Comparative Measures of Naivet é

We propose nonparametric definitions of absolute and comparative naiveté. These definitions leverage both ex-ante choice of menu to identify individuals' projections of their future behavior and ex-post choice from menus to identify their actual behavior. Their main advantage is their independence from any assumed functional form for the utility function representing behavior. An individual is sophisticated if she is indifferent between choosing from a menu ex post or committing to the actual choice from that menu ex ante. She is naive if she prefers the flexibility in the menu, reflecting a mistaken belief that she will act more virtuously than she actually will. One individual is more naive than another if she is both more optimistic about her future behavior while actually being less virtuous. In the case of Strotzian preferences, absolute naiveté implies that beliefs are a convex combination of virtuous and temptation utility, while comparative naiveté implies that the more naive individual's beliefs puts more weight than a more sophisticated individual on her virtuous utility, while her actual behavior puts more weight on the temptation utility. In different specifications of the underlying Strotzian preferences, such as quasi-hyperbolic discounting, the definitions impose further intuitive restrictions, such as inequalities on believed and actual present-bias factors. We propose suitable definitions for random choice. Finally, we discuss the implications of naiveté for welfare and the design of commitment devices