Interval-Based Decisions for Reasoning Systems

This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the interval-valued measures. We advocate a new approach, which makes the following questions moot: 1. which additional criteria to use, and 2. how wide intervals should be. In order to implement the approach, we need more epistemological information. Such information can be generated by a rule of acceptance with a parameter that allows various attitudes toward error, or can simply be declared. In sketch, the argument is: 1. probability intervals are useful and natural in All. systems; 2. wide intervals avoid error, but are useless in some risk sensitive decision-making; 3. one may obtain narrower intervals if one is less cautious; 4. if bodies of knowledge can be ordered by their caution, one should perform the decision analysis with the acceptable body of knowledge that is the most cautious, of those that are useful. The resulting behavior differs from that of a behavioral probabilist (a Bayesian) because in the proposal, 5. intervals based on successive bodies of knowledge are not always nested; 6. if the agent uses a probability for a particular decision, she need not commit to that probability for credence or future decision; and 7. there may be no acceptable body of knowledge that is useful; hence, sometimes no decision is mandated.