Probability and symmetry

The Principle of Indifference, which dictates that we ought to assign two o utcomes equal probability in the absence of known reasons to do otherwise, is vulnerable to well-known objections. Nevertheless, the appeal of the pri nciple, and of symmetry-based assignments of equal probability, persists. W e show that, relative to a given class of symmetries satisfying certain pro perties, we are justified in calling certain outcomes equally probable, and more generally, in defining what we call relative probabilities. Relative probabilities are useful in providing a generalized approach to conditional ization. The technique is illustrated by application to simple examples.