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When the sum of our expectations fails us: The exchange paradox

Norton, JD (1998) When the sum of our expectations fails us: The exchange paradox. Pacific Philosophical Quarterly, 79 (1). 34 - 58. ISSN 0279-0750

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In the exchange paradox, two players receive envelopes containing different amounts of money. The assignment of the amounts ensures each player has the same probability of receiving each possible amount. Nonetheless, for each specific amount a player may find in his envelope, there is a positive expectation of gain if the player swaps envelopes with the other player, in apparent contradiction with the symmetry of the game. I consider a variant form of the paradox that avoids problems with improper probabilities and I argue that in it these expectations give no grounds for a decision to swap since that decision must be based on a summation of all the expectations. But this sum yields a non-convergent series that has no meaningful value. The conflicting recommendations - that it is to one or the other player's advantage to swap - arise from different ways of grouping terms in the sum that yield an illusion of convergence. I describe a generalized exchange paradox, explore some of its properties and display another example. © 1998 University of Southern California and Blackwell Publishers Ltd.


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Item Type: Article
Status: Published
CreatorsEmailPitt UsernameORCID
Norton, JDjdnorton@pitt.eduJDNORTON
Centers: University Centers > Center for Philosophy of Science
Date: 1 January 1998
Date Type: Publication
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Journal or Publication Title: Pacific Philosophical Quarterly
Volume: 79
Number: 1
Page Range: 34 - 58
DOI or Unique Handle: 10.1111/1468-0114.00049
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > History and Philosophy of Science
Refereed: Yes
ISSN: 0279-0750
Date Deposited: 12 Jul 2012 13:38
Last Modified: 02 Feb 2019 15:56


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