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In page Bayesian probability:

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In fact, there are non-Bayesian updating rules that also avoid Dutch books (as discussed in the literature on "probability kinematics"[3] following the publication of Richard C. Jeffreys' rule, which is itself regarded as Bayesian[4]). The additional hypotheses sufficient to (uniquely) specify Bayesian updating are substantial[5] and not universally seen as satisfactory.[6]