Intuitions about Ordered Beliefs Leading to Probabilistic Models
  The general use of subjective probabilities to model belief has been
justified using many axiomatic schemes. For example, ?consistent betting
behavior' arguments are well-known. To those not already convinced of the
unique fitness and generality of probability models, such justifications are
often unconvincing. The present paper explores another rationale for
probability models. ?Qualitative probability,' which is known to provide
stringent constraints on belief representation schemes, is derived from five
simple assumptions about relationships among beliefs. While counterparts of
familiar rationality concepts such as transitivity, dominance, and consistency
are used, the betting context is avoided. The gap between qualitative
probability and probability proper can be bridged by any of several additional
assumptions. The discussion here relies on results common in the recent AI
literature, introducing a sixth simple assumption. The narrative emphasizes
models based on unique complete orderings, but the rationale extends easily to
motivate set-valued representations of partial orderings as well.
