An objective definition of subjective probability

Several attempts have been made to give an objective definition of subjective probability. These attempts can be divided into two approaches. The first approach uses an a priori probability distribution over the set of interpretations of the language that we are using to describe information. The idea is to define such an a priori probability distribution using some general principles such as the insufficient reason principle of Bemoulli and Laplace. The second approach does not start from a set of interpretations among which we try to find the one describing the world, but instead tries to build a partial model of the world. Uncertainty in the available information results in several possible partial models, each presenting a different view of the world. Using the insufficient reason principle, a probability is assigned to each view. This paper will present arguments for using the second approach instead of the first. Furthermore, a new formalization of the second approach, solving the problems of earlier attempts, will be given.