Developments in the theory of risk require yet another evaluation of the behavioral validity of the independence axiom. This axiom plays a central role in most formal statements of expected utility theory, as well as popular alternative models of decision-making under risk, such as rank-dependent utility theory. It also plays a central role in experiments used to characterize the way in which risk preferences deviate from expected utility theory. If someone claims that individuals behave as if they "probability weight" outcomes, and hence violate the independence axiom, it is invariably on the basis of experiments that must assume the independence axiom. We refer to this as the Bipolar Behavioral Hypothesis: behavioral economists are pessimistic about the axiom when it comes to characterizing how individuals directly evaluate two lotteries in a binary choice task, but are optimistic about the axiom when it comes to characterizing how individuals evaluate multiple lotteries that make up the incentive structure for a multiple-task experiment. Building on designs that have a long tradition in experimental economics, we offer direct tests of the axiom and the evidence for probability weighting. We reject the Bipolar Behavioral Hypothesis: we find that nonparametric preferences estimated for the rank-dependent utility model are significantly affected when one elicits choices with procedures that require the independence assumption, as compared to choices with procedures that do not require that assumption. We also demonstrate this result with familiar parametric preference specifications, and draw general implications for the empirical evaluation of theories about risk.
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