A parsimonious theory of evidence-based choice

Abstract

That an agent's possible evidential states form a Boolean algebra (on which it is natural to define a probability measure) is an assertion that ideally should be proved, rather than assumed, in justifying rational choice as a representation of expected utility. A more parsimonious, axiomatic characterization of evidence is provided here. Two primitive entities are evidential states and a relation, more specific than, between evidential states. The axioms specify that more-specific-than is a partial order, there is a minimally specific e-state, and more-specific-than is a separative order. Choice alternatives are another primitive entity. A plan is an assignment of a choice alternative to each evidential state. In general, plans satisfying a version of the sure-thing principle cannot be rationalized by expected utility. But there is such a rationalization if the evidential structure is a tree.