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.
