Revealed Preference for Expected Utility Revisited

It is often easier to identify agents’ preferences for action, holding probabilities fixed, than to delineate all the possible consequences of actions. Under what conditions can such preferences be formulated as if agents maximize expected utility? As Green and Osband (1991) noted, completeness, transitivity, and convexity are necessary but not quite sufficient. One additional condition that appears to be sufficient is transitivity over an extended probability space. A simple geometric treatment makes the argument transparent and intuitively appealing.Convexity formalizes Savage’s (1954) sure-thing principle. In line with Hammond (1988), systematic violations are most likely to occur when information has some value over and above the direct consequences of actions. Specifically, people tend to overweight small probabilities of extreme risks, to treat one-time events as if repeated multiple times, and to let preferences be influenced by how actions are framed. This makes them vulnerable to endorsing sequences of actions that do not serve their broader interest. The resulting tension for public policymaking — should one do good or be perceived as doing good — is best tempered by encouraging more investigation and freer debate