  The ideal Bayesian agent reasons from a global probability model, but real
agents are restricted to simplified models which they know to be adequate only
in restricted circumstances. Very little formal theory has been developed to
help fallibly rational agents manage the process of constructing and revising
small world models. The goal of this paper is to present a theoretical
framework for analyzing model management approaches. For a probability
forecasting problem, a search process over small world models is analyzed as an
approximation to a larger-world model which the agent cannot explicitly
enumerate or compute. Conditions are given under which the sequence of
small-world models converges to the larger-world probabilities.
