2013/03/06 by Robert F. Bordley, Bordley, Robert F.
Computer Science · Decision Sciences · #AI-based Problem Solving and Planning #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Logic, Reasoning, and Knowledge #Multi-Criteria Decision Making #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1303.1508
openalex publication_date 2013/03/06 · openalex created_date 2022/09/19 · openalex updated_date 2026/07/28
Shafer's theory of belief and the Bayesian theory of probability are two\nalternative and mutually inconsistent approaches toward modelling uncertainty\nin artificial intelligence. To help reduce the conflict between these two\napproaches, this paper reexamines expected utility theory-from which Bayesian\nprobability theory is derived. Expected utility theory requires the decision\nmaker to assign a utility to each decision conditioned on every possible event\nthat might occur. But frequently the decision maker cannot foresee all the\nevents that might occur, i.e., one of the possible events is the occurrence of\nan unforeseen event. So once we acknowledge the existence of unforeseen events,\nwe need to develop some way of assigning utilities to decisions conditioned on\nunforeseen events. The commonsensical solution to this problem is to assign\nsimilar utilities to events which are similar. Implementing this commonsensical\nsolution is equivalent to replacing Bayesian subjective probabilities over the\nspace of foreseen and unforeseen events by random set theory probabilities over\nthe space of foreseen events. This leads to an expected utility principle in\nwhich normalized variants of Shafer's commonalities play the role of subjective\nprobabilities. Hence allowing for unforeseen events in decision analysis causes\nBayesian probability theory to become much more similar to Shaferian theory.\n