User talk:Gill110951/Two envelopes problem sources

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Two envelopes problem: sources[edit]

The following is a list of sources, ordered chronologically, that discuss the well-known two-envelope paradox.


  • Maurice Kraitchik, Mathematical Recreations, George Allen & Unwin, London. (2nd edition, 1953, Dover publications, New York).


  • J.E. Littlewood, A Mathematician's Miscellany, Methuen & Co, London.


  • Martin Gardner, Aha! Gotcha: Paradoxes to Puzzle and Delight, W.H. Freeman and Company, New York, p 106.


  • Carlos Rodriguez, Understanding Ignorance, Maximum Entropy and Bayesian Methods, pages 189–204. G Erickson and C R Smith (eds.), Kluwer Academic Publishers. [draft]DjVu
  • Thomas M Cover, Pick the largest number, Open Problems in Communication and Computation, T Cover and B Gopinath, eds., Springer Verlag, p 152.
  • Laurence McGilvery, 'Speaking of Paradoxes . . .' or Are We?, Journal of Recreational Mathematics 19: 15-19.


  • Sandy Zabell, Loss and gain: the exchange paradox, J M Bernardo, M H DeGroot, D V Lindley, and A F M. Smith, editors, Bayesian statistics 3, Proceedings of the third Valencia international meeting, pages 233–236. Clarendon Press, Oxford.
  • Sandy Zabell, Symmetry and and Its Discontents, Brian Skyrms, William Harper, editors, Causation, Chance, and Credence: Proceedings from the Irvine Conference on Probability and Causation, Volume 1, pages 155-190. Kluwer, Dordrecht.
  • Randall Barron, The paradox of the money pump: a resolution, Maximum Entropy and Bayesian Methods, ed J Skilling.
  • Barry Nalebuff, Puzzles: Cider in Your Ear, Continuing Dilemma, The Last Shall Be First, and More, The Journal of Economic Perspectives, 2, 149-156.


  • Barry Nalebuff, Puzzles: The Other Person’s Envelope is Always Greener, Journal of Economic Perspectives 3(1): 171–181.
  • Martin Gardner, Penrose Tiles to Trapdoor Ciphers and the Return of Dr Matrix, The Mathematical Association of America, W H Freeman, New York, p 148.


  • R. Guy, Where the Grass is Greener, contributed to column Flaws, Fallacies and Flimflam, College Mathematics Journal, January, p. 35.


  • Christensen and Utts, Bayesian Resolution of Classical Paradoxes: Two Examples, Technical Report 220, University of California, Davis, Division of Statistics.


  • Ronald Christensen, Jessica Utts, Bayesian Resolution of the 'Exchange Paradox', The American Statistician 46(4): 274–76.
  • Raymond Smullyan, Satan, Cantor, and Infinity Alfred A. Knopf. Oxford: Oxford University Press.
  • David J. Chalmers, The Two-Envelope Paradox: A Complete Analysis?, published online [html]
  • James Cargile, On a Problem about Probability and Decision, Analysis, 52(4): 211-16.
  • Ruma Falk and Clifford Konold, The Psychology of Learning Probability, pp. 151-164 in F.S. and S.P. Gordon (eds), Statistics for the Twenty-First Century, The Mathematical Association of America.


  • David A Binder, Comment on Christensen and Utts (1992), The Amercian Statistician 47(2): 160.
  • Ronald Christensen, Jessica Utts, Reply to Binder, The American Statistician 47(2): 160.
  • Terry Ridgway, Comment on Christensen and Utts (1992), The American Statistician 47(4): 311.
  • Ronald Christensen, Jessica Utts, Reply to Ridgway, The American Statistician 47(4): 311.
  • Paul Anand, The Philosophy of Intransitive Preference, The Economic Journal 103(417): 337-346. [jstor]


