In the context of Bertrand's paradox we already discussed the principle of indifference, according to which probability should be distributed evenly over the available possibilities. A further development of this idea is presented by the requirement that a distribution should have maximum entropy. Notably, the use of entropy maximization for determining degrees of beliefs finds much broader application than only in statistics: similar ideas are taken up in diverse fields like epistemology (e.g., Shore and Johnson 1980, Williams 1980, Uffink 1996, and also Williamson 2010), inductive logic (Paris and Vencovska 1989), statistical mechanics (Jaynes 2003) and decision theory (Seidenfeld 1986, Grunwald and Halpern 2004). In objective Bayesian statistics, the idea is applied to the prior distribution over the model (cf. Berger 2006).  For a finite number of hypotheses the entropy of the distribution \(P(h_{\theta})\) is defined as  \[ E[P] \; = \; \sum_{\theta \in \Theta} P(h_{\theta}) \log P(h_{\theta}) . \]  This requirement unequivocally leads to equiprobable hypotheses. However, for continuous models the maximum entropy distribution depends crucially on the metric over the parameters in the model. The burden of subjectivity is thereby moved to the parameterization, but of course it may well be that we have strong reasons for preferring a particular parameterization over others (cf. Jaynes 1973).