  The problem of combining the evidence concerning an unknown, contained in
each of $k$ Bayesian inference bases, is discussed. This can be considered as a
generalization of the problem of pooling $k$ priors to determine a consensus
prior. The linear opinion pool of Stone (1961) is seen to have the most
appropriate properties for this role. In particular, linear pooling preserves a
consensus with respect to the evidence and other rules do not. While linear
pooling does not preserve prior independence, it is shown that it still behaves
appropriately with respect to the expression of evidence in such a context. For
the general problem of combining evidence, Jeffrey conditionalization plays a
key role.
