Perspectives on a Pair of Envelopes
- Piers Rawling
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with respect to infinite partitions in circumstances of infinite expected utility. Within a probability framework that is only finitely additive, there are failures of dominance with respect to infinite partitions in circumstances of bounded utility with finitely many consequences (see the epilogue).
- Bernoulli, D.: 1738, ‘Specimen Theoriae Novae de Mensura Sortis’ [Exposition of a New Theory of the Measurement of Risk], Proceedings of the St. Petersburg Imperial Academy of Sciences 5.
- Broome, J.: 1995, ‘The Two-Envelope Paradox’, Analysis 55, 6-11.
- Castell, P. and Batens, D.: 1994, ‘The Two Envelope Paradox: The Infinite Case’, Analysis 54, 46-49.
- de Finetti, B.: 1972, Probability, Induction and Statistics, New York: Wiley.
- de Finetti, B.: 1974, Theory of Probability, 2 vols., New York: Wiley.
- Fishburn, P.C.: 1981, ‘Subjective Expected Utility: A Review of Normative Theories’, Theory and Decision 13, 139-199.
- Kahneman, D., Slovic, P. and Tversky, A. (eds.): 1982, Judgment Under Uncertainty: Heuristics and Biases, Cambridge University Press.
- Kadane, J.B., Schervish M.J. and Seidenfeld, T.: 1986, ’statistical Implications of Finitely Additive Probability, Bayesian Inference and Decision Techniques, Goel, P. and Zellner, A. (eds.) Elsevier Science Publishers B.V.
- Lindley, D.V.: 1972, Bayesian Statistics, A Review, Philadelphia: Society for Industrial and Applied Mathematics.
- Nalebuff, B.: 1989, ‘The Other Person’s Envelope is Always Greener’, Journal of Economic Perspectives 3, 171-181.
- Jeffrey, R.: 1983, The Logic of Decision, 2nd ed., University of Chicago Press.
- Rawling, P.: 1993, ‘Choice and Conditional Expected Utility’, Synthese 94, 303-328.
- Rawling, P.: 1994, A Note on the Two Envelopes Problem’, Theory and Decision 36, 97-102.
- Savage, L.: 1972, The Foundations of Statistics, 2nd ed., New York: Dover.
- Seidenfeld, T. and Schervish, M.: 1983, ‘A Conflict Between Finite Additivity and Avoiding Dutch Book’, Philosophy of Science 50(3), 398-412.
- Perspectives on a Pair of Envelopes
Theory and Decision
Volume 43, Issue 3 , pp 253-277
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Pair of envelopes
- countable additivity
- principle of dominance
- finite additivity
- infinite partitions
- Industry Sectors
- Piers Rawling (1)
- Author Affiliations
- 1. Philosophy Department, University of Missouri-St. Louis, St. Louis, MO, 63121-4499, U.S.A