Cognitive Imprecision and Stake-Dependent Risk Attitudes

In an experiment that elicits subjects’ willingness to pay (WTP) for the outcome of a lottery, we document a systematic effect of stake sizes on the magnitude and sign of the relative risk premium, and find that there is a log-linear relationship between the monetary payoff of the lottery and WTP, conditional on the probability of the payoff and its sign. We account quantitatively for this relationship, and the way in which it varies with both the probability and sign of the lottery payoff, in a model in which all departures from risk-neutral bidding are attributed to an optimal adaptation of bidding behavior to the presence of cognitive noise. Moreover, the cognitive noise required by our hypothesis is consistent with patterns of bias and variability in judgments about numerical magnitudes and probabilities that have been observed in other contexts. In addition to providing foundations for the kind of nonlinear distortions in lottery valuation posited by prospect theory, our model explains why the degree of stake-dependence should be greater for certainty-equivalents elicited by requiring subjects to assign a dollar value to lotteries than for those implied by binary choices.