The rationality of irrationality in the Monty Hall problem

Abstract

The rational solution of the Monty Hall problem unsettles many people. Most people, including the authors, think it feels wrong to switch the initial choice of one of the three doors, despite having fully accepted the mathematical proof for its superiority. Many people, if given the choice to switch, think the chances are fifty-fifty between their options, but still strongly prefer to stay with their initial choice. Is there some sense behind these irrational feelings? We entertain the possibility that intuition solves the problem of how to behave in a real game show, not in the abstract textbook version of the Monty Hall problem. A real showmaster sometimes plays evil, either to make the show more interesting, to save money, or because he is in a bad mood. A moody showmaster erases any information advantage the guest could extract by him opening other doors which drives the chance of the car being behind the chosen door towards fifty percent. Furthermore, the showmaster could try to read or manipulate the guest's strategy to the guest's disadvantage. Given this, the preference to stay with the initial choice turns out to be a very rational defense strategy of the show's guest against the threat of being manipulated by its host. Thus, the intuitive feelings most people have about the Monty Hall problem coincide with what would be a rational strategy for a real-world game show. Although these investigations are mainly intended to be an entertaining mathematical commentary on an information-theoretic puzzle, they touch on interesting psychological questions.