  • Jordan Howard Sobel, Two Envelopes, Theory and Decision, 36: 69–96.
  • Frank Jackson, Peter Menzies, Graham Oppy, The Two Envelope 'Paradox', Analysis 54(1): 43–45.
  • Paul Castell, Diderik Batens, The Two Envelope Paradox: The Infinite Case, Analysis 54(1): 46–49.
  • Piers Rawling. A note on the two envelopes problem Theory and Decision 36(1): 97-102.
  • Elliot Linzer, The Two Envelope Paradox, The American Mathematical Monthly 101(5): 417-419.
  • Sheldon M Ross, Comment on Christensen and Utts (1992), The American Statistician 48(3): 267.
  • Ronald Christensen, Jessica Utts, Reply to Ross, The American Statistician 48(3): 268.


  • John Broome, The Two-envelope Paradox, Analysis 55: 6–11.
  • Charles Chihara, The Mystery of Julius: A Paradox in Decision Theory Philosophical Studies 80: 1–16.
  • S J Brams, D M Kilgour, The box problem: To switch or not to switch Mathematics Magazine 68: 27–34.
  • Kyung Chae, A resolution of the ’exchange paradox’, Int. J. Math. Educ. Sci. Technol. 26(4): 553-558.


  • Nelson M Blachman, Ronald Christensen, Jessica Utts and David J Finney, Comment on Christensen and Utts, Bayesian resolution of the ‘Exchange Paradox’(1992), The American Statistician 50(1): 98–99 [jstor]
  • F T Bruss, The Fallacy of the Two Envelopes Problem, The Mathematical Scientist 21(2): 112–119.


  • McGrew, Shier, Silverstein, The Two-Envelope Paradox Resolved Analysis 57(1): 28–33.
  • Alexander D Scott, Michael Scott, What’s in the Two Envelope Paradox? Analysis 57(1): 34–41.
  • Frank Arntzenius, David McCarthy, The two envelope paradox and infinite expectations, Analysis 57(1): 42–50.
  • Piers Rawling, Perspectives on a pair of envelopes, Theory and Decision 43: 253–277.
  • K G Merryfield, N Viet, S Watson, The Wallet Paradox Amer. Math. Monthly 104(7): 647-649.
  • Raymond Smullyan, The Riddle of Scheherazade, and Other Amazing Puzzles, Ancient and Modern Knopf, New York.


  • John D Norton, When the sum of our expectations fails us: The exchange paradox Pacific Philosophical Quarterly 79: 34–58. [pdf]
  • S J Brams, D M Kilgour, The fallacy of the two envelopes problem, Mathematical Scientist 23: 58–59.


  • Carl G Wagner, Misadventures in conditional expectation: The two-envelope problem, Erkenntnis 51: 233–241.


  • M Clark, N Shackel, The Two-Envelope Paradox, Mind 109(435): 415–442.
  • Wilfried Hausmann, On The Two Envelope Paradox, unpublished?
  • Terry Horgan, The Two-Envelope Paradox, Nonstandard Expected Utility, and the Intensionality of Probability, Noûs 34(4): 578-603.
  • Z Schuss, To switch or not to switch, this is the question!, unpublished.
  • Ian Stewart, Mathematical Recreations: Paradox Lost Scientific American 6: 88–89.
  • Christopher M. Langan, Paradox Resolved: The Kraitchik and 2-Envelopes Paradoxes, unpublished [html]


  • Olav Gjelsvik, Can Two Envelopes Shake The Foundations of Decision Theory?, unpublished?
  • Terry Horgan, The Two-Envelope Paradox and the Foundations of Rational Decision Theory, unpublished.
  • N M Blachman, D M Kilgour, Elusive optimality in the box problem, Mathematics Magazine 74: 171-181.
  • Peter Winkler, Murray Hill, Games people don't play, Puzzlers' Tribute, David Wolfe and Tom Rodgers (eds), A K Peters Ltd.


