Probabilistic reasoning in the two-envelope problem

• Published in: Thinking & reasoning Vol. 21; no. 3; pp. 295 - 316
• Main Author: Burns, Bruce D.
• Format: Journal Article
• Language: English
• Published: Hove Routledge 03.07.2015; Taylor & Francis Ltd
• Subjects: Mathematical modeling; Probabilistic reasoning; Two-envelope problem
• ISSN: 1354-6783; 1464-0708
• DOI: 10.1080/13546783.2014.971055

In the two-envelope problem, a reasoner is offered two envelopes, one containing exactly twice the money in the other. After observing the amount in one envelope, it can be traded for the unseen contents of the other. It appears that it should not matter whether the envelope is traded, but recent mathematical analyses have shown that gains could be made if trading was a probabilistic function of amount observed. As a problem with a purely probabilistic solution, it provides a potentially interesting way to test people's consistency with probabilistic models. Three experiments did this by varying the size of both the observed and maximum amounts, and their possible distribution. The results showed that trading decisions were affected by where the observed amount in the opened envelope fell in the distribution, though its size did not always do so. This suggests that participants' trade decisions could be affected by the perceived probabilities of different observed amounts, which is consistent with the probabilistic solution to the problem.