Risk Aversion as a Perceptual Bias

The theory of expected utility maximization (EUM) explains risk aversion as due to diminishing marginal utility of wealth. However, observed choices between risky lotteries are difficult to reconcile with EUM: for example, in the laboratory, subjects' responses on individual trials involve a random element, and cannot be predicted purely from the terms offered; and subjects often appear to be too risk averse with regard to small gambles (while still accepting sufficiently favorable large gambles) to be consistent with any utility-of-wealth function. We propose a unified explanation for both anomalies, similar to the explanation given for related phenomena in the case of perceptual judgments: they result from judgments based on imprecise (and noisy) mental representation of the decision situation. In this model, risk aversion is predicted without any need for a nonlinear utility-of-wealth function, and instead results from a sort of perceptual bias --- but one that represents an optimal Bayesian decision, given the limitations of the mental representation of the situation. We propose a specific quantitative model of the mental representation of a simple lottery choice problem, based on other evidence regarding numerical cognition, and test its ability to explain the choice frequencies that we observe in a laboratory experiment.