Representation Dependence in Probabilistic Inference

Non-deductive reasoning systems are often representation dependent, representing the same situation in two different ways may cause such a system to return two different answers. This is generally viewed as a significant problem. For example, the principle of maximum entropy has been subjected to much criticism due to its representation dependence. There has, however, been almost no work investigating representation dependence. In this paper, we formalize this notion and show that it is not a problem specific to maximum entropy. In fact, we show that any probabilistic inference system that sanctions certain important patterns of reasoning, such as a minimal default assumption of independence, must suffer from representation dependence. We then show that invariance under a restricted class of representation changes can form a reasonable compromise between representation independence and other desiderata.