Probabilistic reasoning in the two-envelope problem


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. Until recently it was argued that it did not matter whether the envelope was traded or not, but Abbott, Davis & Parrondo (2010) showed that gains could be made if trading was a probabilistic function of amount observed. Three experiments varied where the observed and maximum amounts fell in a possible distribution and tested whether this affected choices. Trading was less likely for lower observed amount than higher, but this effect differed depending on the stated distribution. This suggests that participants’ trade decisions were affected by where observations fit in the distribution, and thus their probabilities. The modeling tools used here may be applicable to other reasoning phenomena.

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