Non-deductive reasoning systems are often <I>representation
dependent</I>: 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 
<I>principle of maximum entropy</I> 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.
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