When biases under risk are optimal under uncertainty and learning. Overestimation of low probabilities and status quo bias

In experimental economics, it is observed that individuals having to choose between loteries behave as if they overweigh small probabilities. Somewhat related is the observation that low probability-vivid consequences events are often given a weight that is much higher than their observed frequencies (like plane accidents, for instance). Our claim is that such biases may result from the observation that, under uncertainty, probabilities are not given but are sequentially learnt by trials. We show that overweighting of low probability events may be a byproduct of optimal sequential decision-making under uncertainty and learning. Our model extends an analysis made by Haselton and Nettle (The paranoid optimist: An integrative evolutionary model of cognitive biases, 2006) to the situation of dynamic learning exhibiting a multi-armed bandit structure. A decision maker (DM) does not know a priori the objective probability driving the ocurrence of a “bad” event, but learns it a posteriori by experience (trials). However, the DM can also decide to avoid being confronted possibly to such bad event, but at the price of an avoidance cost. We define a critical probability by the ratio between costs of encounter and costs of avoidance. We show that, for a rare event with probability lower than the critical probability, following an optimal strategy leads to either experimenting forever and rightly evaluating the unknown probability or experimenting followed by forever avoiding and overestimating the unknown probability. We conclude that behaviors considered as biases under risk – overweighting of small probabilities and status quo bias – are features of optimal behavior under uncertainty and learning. As far as minimizing mean discounted costs enhances fitness (better survival and reproduction), natural selection may have favored such biases in individuals. Université Paris–Est, CERMICS, 6–8 avenue Blaise Pascal, 77455 Marne la Vallée Cedex 2, France. [email protected]