  (2.1e) captures one core message of Bayes' Theorem for theories of confirmation.  Let's say that H is uniformly better than H* as predictor of E's truth-value when (a) H predicts E more strongly than H* does, and (b) ~H predicts ~E more strongly than ~H* does.  According to the weak likelihood principle, hypotheses that are uniformly better predictors of the data are better supported by the data.  For example, the fact that little Johnny is a Christian is better evidence for thinking that his parents are Christian than for thinking that they are Hindu because (a) a far higher proportion of Christian parents than Hindu have Christian children, and (b) a far higher proportion of non-Christian parents than non-Hindu parents have non-Christian children.