Theoretical Investigation of Belief Revisions in Auditing

In this paper we examine the empirical findings of belief revision under two alternatives: the Bayesian framework and the Dempster-Shafer theory of belief functions. Bayesian theory is very stringent in its requirement that the probability of mutually exclusive and collectively exhaustive events sum to one. It requires that the belief be increased in light of supporting evidence, and be decreased in light of conflicting evidence. These results are consistent with the empirical findings. However, the Bayesian analysis entails the largest increase (decrease) in belief for medium priors in light of supporting (conflicting) evidence. This is contrary to empirical findings. The largest increase was observed for smallest priors when presented with supporting evidence. The largest decrease was observed for highest priors when presented with conflicting evidence. Further, Bayesian theory fails to explain the ‘recency’ and the ‘dilution’ effects. In the belief-function formalism, the belief in a proposition increases in light of supporting (positive) evidence. Further, the largest increase is for the lowest priors. This is consistent with the empirical findings. The belief in a proposition decreases in light of conflicting (negative) evidence and the largest decrease is for medium priors. This is not totally consistent with the empirical findings. However, with discounting we can attain the largest decrease for the highest prior, consistent with the empirical findings. By incorporating discounting in belief functions, we are able to model the ‘recency’ and the ‘dilution’ effects.