"Bayesian" is normative in the sense that if you think that plausibility assessments should follow Cox's assumptions, then they ought to be isomorphic to probabilities and updated using Bayes' Rule.

(Note that Cox's argument requires an unintuitive mathematical assumption (as discussed by Halpern, references at the Wikipedia link). Frank J. Tipler of Omega Point infamy has a paper on the arXiv claiming to avoid this assumption.)