Dissecting the Monty Hall Anomaly

Abstract

We assess competing explanations of irrational behavior in the Monty Hall problem by creating new variants of the problem. Some variants employ a feature that automates the merging of probabilities, thus rendering transparent the probabilistic advantage of the rational choice. That feature also enables systematic variation in informational asymmetry, and in ordering of actions. Data from 77 subjects, each of whom makes 30 binary decisions, indicate that automated merging raises the fraction of rational choices from around 40% to over 80%. Other features examined have much less impact, indicating the importance of a Bayesian updating failure. (JEL C91, D02, D81, D83)

The Monty Hall problem as a multifaceted experiential learning exercise in quantitative business courses

“…The MHP has spawned a remarkable amount of attention and controversy. The vast literature regarding the MHP spans myriad disciplines from mathematics, statistics, game theory, quantum information theory, psychology, philosophy, ethology (Gill, 2011), education, sports science, medical decisionmaking, animal science (James et al, 2018), and behavioral economics (Whitmeyer, 2017) to sociology and religion (Bennett, 2018). Interest in the MHP has not been restricted to academic researchers; it may also be found in the popular press (e.g., The Economist, 1999;Tierney, 2008), on YouTube, and in the 2008 Columbia Pictures' movie 21.…”

“…• loss aversion: "changes that result in losses loom larger psychologically than do those that result in gains" (e.g., Massad et al, 2018: 1), • illusion of control: belief in the "ability to guess (or influence) the true state" (e.g., James et al, 2018James et al, : 1819), • escalation of commitment: having "a sense of ownership and [being] reluctant to abandon their initial nomination" (e.g., James et. al, 2018James et.…”

“…Even so, among that group, why would they not, then, switch as often as stay? The literature traces this oddity to cognitive phenomena such as escalation of commitment (e.g., James et al, 2018) and confirmation bias (Wason, 1960). The active learning exercises proposed in this article offer students the opportunity to wrestle with both the probabilistic and psychological aspects of the MHP in particular and decision-making in general.…”