On Second Thoughts, Selective Memory, and Resulting Behavioral Biases∗ Preliminary

A proposed model of information processing generates a prediction about the constrainedoptimal stochastic choice that is robust to details of the feasible information structures. A decision-maker processes payoff-relevant information until she reaches her cognitive constraint, at which point she either terminates the decision process and chooses an action, or restarts the process. By conditioning the probability of termination on the information collected, the decision-maker controls the correlation between the payoff state and her terminal action. The constrained-optimal stochastic choice rule satisfies a second-thought-free condition: Given her information, the agent and the end of her decision-making is indifferent between terminating and restarting the decision process. The condition partially identifies preferences from choice data. The constrained-optimal choice rule exhibits (i) confirmation bias, (ii) speed-accuracy complementarity, (iii) overweighting of rare events, and (iv) salience effect: (i) The decision process is likely to terminate at an information set supporting a choice that is attractive a priori. (ii) A delayed response indicates second thoughts and a surprising state, in which mistakes occur often. (iii) A constrained-optimal belief formation process pays great attention to a priori rare events such as flight accidents, since surprising events are more informative than expected events. (iv) In perceptual tasks, the constrained-optimal perception discriminates in favor of distinct states that are easily distinguished from other states. keywords: bounded rationality, cognitive constraints, information processing, stochastic choice, confirmation bias, speed-accuracy complementarity, probability weighting, salience. JEL codes: D03, D80, D81, D83, D89, D90. ∗We thank Alessandro Pavan, Philip Reny, Colin Stewart, colleagues in the University of Edinburgh and the audiences at Bocconi University and workshops and conferences in Erice, Alghero, Faro, and Gerzensee. Ludmila Matysková and Jan Šedek provided excellent research assistance. Deborah Novakova has helped with English. Jakub Steiner has received financial support from the Czech Science Foundation grant 16-00703S.