Aggregating subjective probabilities: some limitative theorems

1 Introduction Suppose that n individuals, labeled 1,..., n 9 wish to assign consensual probabilities to a sequence of events E u ..., E k which partition some set of possibilities. Let their subjective assignments be registered in an n x k matrix P = (Pij), where py denotes the subjective probability assigned by individual / to event Ej. The question of how to aggregate the probabilities in P into a single sequence of consensual probabilities may be abstractly modeled as the problem of choosing a mapping (hereafter called a probability aggregation method, or PAM)