For many years the neoclassical economic paradigm for consumer theory has been based on axioms of rational behavior equivalent to utility maximization for decisions under complete certainty and another set of axioms equivalent to expected utility (EU) maximization for decisions under risk (von Neumann and Morgenstern). Recently, however, this theory has come under fire both from within the economics profession and from outside due to a growing body of evidence suggesting that actual choices display consistent and predictable violations of the behavioral implications of these axioms, particularly within the context of risk and uncertainty. At least since the 1950s, with Simon's work on bounded rationality, alternative models of behavior have been proposed. In the past few years this area has received increasing emphasis. Notable contributions include the work of Akerlof and Dickens on cognitive dissonance, Kahneman and Tversky on prospect theory, Heiner on reliability theory, Bell and Loomes and Sugden on regret theory, and Machina on local approximations to EU functions. To date, work on these alternative theories has focused on empirical testing of their predictions and their abilities to explain the observed violations of expected utility theory. No attempt has yet been made to study formally the implications of these alternatives for welfare analysis and the definition and measurement of the costs or benefits resulting from projects or events. Yet, since the estimates of such costs or benefits often play an important role in public decisions, it is important to know whether the standard welfare results based on the EU model continue to hold under what appear to be more realistic theories of choice under uncertainty. This paper explores this question in the context of one particular theory, namely regret theory. This does not imply that the various paradigms are necessarily mutually exclusive. For example, regret may be an important factor in decision making, and at the same time individuals may display bias concerning small probability events as discussed by Kahneman and Tversky. However, this paper will focus only on regret to simplify the analysis. Regret theory was chosen from among the different alternative theories because it has intuitive appeal, it contains EU theory as a special case, and it is capable of explaining some observed forms of behavior that are inconsistent with EU theory but that are observed consistently in various empirical contexts. In addition, decisions under regret theory can be formulated within a mathematical optimization framework similar to that used for EU