 The second defect is the following. Suppose the individuals in \(N\) learn some new information that prompts them to revise their opinions on the propositions in \(X\), where revision takes the form of Bayesian conditionalization or some generalization of it. It is plausible to require that if we aggregate their post-revision probability assignments, the result will be the same as the one we would have got if we had first aggregated the pre-revision probability assignments and then revised the resulting collective probability assignments on the basis of the learnt information. More formally expressed, suppose \(L\) is the learnt information, and suppose \(Pr_1 |L, Pr_2 |L, \ldots ,Pr_n|L\) are the results of conditionalizing the \(n\) individuals’ opinion functions on the new  information.[16]  Then, assuming that all the profiles involved are in the domain of our opinion pooling rule, we require that aggregation (via \(F)\) and revision (via |) commute, i.e.,