  • Jeff Speaks, The two-envelope paradox and inference from an unknown, unpublished?
  • David Chalmers, The St. Petersburg Two-Envelope Paradox, Analysis 62(2): 155-57.
  • James Chase, The Non-Probabilistic Two Envelope Paradox, Analysis 62(2): 157–60.
  • Aaron S Edlin, Forward Discount Bias, Nalebuff’s Envelope Puzzle, and the Siegel Paradox in Foreign Exchange, Topics in Theoretical Economics 2(1).
  • Olav Gjelsvik, Paradox lost, but in which envelope? Croatian Journal of Philosophy II(6): 353–62.


  • Friedel Bolle, The Envelope Paradox, the Siegel Paradox, and the Impossibility of Random Walks in Equity and Financial Markets, unpublished?
  • Graham Priest, Greg Restall, Envelopes and Indifference, published online [pdf]
  • Casper Albers, Trying to resolve the two-envelope problem, Chapter 2 of his thesis Distributional Inference: The Limits of Reason, March 2003. (Has also appeared as Albers, Casper J.; Kooi, Barteld P. and Schaafsma, Willem (2005), Trying to resolve the two-envelope problem, Synthese, 145(1): 89–109)
  • Gary Malinas, "Two envelope problems and the roles of ignorance, Acta Analytica 18(30/31): 217–225.
  • C J G Meacham, J Weisberg, Clark and Shackel on the Two-Envelope Paradox, Mind 112(448): 685-689.
  • Michael Clark, Nicholas Shackel, Decision Theory, Symmetry and Causal Structure: Reply to Meacham and Weisberg, Mind 112(448): 691-701.
  • Terry Horgan, The Two-Envelope Paradox and the Foundations of Rational Decision Theory, unpublished [html]
  • Frank Arntzenius, Adam Elga, John Hawthorne, Bayesianism, Infinite Decisions, and Binding, unpublished draft [pdf]


  • Eric Schwitzgebel, Josh Dever, Using Variables Within the Expectation Formula, Kluwer Academic Publishers.
  • Dov Samet, Iddo Samet, David Schmeidler, One Observation behind Two-Envelope Puzzles, The American Mathematical Monthly 111(4): 347–51. [abstract]
  • R Jeffrey, Subjective probability: The real thing, Cambridge University Press.
  • Bruce Langtry. The Classical and Maximin Versions of the Two-Envelope Paradox, Australasian Journal of Logic 2: 30–43.
  • Robert A. Agnew, "On the Two-Box Paradox", Mathematics Magazine 77(4): 302–308. [pdf]
  • Keith Devlin, The Two Envelopes Paradox, published online [html]
  • Brian Weatherson, How Surprising is the Two Envelope Paradox, unpublished [html]
  • Tom Loredo, The Two-Envelope Paradox, unpublished.


  • Jan Poland, The Two Envelopes Paradox in a Short Story, unpublished.
  • C J Albers, B P Kooi, W Schaafsma, Trying to resolve the two-envelope problem, Synthese 145: 89–109.
  • Franz Dietrich, Christian List, The Two-Envelope Paradox: An Axiomatic Approach, Mind 114(454): 239-248.
  • Richard Harter, The two envelopes puzzle, unpublished [html]
  • Amos Storkey, Money Trouble and Money Trouble – Solution, unpublished.
  • P Rawling, A note on the two envelopes problem, Theory and Decision 36(1): 97-102.
  • Ned Markosian, A simple solution to the two-envelope problem, unpublished.


  • Rich Turner and Tom Quilter, The Two Envelopes Problem, published online [pdf].
  • Adom Giffin, The Error in the Two Envelope Paradox, arXiv:physics/0608172v1
  • Raymond Nickerson and Ruma Falk, The exchange paradox: Probabilistic and cognitive analysis of a psychological conundrum, Thinking & Reasoning 12(2): 181–213.
  • Dennis V Lindley, Understanding Uncertainty, Wiley, NY.
  • D R Cox, Principles of Statistical Inference, Cambridge University Press.
  • Eric Schwitzgebel and Josh Dever, The Two Envelope Paradox and Using Variables Within the Expectation Formula, Department of Philosophy, UC Riverside, published online [pdf].
  • Randall Barron, Continuous Version of the Two Envelopes Puzzle, published online [pdf]
  • John Kay, Don’t box yourself in when making decisions, Financial Times, August 22.
  • Graham Oppy, Philosophical Perspectives on Infinity, Cambridge University Press, pp 185-194.


