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

Aureli Alabert*, Mercè Farré

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

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.

Original languageEnglish
JournalSocial Choice and Welfare
DOIs
Publication statusAccepted in press - 2021

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