Mean-variance or prospect theory? The nature of value representations in the human brain.

Whether investing in financial markets or deciding whom to ask on a date, our decisions are often taken in risky environments. Although traditional economic theories assume that we behave rationally in such environments, extensive evidence indicates that we are susceptible to systematic biases and inconsistencies when making risky decisions. For instance, people and other animals are not only sensitive to expected reward but also risk and can be either risk-averse or risk-prone depending on the context of a gamble. Two current theories have emerged in the field of “neuroeconomics” in an attempt to explain such phenomena. First, the meanrisk approach posits that the expected payoff (or mean reward) associated with a prospect is weighted by the prospect’s risk (or known outcome variance) (D’Acremont and Bossaerts, 2008). For example, in one formulation called the mean–variance model, the expected value (VMR) is equal to the mean payoff ( ) minus the outcome variance ( ), which is weighted by the individual’s susceptibility to risk (b): VMR b , where b 0 will produce risk aversion. A second theory, termed prospect theory, postulates the existence of separate nonlinear utility (i.e., reward magnitude) and reward probability (i.e., reward likelihood) functions (Rangel et al., 2008). According to prospect theory, the value of a prospect (VPT) is determined by the product of nonlinear probability w( ps) and utility u(xs) functions across states, as follows: