This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
This project models decision-making and learning in complex environments. One would expect most decision makers to be aware of such complexity and to realize that they have at best a limited understanding of the factors that determine the outcomes of any chosen course of action. Such awareness leads an individual to be modest is her ambitions about what can be learned and it also influences her actions. Our focus is on understanding and modeling formally these effects on learning and choice behaviors.
The settings considered are those of repeated experiments, where experiment is defined as the realtization of some chance event, such as the observation of an economic variable such as the rate of return to a financial asset or the annual growth rate for a particular country. An experiment can be thought of as part of a statistical model of the observations of interest. It is common in such settings that there is symmetry of evidence about the experiments; that is no information is given that would imply a distinction between them. However, there may be little information about any of the experiments, in which case there is little evidence of symmetry. A thoughtful and cautious individual would admit the possibility that the experiments may differ in some way, even if she cannot specify how. This will influence her behavior. After formulating this distinction in a precise way through a mathematical model, we show that the dominant model of choice in economics and Bayesian statistics (expected utility theory) cannot accommodate the distinction. Then we develop an alternative axiomatically-based model that can. The modeling of learning centers on the question of how to use the outcomes of past experiments to predict those of future experiments when these may differ in ways that are only poorly understood.
Numerous decision making problems fit into this framework. For example, consider a medical decision-maker who must prescribe treatment for patients that have similar histories, but who may nevertheless differ since histories are invariably incomplete. Our model can serve as a normative guide as well as suggesting experiments to test the descriptive validity of the axioms. Of particular promise are applications to statistical decision-making. Invariably in statistical analysis symmetry is assumed at some level, perhaps after correcting for perceived differences. Standard methods presume that, after such corrections, the identical statistical model applies to all other observations in he data set. This presumption is particularly problematic when analyzing open-ended theories, where it is impossible to account for all possible differences. A prime example is the empirical literature attempting to explain cross-country differences in growth rates, in which case an experiment corresponds to a country, and where open-endedness is widely recognized. Thus we pursue statistical procedures that permit the analyst to express a judgement of similarity but also a concern that the relevant experiments may differ, even if she cannot specify how. In addition, by providing solid decision-theoretic foundations for statistical methods, we render them well-suited to policy analysis.
