Talk:Two envelopes problem/Literature

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

“ Indeed if there is anything inherently unbounded about the two-envelope paradox, it is that each search will uncover at least one more reference. ”

— Paul Syverson

1943

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

1951

• David Blackwell, On the translation parameter problem for discrete variables, Ann. Math. Stat. 22 (1951) 391–399.

1953

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

1982

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

1986

• Gábor Székely, Paradoxes in probability theory and mathematical statistics, Reidel Publishing Company.

1987

• 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.

1988

• Sandy Zabell, Discussion of 'De Finetti's theorem, induction, and A(n) or Bayesian nonparametric predictive inference' by B M Hill, 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 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.

1989

• Barry Nalebuff, Puzzles: The Other Person’s Envelope is Always Greener, Journal of Economic Perspectives 3(1): 171–181 [pdf]
• 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.

1990

• R Guy, Where the Grass is Greener, contributed to column Flaws, Fallacies and Flimflam, College Mathematics Journal, January, p. 35. Included in the book Mathematical Fallacies, Flaws and Flimflam by column editor Edward J. Barbeau (2000), pp. 78-81, published by Mathematical Association of America.

1991

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

1992

• 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.
• 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.
• Marilyn Vos Savant, column Ask Marilyn, September 20, Parade Magazine.
• Deborah Hecht, contribution to column Reader reflections, Mathematics Teacher, 85, pp. 90-91.

1993

• 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.
• Arthur Falk, Summer 1991: The "Monty Hall" Problem; Fall 1993: The Two Envelopes Puzzle; And Now: Doomsday, Proceedings of the Heraclitean Society 17: 64.

1994

• 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.
• David J Chalmers, The Two-Envelope Paradox: A Complete Analysis?, published online [html]

1995

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

1996

• Nelson Blachman, Ronald Christensen and Jessica Utts, Comment on Christensen and Utts, Bayesian resolution of the ‘Exchange Paradox’(1992), The American Statistician 50(1): 98–99 [jstor]
• F. Thomas Bruss, The Fallacy of the Two Envelopes Problem, The Mathematical Scientist 21(2): 112–119.

1997

• Timothy McGrew, David Shier, Harry Silverstein, The Two-Envelope Paradox Resolved Analysis 57(1): 28–33.
• Alexander 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.
• Kent Merryfield, Ngo Viet, Saleem Watson, The Wallet Paradox American Mathematical Monthly 104(7): 647-649.
• Raymond Smullyan, The Riddle of Scheherazade, and Other Amazing Puzzles, Ancient and Modern Knopf, New York.

1998

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

1999

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

2000

• Michael Clark, Nicholas Shackel, The Two-Envelope Paradox, Mind 109(435): 415–442.
• Wilfried Hausmann, On The Two Envelope Paradox, Friedberger Hochschulschriften, volume 5. Fachhochschule Giessen-Friedberg.
• 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]
• Niall Shanks, Robert B Gardner (ed) Logic, Probability and Science, pp. 49-76.
• F. Thomas Bruss, Ludger Rüsendorf, The Switching Problem and Conditionally Specified Distributions, Mathematical Scientist 25: 47-53 [ps]
• Piers Rawling, The Exchange Paradox, Finite Additivity, and the Principle of Dominance, Poznan Studies in the Philosophy of the Sciences and the Humanities 71: 49-76.
• Robert B Gardner, The Exchange Paradox, Finite Additivity, and the Principle of Dominance Commentary, Poznan Studies in the Philosophy of the Sciences and the Humanities 71: 49-76.

2001

• 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.
• Nelson Blachman, Marc 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.
• Yudi Pawitan, In All Likelihood: Statistical Modeling and Inference Using the Likelihood, Oxford University Press, Oxford.

2002

• 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.
• Edwin F Meyer, Risk Management and the Two Envelope Paradox, Journal of Recreational Mathematics 31 (4) 2002-03 275-279.
• Mikelis Bickis, Eric Neufeld, A Variation on the Paradox of Two Envelopes, FLAIRS Conference.
• Monte Cook, Getting Clear on the Two-Envelope Paradox, Southwest Philosophy Review 18(1): 45-51.
• William L Vanderburgh, A Commentary on Cook's “Getting Clear on the Two-Envelope Paradox”, Southwest Philosophy Review 18(2): 95-99.

