Acta Analytica 25 (4):479-498 (2010)

In the two-envelope problem, one is offered a choice between two envelopes, one containing twice as much money as the other. After seeing the contents of the chosen envelope, the chooser is offered the opportunity to make an exchange for the other envelope. However, it appears to be advantageous to switch, regardless of what is observed in the chosen envelope. This problem has an extensive literature with connections to probability and decision theory. The literature is roughly divided between those that attempt to explain what is flawed in arguments for the advantage of switching and those that attempt to explain when such arguments can be correct if counterintuitive. We observe that arguments in the literature of the two-envelope problem that the problem is paradoxical are not supported by the probability distributions meant to illustrate the paradoxical nature. To correct this, we present a distribution that does support the usual arguments. Aside from questions about the interpretation of variables, algebraic ambiguity, modal confusions and the like, most of the interesting aspects of the two-envelope problem are assumed to require probability distributions on an infinite space. Our next main contribution is to show that the same counterintuitive arguments can be reflected in finite versions of the problem; thus they do not inherently require reasoning about infinite values. A topological representation of the problem is presented that captures both finite and infinite cases, explicating intuitions underlying the arguments both that there is an advantage to switching and that there is not.
Keywords Conditional expectation  Exchange paradox  Epistemic possibility  Bounded and unbounded values  Decision theory  Topology
Categories (categorize this paper)
DOI 10.1007/s12136-010-0096-7
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 60,842
Through your library

References found in this work BETA

Subjective Probability: The Real Thing.Richard Jeffrey - 2002 - Cambridge University Press.
The Two-Envelope Paradox.John Broome - 1995 - Analysis 55 (1):6 - 11.
The Two-Envelope Paradox.Michael Clark & Nicholas Shackel - 2000 - Mind 109 (435):415--442.

View all 29 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles


Added to PP index

Total views
75 ( #139,114 of 2,438,909 )

Recent downloads (6 months)
2 ( #283,061 of 2,438,909 )

How can I increase my downloads?


My notes