NDLI: Opening Two Envelopes

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Opening Two Envelopes

Content Provider	Springer Nature Link
Author	Syverson, Paul
Copyright Year	2010
Abstract	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.
Starting Page	479
Ending Page	498
Page Count	20
File Format	PDF
ISSN	03535150
Journal	Acta Analytica
Volume Number	25
Issue Number	4
e-ISSN	18746349
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-04-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Conditional expectation Exchange paradox Epistemic possibility Bounded and unbounded values Decision theory Topology Philosophy of Mind Epistemology Metaphysics Logic Philosophy
Content Type	Text
Resource Type	Article
Subject	Philosophy

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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