The Doctrinal Paradox in Deliberative Process and in Majority Voting

This paper proposes a new approach analyzing to the doctrinal paradox by considering a deliberative process (which can be represented by an agent-based model) in comparison with classical (binary) majority voting and an aggregation of (continuous) degrees of belief prior to majority voting. This model is a multivariate extension of the Hegselmann-Krause opinion dynamics model. From a quantitative comparison of the final sentences resulting from a (binary and continuous) majority-voting and deliberative method, several results emerge. First, for a small jury, binary majority voting leads to the doctrinal paradox less often than continuous majority voting and the interaction process. Second, when the jury gets bigger, letting the jury members interact minimizes the occurrence of the doctrinal paradox. Third, once agents respect the principle of reason for updating their opinions, they can totally avoid the doctrinal paradox, which is impossible with majority voting. Fourth, we notice that even if sometimes the majority-voting and the deliberative process produce the same rate of occurrence of the paradox, it does not imply that their verdict will be the same for a given trial: the verdict differs in maximum 25% of the time for small juries, but this discrepancy fades out for larger juries.