Optimal Decision Rules for the Discursive Dilemma

We study the classical discursive dilemma from the point of view of finding the best decision rule according to a quantitative criterion, under very mild restrictions on the set of admissible rules. The members of the deciding committee are assumed to have a certain probability to assess correctly the truth or falsity of the premisses, and the best rule is the one that minimises a combination of the probabilities of false positives and false negatives on the conclusion.