Narrow Bracketing and Dominated Choices

An experiment by Tversky and Kahneman (1981) illustrates that people's tendency to evaluate risky decisions separately can lead them to choose combinations of choices that are first-order stochastically dominated by other available combinations. We investigate the generality of this effect both theoretically and experimentally. We show that for any decisionmaker who does not have constant-absolute-risk-averse preferences and who evaluates her decisions one by one, there exists a simple pair of independent binary decisions where the decisionmaker will make a dominated combination of choices. We also characterize, as a function of a person's preferences, the amount of money that she can lose due to a single mistake of this kind. The theory is accompanied by both a real-stakes laboratory experiment and a large-sample survey from the general U.S. population. Replicating Tversky and Kahneman's original experiment where decisionmakers with prototypical prospect-theory preferences will choose a dominated combination, we find that 28% of the participants do so. In the survey we ask the respondents about several hypothetical large-stakes choices, and find higher proportions of dominated choice combinations. A statistical model that estimates preferences from the survey results is best fit by assuming people have utility functions that are close to prospect-theory value functions and that about 83% of people bracket narrowly. None of these results varies strongly with the personal characteristics of participants. We also demonstrate directly that dominated choices are driven by narrow bracketing: when we eliminate the possibility of narrow bracketing by using a combined presentation of the decisions, the dominated choices are eliminated in the laboratory experiment and are greatly reduced in the survey.