Cognitive Imprecision and Small-Stakes Risk Aversion
NBER Working Paper No. 24978
Observed choices between risky lotteries are difficult to reconcile with expected utility maximization, both because subjects appear to be too risk averse with regard to small gambles for this to be explained by diminishing marginal utility of wealth, as stressed by Rabin (2000), and because subjects' responses involve a random element. 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 representations of the decision situation. In this model, risk aversion results from a sort of perceptual bias — but one that represents an optimal decision rule, given the imprecision of the mental representation of the situation. We propose a quantitative model of the noisy mental representation of simple lotteries, based on other evidence regarding numerical cognition, and test its ability to explain the choice frequencies that we observe in a laboratory experiment. Our model is more consistent with the laboratory data than random versions of expected utility theory or prospect theory, using both in-sample and out-of-sample tests of model fit.
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Document Object Identifier (DOI): 10.3386/w24978