Nonlinear Decision Weights in Choice Under Uncertainty

In most real-world decisions, consequences are tied explicitly to the outcome of events. Previous studies of decision making under uncertainty have indicated that the psychological weight attached to an event, called a decision weight, usually differs from the probability of that event. We investigate two sources of nonlinearity of decision weights: subadditivity of probability judgments, and the overweighting of small probabilities and underweighting of medium and large probabilities. These two sources of nonlinearity are combined into a two-stage model of choice under uncertainty. In the first stage, events are taken into subjective probability judgments, and the second stage takes probability judgments into decision weights. We then characterize the curvature of the decision weights by extending a condition employed by Wu and Gonzalez (1996) in the domain of risk to the domain of uncertainty and show that the nonlinearity of decision weights can be decomposed into subadditivity of probability judgments and the curvature of the probability weighting function. Empirical tests support the proposed two-stage model and indicate that decision weights are concave then convex. More specifically, our results lend support for a new property of subjective probability judgments, interior additivity (subadditive at the boundaries, but additive away from the boundaries), and show that the probability weighting function is inverse S-shaped as in Wu and Gonzalez (1996).