 Such a rule is defined as follows. Let \(w_1, w_2 , \ldots ,w_n \ge 0\) be an assignment of weights to the \(n\) individuals with \(w_{1 }+ w_{2 }+ \ldots_{ }+ w_n = 1\). Then the corresponding linear pooling rule assigns to each profile \(\langle Pr_1, Pr_2,\ldots, Pr_n\rangle\) of probabilistically coherent opinion functions the collective opinion function \(Pr = w_1 Pr_1 + w_2 Pr_2 + \ldots + w_n Pr_n.\) Thus the collective probability assigned to each proposition \(p \in X\) is a weighted linear average of the individual probabilities assigned to \(p\). Linear pooling rules range from ones with perfectly equal weights (which thereby satisfy anonymity) to ones that concentrate all weight on one individual (i.e., dictatorships). A noteworthy lesson is that essentially the same conditions that characterize the class of dictatorial aggregation rules in the case of binary judgment aggregation now characterize the class of linear pooling rules.