Similarity-Based Mistakes in Choice

We characterize the following choice procedure. The decision maker is endowed with a preference and a similarity - a reflexive binary relation over alternatives. In any choice problem she includes in her choice set all options that are similar to her most preferred feasible alternative. Hence an inferior option may end up,by mistake, being chosen because it is similar to a better one. We characterize this boundedly rational behavior by suitably weakening the rationalizability axiom of Arrow (1959). We also characterize a generalization where the decision maker chooses alternatives potentially on the basis of their similarities to attractive yet infeasible alternatives. We show that if similarity-based mistakes cause a departure from rationalizability, they lead to cyclical behavior.