Mercè Farré

    (Universitat Autònoma de Barcelona)

Abstract

The doctrinal paradox is analysed from a probabilistic point of view assuming a simple parametric model for the committee’s behaviour. The well known premise-based and conclusion-based majority rules are compared in this model, by means of the concepts of false positive rate (FPR), false negative rate (FNR) and Receiver Operating Characteristics (ROC) space. We introduce also a new rule that we call path-based, which is somehow halfway between the other two. Under our model assumptions, the premise-based rule is shown to be the best of the three according to an optimality criterion based in ROC maps, for all values of the model parameters (committee size and competence of its members), when equal weight is given to FPR and FNR. We extend this result to prove that, for unequal weights of FNR and FPR, the relative goodness of the rules depends on the values of the competence and the weights, in a way which is precisely described. The results are illustrated with some numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:58:y:2022:i:4:d:10.1007_s00355-021-01372-5
    DOI: 10.1007/s00355-021-01372-5
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.

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