Intuitions about Ordered Beliefs Leading to Probabilistic Models
This work addresses the problem of convincing skeptics about the fitness of probability models in AI and decision theory, offering an incremental approach based on qualitative reasoning.
The paper tackles the challenge of justifying probabilistic models for belief representation by deriving 'qualitative probability' from five simple assumptions about belief relationships, bridging the gap to full probability with an additional assumption, and extending the rationale to set-valued representations of partial orderings.
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.