2003

• Friedel Bolle, The Envelope Paradox, the Siegel Paradox, and the Impossibility of Random Walks in Equity and Financial Markets, unpublished?
• 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, Kooi, and Schaafsma, Trying to resolve the two-envelope problem, Synthese 145(1): 89–109 (2005))
• Gary Malinas, Two envelope problems and the roles of ignorance, Acta Analytica 18(30/31): 217–225.
• Christoffer Meacham, Jonathan 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]
• Oldford, Probability, problems, and paradoxes pictured by eikosograms, page 22, unpublished.

2004

• 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] JSTOR 3219290
• 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.
• David Hand, Measurement Theory and Practice: The World Through Quantification, London: Arnold, ISBN 0-340-67783-X, Chapter 2.
• Frank Arntzenius, Adam Elga, John Hawthorne, Bayesianism, Infinite Decisions, and Binding, Mind 113(450): 251-283, [jstor], draft [pdf]

2005

• Jan Poland, The Two Envelopes Paradox in a Short Story, unpublished.
• Casper Albers, Barteld Kooi, Willem 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.
• John Williams, Simply Avoid Being Enveloped by Paradox, Research Collection School of Social Sciences, paper 69. Singapore Management University, Cognitive Psychology.

2006

• 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, pp 217-220.
• D R Cox, Principles of Statistical Inference, Cambridge University Press.
• 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.
• Gary Malinas, Two Envelope Problems, The Proceedings of the Twenty-First World Congress of Philosophy, volume 9, pp 153-158.

2007

• 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.
• Eric Schwitzgebel and Josh Dever, The Two Envelope Paradox and Using Variables Within the Expectation Formula, Department of Philosophy, UC Riverside, prepublication [pdf] (see also journal published version, 2008)
• John Simons, Almost always swapping can be profitable, not the final word on the box paradox, unpublished?
• David J. Runger, The Two Envelopes Paradox: Exploring Expected Value and Rational Choice, published online [pdf]

2008

• 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, 283-290 [pdf].
• Aris Spanos, The Two Envelope (Exchange) Paradox Revisited, Department of Economics, Virginia Tech, unpublished?
• Quintana, J.M., O’Reilly, F., Demystifying the Two-Envelope Paradox?, Preimpreso No. 148 Septiembre de 2008, IIMAS, UNAM, Mexico.

2009

• 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. [pdf]
• 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.
• Martin Peterson, An Introduction to Decision Theory, Cambridge University Press, Chapter 4.7: 86-90.
• Theodore P. Hill, "Knowing When to Stop". American Scientist, Vol. 97, 126-133 (2009).

2010

• Peter Sutton, The Epoch of Incredulity: A Response to Katz and Olin’s ‘A Tale of Two Envelopes’ Mind 119(473): 159-169.
• Bernard 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 Cooke, Two Envelopes, two paradoxes, The Reasoner 4(5): 74 - 75 [pdf]
• Derek Abbott, Bruce Davis, Juan Parrondo, The two-envelope problem revisited, Fluctuation and Noise Letters 9(1): 1–8 [pdf]
• Jeremy Gwiazda, Repeated St Petersburg two-envelope trials and expected value, The Reasoner 6(3): 37 - 39[1].
• William Briggs, The Two-Envelope Problem Solution: Part I & II, published online Part I Part II
• Robert Marks, Jawdropping Probability: The Two Envelope Problem & Bermoulli’s Wager, published online [pdf]

2011

• 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 [pdf]
• Raam Gokhale, The Two Envelopes Problem: a ‘Back of the Envelope’ Solution, published online [html]
• Bruce D Burns, Adaptive uses of random criterion: The largest number problem, the two- envelope problem, and the anchoring and adjustment heuristic, in L Carlson, C Hoelscher, & T F Shipley (Eds.), Proceedings of the 33rd Annual Conference of the Cognitive Science Society: 978-983, Austin, TX: Cognitive Science Society [pdf]
• Ned Markosian, A Simple Solution to the Two Envelope Problem, Logos & Episteme, II, 3: 347-357 [pdf]
• Arthur Baraov, et al. Adaptive Strategies in the Iterated Exchange Problem, AIP Conference Proceedings-American Institute of Physics, Vol 1305, No. 1 [pdf]
• Aljoša Volčič, A Paradox in the Two Envelope Paradox? Bollettino dell’Unione Matematica Italiana, Serie 9, Vol. 4, n.3: 337–345 [pdf]

2012

• Eric Bliss, A Concise Resolution to the Two Envelope Paradox, arXiv:1202.4669v3 [pdf]
• R A Vázquez, The two envelopes probability paradox: Much ado about nothing, arXiv:1206.4805v1 [pdf]

