- Jordan Howard Sobel
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“You have been given either envelopeA orB. B contains either one-half or twice the money inA. Do you want to switch? Now you open your envelope? Are you still happy to stand pat?”
Answers depend on whether you think there is an upper bound to the money inA. You should no longer be indifferent if you think there is not an upper bound, but, if you think there is a certain upper boundU, you should want to switch or not depending on whether your envelope holds less thanU.
Expected monetary values are extended to acts with infinitely many equally possible monetary values. It is maintained that though strong dominance under infinite partitions does not in the absence of an upper bound for values imply greater expected value, ‘univocal strong dominance’ is even then properly decisive for choice.
- Henle, James M. and Kleingberg, Eugene M.: 1979,Infinitesimal Calculus, Cambridge, Mass.: The MIT Press.
- Bernstein, Allen R. and Wattenberg, Frank: 1969, Nonstandard measure theory’, in W. A. J. Luxemburg (Ed.),Applications of Model Theory to Algebra, Analysis, and Probability, New York: Holt, Rinehart and Winston.
- Hosiasson-Lindenbaum, Janina: 1940, ‘On confirmation’,Journal of Symbolic Logic 5, 133–149.
- Jeffrey, Richard C.: 1983,The Logic of Decision: Second Edition, Chicago: University of Chicago Press.
- Marinoff, Louis: 1993, ‘Three pseudo-paradoxes in ‘quantum’ decision theory: Apparent effects of observation on probability and utility’,Theory and Decision 35, 55–76.
- Nalebuff, Barry: 1989, ‘Puzzles: The other person's envelope is always greener’,Journal of Economic Perspectives 3, 171–181.
- Robinson, Abraham: 1966,Non-Standard Analysis, Amsterdam: North-Holland Publishing Company.
- Sobel, Jordan Howard: 1987, ‘Self-doubts and Dutch strategies’,Australasian Journal of Philosophy 65, 56–81.
- Sobel, Jordan Howard: 1988, ‘Metatickles, ratificationism, and Newcomb-like problems without dominance’, in B. R. Munier, (Ed.),Risk, Decision and Rationality, Dordrecht: Reidel, pp. 438–501.
- Sobel, Jordan Howard: 1990, ‘Conditional probability, conditionalization, and Dutch books’, Vol. 1, in A. Fine, M. Forbes, and L. Wessels, (Eds.),PSA 1990, East Lansing, pp. 503–516.
- Zabell, Sandy: 1988, ‘Comment on a paper by Bruce M. Hill’, in J. M. Bernadoet al., (Eds.),Bayesian Statistics 3: Proceedings of the Third Valencia International Meeting, Oxford: Clarendon Press, pp. 233–236.
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Theory and Decision
Volume 36, Issue 1 , pp 69-96
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- Print ISSN
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- Kluwer Academic Publishers
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- Expected monetary values
- bounded and unbounded values
- infinite values
- Industry Sectors
- Author Affiliations
- 1. Scarborough College, University of Toronto, 1265 Military Trail, M1C IA4, Scaborough, Ontario, Canada