Attitudes to risk and uncertainty: new insights from an experiment using interval prospects

The predominant way of eliciting risk attitudes is to ask decision-makers to choose between discrete monetary lotteries with known probabilities attached to the payoffs. Yet, arguably, most choices made day-to-day entail continuous outcomes where objective distributions are unknown. This paper investigates responses to continuous “prospects,” employing parametric methods based upon prospect theory under conditions of risk and uncertainty. We find that behavior under uncertainty seemed to mirror that of risk, but there appear to be some differences in how participants dealt with the uncertainty frame compared to risk. Participants appear not to treat “equally likely” outcomes as being “equally likely,” thus demonstrated cumulative probability warping suggested by prospect theory. Participants’ behavior was difficult to fully reconcile with prospect theory, at least to the extent that it is commonly parameterized, perhaps due to endpoints (in particular zero endpoints) being “salient.” Since continuous interval densities have zero mass at zero, this result is curious and has not been reported in experiments using discrete lotteries. We conjecture that although participants on one level understood the nature of the continuous prospects, the format induced a focus on endpoints over and above what would be warranted by the objective distributions given to them.