David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Frank Arntzenius & David McCarthy (1997). The Two Envelope Paradox and Infinite Expectations. Analysis 57 (1):42–50.
John Broome (1995). The Two-Envelope Paradox. Analysis 55 (1):6 - 11.
Paul Castell & Diderik Batens (1994). The Two Envelope Paradox: The Infinite Case. Analysis 54 (1):46 - 49.
David J. Chalmers (2002). The St. Petersburg Two-Envelope Paradox. Analysis 62 (274):155–157.
Citations of this work BETA
No citations found.
Similar books and articles
Michael Clark & Nicholas Shackel (2000). The Two-Envelope Paradox. Mind 109 (435):415--442.
Olav Gjelsvik (2002). Paradox Lost, but in Which Envelope? Croatian Journal of Philosophy 2 (3):353-362.
Raymond S. Nickerson & Ruma Falk (2006). The Exchange Paradox: Probabilistic and Cognitive Analysis of a Psychological Conundrum. Thinking and Reasoning 12 (2):181 – 213.
Gary Malinas (2003). Two Envelope Problems and the Roles of Ignorance. Acta Analytica 18 (1-2):217-225.
Casper J. Albers, Barteld P. Kooi & Willem Schaafsma (2005). Trying to Resolve the Two-Envelope Problem. Synthese 145 (1):89 - 109.
W. Schaafsma, B. P. Kooi & C. Albers (2005). Trying to Resolve the Two-Envelope Problem. Synthese 145 (1):89-109.
Added to index2010-04-03
Total downloads42 ( #46,372 of 1,413,361 )
Recent downloads (6 months)2 ( #94,237 of 1,413,361 )
How can I increase my downloads?