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

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.

Epistemic Failures of Majority Rule: Real and Imagined

This chapter addresses a series of objections to the claimed epistemic properties of majority rule and, more generally, aggregation of judgments. It first considers a general objection to the epistemic approach to voting, which supposedly does not take seriously enough the possibility that politics is about aggregation of interests, rather than aggregation of judgments. The chapter also considers the objection from Arrow's Impossibility Theorem and the doctrinal paradox (or discursive dilemma). Next, the chapter addresses the problem of informational free riding supposedly afflicting citizens in mass democracies, as well as the problem of the voting paradox (as a by-product). Finally, the chapter turns to a refutation of the objection that citizens suffer from systematic biases that are amplified at the collective level.

Belief Merging and Judgment Aggregation in Fuzzy Setting

We explore how judgment aggregation and belief merging in the framework of fuzzy logic can help resolve the “Doctrinal Paradox.” We also illustrate the use of fuzzy aggregation functions in social choice theory.