List and Pettit

Abstract

Christian List and Philip Pettit formulate a "doctrinal paradox", compare it and extensions of it to more general cases, to the Condorcet paradox and its extension to a more general case formulated by Kenneth Arrow. Their treatment is illuminating both conceptually and formally. Another comparison that is worth exploring is between the doctrinal paradox and the well-known lottery paradox. List and Pettit present their problem as one of aggregating sets of judg ments rather than aggregating sets of preferences. Judgments are "modeled on acts of acceptance or rejection of certain propositions". Degrees of cre dence are not recognized, "either someone accepts a certain proposition or not". To accept a proposition is, I take it, to rule out its negation as not possibly true where "possible" means doxastically possible. If agent X does not accept proposition h, this can mean that X accepts the negation ~ h and, hence, rules h out as doxastically impossible. On this reading, if X must either accept h or fail to do so, X is required to be opinionated. According to another reading X fails to rule h out as impossible. On this reading, X is not required to be opinionated by the stipulation that either someone accepts a certain proposition or not. It turns out that List and Pettit adopt the opinionated interpretation. We are given a set S of propositions. Individual i accepts or rejects elements of S in a manner that yields a consistent and deductively closed subset of S that is also complete in the sense that for any h in S either h or ~ h is in f s personal set of judgments. That is to say, each individual's personal set of judgments is maximally consistent in the set S of proposi tions and, hence, is opinionated in the set S. Each individual is required to be opinionated. The meets of the maximally consistent sets constitute an exclusive and exhaustive set W of propositions relative to the background assumptions that characterize the model of the situation being explored. It is assumed that the cardinality of W is finite and not less than 3. The number N of individuals is finite and not less than 2. The challenge is to identify an ag