  • Jeff Chen, The Puzzle of the Two-Envelope Puzzle—a Logical Approach, published online [abstract]
  • Bernard D Katz, Doris Olin, A Tale of Two Envelopes, Mind 116(464): 903-926.
  • Igor Douven, A Three-step Solution to the Two-envelope Paradox, Logique et Analyse 50(200) [pdf]
  • Aris Spanos, The Exchange (or Two Envelope) Paradox Revisited, published online.
  • Moshe Sniedovich, The Two-Envelope Paradox: A Primer for Dummies, unpublished draft.
  • Peter Olofsson, Probabilities: the little numbers that rule our lives, John Wiley & Sons, New Jersey, pages 129-132.


  • Ruma Falk, The Unrelenting Exchange Paradox, Teaching Statistics 30(3): 86-88.
  • Susan F Butler, Raymond S Nickerson, Keep or Trade? An Experimental Study of the Exchange Paradox, Thinking and Reasoning 14(4): 365–394.
  • Eric Schwitzgebel, Josh Dever, The Two Envelope Paradox and Using Variables Within the Expectation Formula, Sorites 20: 135-140 [pdf].
  • Graham Priest, Greg Restall, Envelopes and indifference, C Dégremont, L Keiff, H Rückert (eds.), Dialogues, Logics and Other Strange Things: Essays in Honour of Shahid Rahman, London: College Publications, 277-284 [pdf].


  • Mark D McDonnell, Derek Abbott, Randomized switching in the two-envelope problem, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465: 3309–3322. [abstract]
  • Don Fallis, Taking the Two Envelope Paradox to the Limit, Southwest Philosophy Review 25(2). [abstract]
  • Byeong-Uk Yi, The Two-envelope Paradox With No Probability, unpublished draft [pdf]
  • Melinda Roberts, The Nonidentity Problem and the Two Envelope Problem: When is One Act Better for a Person than Another? Chapter 10 of M A Roberts, D T Wasserman (eds.), Harming Future Persons, International Library 201 of Ethics, Law, and the New Medicine 35.
  • Tad Boniecki, Two Envelope Paradox Solution, unpublished [html]
  • Ruma Falk, Raymond Nickerson, An inside look at the two envelopes paradox, Teaching Statistics 31(2): 39-41.


  • Peter A. Sutton, The Epoch of Incredulity: A Response to Katz and Olin’s ‘A Tale of Two Envelopes’ Mind 119(473): 159-169.
  • Bernard D Katz, Doris Olin, Conditionals, Probabilities, and Utilities: More on Two Envelopes Mind 119(473): 172-183.
  • Federico O’Reilly, Is there a two-envelope paradox?, published online [pdf]
  • Paul Syverson, Opening Two Envelopes, Acta Analytica 25:479–498.
  • Martin C. Cooke, Two Envelopes, two paradoxes, The Reasoner 4(5): 74 - 75 [pdf]
  • Derek Abbott, Bruce R Davis, The two-envelope problem revisited, Fluctuation and Noise Letters 9(1): 1–8.
  • Jeremy Gwiazda, Repeated St Petersburg two-envelope trials and expected value, unpublished draft.


  • Mark D McDonnell, Alex J Grant, Ingmar Land, Badri N Vellambi, Derek Abbott, Ken Lever, Gain from the two-envelope problem via information asymmetry: on the suboptimality of randomized switching, Proceedings of the Royal Society.
  • Richard D Gill, Anna Karenina and The Two Envelopes Problem, unpublished draft [pdf]