Let's make a deal in the classroom: Institutional solutions to the Monty Hall Dilemma

ABSTRACT

The authors describe how the Monty Hall Dilemma, a well-known choice anomaly, can be demonstrated with a simple and versatile classroom experiment. In addition to demonstrating the anomaly, the experiment can be used to introduce students to some institutional modifications that have been shown to ameliorate it. This experiment, which can be tailored by instructors to meet specific learning objectives for a variety of courses, can also be used to frame broader discussions about rationality, institutions, and choices under uncertainty.

KEYWORDS:

• institutions
• Monty Hall Dilemma
• rational choice

JEL CODES:

• A20
• A22

Notes

1. The majority of laboratory experiments exploring the MHD involve multiple decision-making periods. The number of periods tends to range from 10 to 40. Studies exploring the basic MHD often find switch rates below 20 percent in initial periods, and rarely find switch rates much above 75 percent even in the final periods.

2. Note that in a later column, vos Savant (2003) introduced an alternative to the MHD, which has a more intuitive solution. It involves a multiple choice problem with three possible answers. After the student selects an answer, an incorrect answer is revealed independently of the answer originally selected by the student, leaving the probability of winning from staying or switching equal. This example could be used to aid understanding of the MHD by differentiating between the optimal solutions.

3. For example, Smith (1982) finds that individual anomalies can be eliminated by the double auction market institution. Gode and Sunder (1993) show that markets can generate allocative efficiency even when populated by zero-intelligence computerized traders. Kluger and Wyatt (2004) find that in asset markets in which as few as only one third of the traders correctly estimated probabilities in earlier individual trials of the MHD, market prices reflect the correct probability beliefs.

4. Both versions of the experiment are flexible in terms of the number of students that can be involved. The Small Groups version could also be run in a large class, but it would require more organization and monitoring. Additionally, the Entire Class version could easily be run in very small classes, and we have effectively conducted the Small Groups version with classes as small as 10 students.

5. Instructions, record sheets, suggested procedures, a card template, and a more detailed working paper version of the article are available at the following Web site: https://cbe.wwu.edu/econ/working-papers.

6. The class leader could be chosen in a variety of ways. For example, they could be selected in a competitive manner through a trivia quiz, randomly selected, or they could simply be someone who is already seen as a leader in the class for various reasons. The position of class leader could also be rotated each period.

7. If desired, this reporting could initially be left out and then added in later in the experiment to illustrate the effects of learning from others (fictitious in this case).

8. Note that if class points (bonus or otherwise) are used as the reward medium, the instructor can determine the weight they wish to place on experiment participation for the course. It usually works well to make it worthwhile to participate, but not so valuable as to dramatically change a student's course grade. (Most students enjoy participating and do not tend to need much additional motivation.) Everyone would receive the same exchange rate for Part I and varying exchange rates that decrease with rank for Part II. The instructor can determine appropriate exchange rates prior to running the experiment, or for simplicity, wait and determine them afterwards. Determining them beforehand requires calculating the average expected experimental point earnings, which are based on the number of periods planned for each part and respective expected switch rates. (In our experience, the switch rates observed in the classroom tend to vary based on the version used and student backgrounds and experience, but we often see average switch rates around 40 to 50 percent across periods in Part I, with significant increases, often nearing 100 percent, in the final periods of Part II.) Determining exchange rates afterwards simply means setting them such that the average observed experimental earnings translate into the average number of class points the instructor wishes to award. Initially informing the class that more experimental earnings translate into more class points is typically enough to motivate them to take the task seriously in our experience.

9. While students typically find it easy to follow the instructions, we have occasionally encountered students who misunderstand their roles. This is generally avoided with an initial trial run. The template we include in the online appendix provides instructors with another tool that can help avoid any confusion.