 Subjective probability theory models ignorance with respect to a proposition \(A\) by assigning probability of .5 to \(A\) and its complement \(\neg A\). More generally, an agent with subjective probability Pr is said to be ignorant with respect to the partition \(\{A_{1},\ldots,A_{n}\}\) if and only if \(\Pr(A_{i}) = 1/n\). The Principle of Indifference requires a doxastic agent to distribute her subjective probabilities in this fashion whenever, roughly, the agent lacks evidence of the relevant kind. Leitgeb and Pettigrew (2010b) give an accuracy argument for the principle of indifference. However, the principle leads to contradictory results if the partition in question is not held fixed. For a simple example, suppose that Sophia is ignorant about the color of a certain marble. Then, she must be nearly certain that it is not Blue. In this case, ignorance about one thing entails that she is very opinionated about another. But presumably she is also ignorant about whether or not the color is Blue. For more on this, see the discussion of Bertrand’s paradox in Kneale (1949) and Section 3.1 of the entry on  interpretations of probability.  A more cautious version of the principle of indifference, also applicable if the partition contains a countable infinity of elements, is the principle of maximum entropy. It requires the agent to adopt one of those probability measures Pr as her degree of belief function over (the \(\sigma\)-field generated by) the countable partition \(\{A_{i}\}\) that maximize the quantity \(-\sum_{i} \Pr(A_{i}) \log \Pr(A_{i})\). The latter is known as the entropy of Pr with respect to the partition \(\{A_{i}\}\). See Paris (1994).