Decoding model for decision task under risk

In decision making under risk, probability of each outcome is known by all decision-makers. This is the case for instance, when one wants to choose between equestrian bets. There is a gain associated with each horses and an odds. This odds represents the horse’s probability of winning. Historically, theoretical models assumed that decision makers were rational and therefore sought to maximize gain over the different bets. However, experiences have shown that human decision-maker deviates from rational choices. Different explanations have been proposed. First, a utility function was introduced which led to the so called ”expected utility theory.” A utility is assigned to each outcome depending on the subject. This explained risk aversion ie the preference of a sure gain over a risky gain even if statically, the risky gain is more advantageous. However, the theory fails to explain some behavior as the change in preferences when outcomes are reversed (changed sign). While, later prospect theory did. It is based on the fact that decision-makers tended to overestimate probabilities close to 0 and underestimate the one close to 1. Therefore, the brain does not use probabilities but rather distorted probabilities. Recently, based on that idea, Zhang and Maloney gave a functional form for distorted probabilities. They used it in a new kind of model for decision making. Concretely, the brain constructs a noisy internal representation of outcomes. This phase is called coding. Then, from these internal representations, the brain makes a decision. Zhang and Maloney examined coding for probabilities and not for outcomes. In this master thesis, we continue Zhang and Maloney’s work, focusing on decoding and building a model describing decoding of probabilities. We assumed that the subject makes his decision by maximizing his expected gain. We managed to derive an expression for the indifference point ie the probability for which the subject doesn’t have any preference between the two prospects, under the assumptions of rational limit and optimal coding. This means that the noise that perturbs the internal representation of the probability tends to zero. And the optimal coding refers to the fact that the subject will code only a specific interval of probabilities which contains the rational indifference point (the rational point with a noise for the internal representation equals to zero). That expression depends on the prior parameters, therefore we were able to understand the effect of a change in mean and width prior on the indifference point. We also managed to derive an expression for the probability of choosing the sure prospect when the subject is faced to one sure prospect and one risky. From that expression, we were able to understand for which range of the prior parameters, the subject will be risk averse. This fact tells us also that perceptual bias can account for risk aversion and risk seeking. And we finally manage to get an expression for the distorted probability measured by Zhang and Maloney. That expression is different from the one they tried to construct and above all is derived from general considerations not by putting together ad-hoc ingredients.