Efficient Coding and Risky Choice

We present a model of risky choice in which the decision maker (DM) perceives a lottery payoff with noise due to the brain’s limited capacity to represent information. We model perception using the principle of efficient coding, the notion that perception is more precise for frequently occurring stimuli. Our model shows that it is efficient for risk taking to be more sensitive to those payoffs that the DM encounters more frequently. The model also predicts that the DM’s value function fluctuates with the recently encountered distribution of payoffs. To test the model, we manipulate the distribution of payoffs in a laboratory experiment. We find that risk taking is indeed more sensitive to those payoffs that are presented more frequently. Moreover, we conduct an additional test of efficient coding by incentivizing subjects to classify which of two symbolic numbers is larger. We find higher accuracy for those numbers that subjects have more frequently observed, providing further evidence that perception of a given numerical quantity varies with the recent environment. Overall, our experimental results suggest that risk taking depends systematically on the payoff distribution to which the DM’s perceptual system has recently adapted.