Positively correlated choice

We provide an axiomatic foundation for a choice model with two periods between which preferences are updated, but the second period choices are positively correlated with past choices in a manner that is unrelated to the agent’s preferences. Specifically, in our model, the agent chooses alternative $x$ over alternative $y$ in contrast to his past choice if and only if the difference between the utility of $x$ and that of $y$ is higher than some fixed cost. While restrictive in its nature, this representation captures several related but distinctive phenomena: a taste for consistency, cognitive dissonance, the escalation of commitment, passive choice, and habit formation. We also provide a representation that allows for a more general form of cost and the revealed preference implications of our models. Finally, we connect our representation to the theories of imperfect discrimination.