2013

• William Eckhardt, The Two-Envelopes Problem, Chapter 8 of his book Paradoxes in Probability Theory, pp 47-58, SpringerBriefs in Philosophy.
• Aris Spanos, The Two Envelope Problem: a Paradox or Fallacious Reasoning?, arXiv:1301.0118 [stat.ME].
• Chunghyoung Lee, The Two-envelope Paradox: Asymmetrical Cases, Mind, Volume 122, Issue 485, pp 1-26.
• Bruce Burns, Probabilistic reasoning in the two-envelope problem, Paper presented at the 35th Annual Meeting of the Cognitive Science Society (COGSCI 2013), Austin, Texas: Cognitive Science Society.
• Miles Mathis, The Two-Envelopes Paradox, published online [pdf]
• Byeong-Uk Yi, Conditionals and a two-envelope paradox, Journal of Philosophy 110(5): 233-257.

2014

• Leo Gerville-Reache, Why do we change whatever amount we found in the first envelope: the Wikipedia two envelopes problem commented., arXiv:1402.3311 [pdf]
• Panagiotis Tsikogiannopoulos, Variations on the Two Envelopes Problem, Hellenic Mathematical Society, Mathematical Review 77-78: 3-25. English version at arXiv:1411.2823 [pdf]
• Mitchell and O’Brien, The two envelope problem: there is no conundrum, Teaching Mathematics and its Applications: https://doi.org/10.1093/teamat/hru019 .
• Shiro Ishikawa, The two envelopes paradox in non-Bayesian and Bayesian statistics, arXiv:1408.4916 [pdf]
• Michael Powers, The Insurance Two-Envelope Paradox: Implications for Utility Modeling, Preliminary draft [pdf]
• Nick Ergodos, The Enigma Of Probability, Journal of Cognition and Neuroethics 2(1) : 37–71. [pdf]
• Raymond S. Nickerson, Susan F. Butler, Nathaniel Delaney-Busch and Michael Carlin, Keep or trade? Effects of pay-off range on decisions with the two-envelopes problem, Thinking and Reasoning 20(4): 472-499.
• Panagiotis Tsikogiannopoulos, Solving the two envelopes problem with the Intermediate Amount Strategy, Hellenic Mathematical Society, Mathematical Review 79-80: 102-118. English version at arXiv:1502.06476 [pdf]
• Jeffrey Brian Tyler, The Two-Envelope Problem: An Informed Choice, master thesis, University of South Africa [pdf]

2015

• Michael R. Powers, Paradox-Proof Utility Functions for Heavy-Tailed Payoffs: Two Instructive Two-Envelope Problems, Risks 3(1), 26-34; doi:10.3390/risks3010026. [pdf]
• Markovitch J. S., The Psychology of The Two Envelope Problem, published online [pdf]
• Martin Egozcue, Luis Fuentes García, An Optimal Threshold Strategy in the Two-Envelope Problem with Partial Information, Journal of Applied Probability, Vol. 52, No. 1: 298-304, [pdf]

2017

• Chloé de Canson, The Paradox of the Two Envelopes, published online [pdf]
• Kang Hao Cheong, David B. Saakian, and Rubina Zadourian, Allison mixture and the two-envelope problem, Physical Review E 96(6). [pdf]
• Yudi Pawitan and Youngjo Lee, Wallet game: probability, likelihood, and extended likelihood, The American Statistician 71(2): 120-122.

2018

• Casper Storm Hansen, Two Envelopes and Binding, Australasian Journal of Philosophy 96(3): 508-518.

2019

• Joseph Tzur, Arie Jacobi, Decision Making Under Uncertainty and the Two-Envelope Paradox, forthcoming in the Journal of Theoretical Accounting research [pdf]

2020

• Stephen Portnoy, The Two-Envelope Problem for General Distributions, published online [pdf]

2021

• Richard D Gill, Anna Karenina and The Two Envelopes Problem, Australian & New Zealand Journal of Statistics 63(1): 201–218 [pdf]

2022

• Christian Hugo Hoffmann, Rationality applied: resolving the two envelopes problem, Theory and Decision: published online as Open access [pdf]

2023

• Zachary Goodsell, Unbounded Utility, Dissertation, University of Southern California [pdf]
• Gabriel de Longeaux, The Two Envelopes Problem, published online in Towards Data Science [html]