The exchange paradox: Probabilistic and cognitive analysis of a psychological conundrum

Thinking and Reasoning

Volumn 12, Issue 2, 2006, Pages 181-213

  Nickerson, Raymond S ^a,c   Falk, Ruma ^b  

^a TUFTS UNIVERSITY   (United States)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^c NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646767078     PISSN: 13546783     EISSN: 14640708     Source Type: Journal    
DOI: 10.1353/lap.2006.0022     Document Type: Article

References (71)

1. Agnew, R. A. (2004). On the two-box paradox. Mathematics Magazine, 77(4), 302-308.
2. Albert, J. H. (2003). College students' conceptions of probability. The American Statistician, 57(1), 37-45.
3. Bakan, D. (1966). The test of significance in psychological research. Psychological Bulletin. 66, 432-437.
4. Barbeau, E. (2000). Mathematical fallacies, flaws, and flimflam. Washington, DC: The Mathematical Association of America.
5. Bar-Hillel, M., & Falk, R. (1982). Some teasers concerning conditional probabilities. Cognition, 11, 109-122.
6. Benartzi, S., & Thaller, R. H. (2001). Naive diversification strategies in defined contribution saving plans. The American Economic Review, 91(1), 79-98.
7. Blachman, N. M., Christensen, R., & Utts, J. M. (1996). Comment on Christensen and Utts (1992). The American Statistician, 50, 98-99.
8. Blachman, N. M., & Kilgour, D. M. (2001), Elusive optimality in the box problem. Mathematics Magazine, 74(3), 171-181.
9. Brams, S. J., & Kilgour, D. M. (1995a). Letter to the editor, response to Mixon (1995). Mathematics Magazine, 68, 322-323.
10. Brams, S. J., & Kilgour, D. M. (1995b). The box problem: To switch or not to switch. Mathematics Magazine, 68(1), 27-34.
11. [See review in Chance News, 4.04, 16 February to 3 March, 1995.]
12. Broome, J. (1995). The two-envelope paradox. Analysis, 55, 6-11.
13. Brown, A. C. (1995). Neckties, wallets, and money for nothing. Journal of Recreational Mathematics, 27, 116-122.
14. Bruss, F. T. (1996). The fallacy of the two envelopes problem. Mathematical Scientist, 21, 112-119.
15. Cargile, J. (1992). On a problem about probability and decision. Analysis, 52, 211-216.
16. Carnap, R. (1953). What is probability? Scientific American, 189(3), 128-138.
17. Carroll, L. (1958). Pillow problems and a tangled tale. New York: Dover. (Pillow problems originally published in 1895.)
18. Carroll, M. T., Jones, M. A., & Rykken, E. K. (2001). The wallet paradox revisited. Mathematics Magazine, 74, 378-383.
19. Castell, P., & Batens, D. (1994). The two envelope paradox: The infinite case. Analysis, 54, 46-49.
20. Christensen, R., & Utts, J. (1992). Bayesian resolution of the "exchange paradox.'' The American Statistician, 46, 274-276. [See Blachman, Christensen, & Utts, 1996, for correction of errors.]
21. Cohen, J. (1994). The earth is round (p < .05). American Psychologist, 49, 997-1003.
22. Edwards, W., Lindman, H., & Savage, L. J. (1963). Bayesian statistical inference for psychological research. Psychological Review, 70(3), 193-242.
23. Falk, R. (1992). A closer look at the probabilities of the notorious three prisoners. Cognition, 43, 197-223.
24. Falk, R. (1994). Infinity: A cognitive challenge. Theory & Psychology, 4(1), 35-60.
25. Falk, R., & Greenbaum, C. W. (1995). Significance tests die hard: The amazing persistence of a probabilistic misconception. Theory & Psychology, 5, 75-98.
26. Falk, R, & Konold, C. (1992). The psychology of learning probability. In F. S. Gordon & S. P. Gordon (Eds.), Statistics for the twenty-first century (pp. 151-164). Washington, DC: The Mathematical Association of America.
27. Falk, R., & Samuel-Cahn, E. (2001). Lewis Carroll's obtuse problem. Teaching Statistics, 23(3), 72-75.
28. Falletta, N. (1983). The paradoxicon: A collection of contradictory challenges, problematical puzzles, and impossible illustrations. New York: Wiley.
29. Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Dordrecht, the Netherlands: Reidel.
30. Fischhoff, B., & Bruine de Bruin, W. (1999). Fifty-fifty = 50%? Journal of Behavioural Decision Making, 12, 149-163.
31. Fisher, R. A. (1934). The effect of methods of ascertainment upon the estimation of frequencies. Annals of Eugenics, 6, 13-25.
32. Fox, C. R., & Rottenstreich, Y. (2003). Partition priming in judgment under uncertainty. Psychological Science. 14(3), 195-200.
33. Gardner, M. (1982). Aha! Gotcha: Paradoxes to puzzle and delight. San Francisco: Freeman.
34. Gigerenzer, G., Swijtink, Z., Porter, T., Daston, L., Beatty, J., & Krüger, L. (1989). The empire of chance: How probability changed science and everyday life. Cambridge: Cambridge University Press.
35. Gillman, L. (1992). The car and the goats. American Mathematical Monthly, 99, 3-7.
36. Guy, R. K. (1993). There are three times as many obtuse-angled triangles as there are acute-angled ones. Mathematics Magazine, 66(3), 175-179.
37. Hacking, I. (1975). The emergence of probability. Cambridge: Cambridge University Press.
38. Hays, W. L., & Winkler, R. L. (1971). Statistics: Probability, inference and decision. New York: Holt, Rinehart & Winston.
39. Hoffman, P. (1998). The man who loved only numbers: The story of Paul Erdös and the search for mathematical truth. New York: Hyperion.
40. Jackson, F., Menzies, P., & Oppy, G. (1994). The two envelope "paradox." Analysis, 54, 43-45.
41. Jeffreys, H. (1939). Theory of probability. Oxford: Clarendon Press.
42. Kraitchik, M. (1953). Mathematical recreations (2nd ed.). New York: Dover.
43. Krauss, S., & Wang, X. T. (2003). The psychology of the Monty Hall problem: Discovering psychological mechanisms for solving a tenacious brain teaser. Journal of Experimental Psychology: General, 132(1), 3-22.
44. Linzer, E. (1994). The two-envelope paradox. The American Mathematical Monthly, 101, 417-419.
45. Marinoff, L. (1993). Three pseudo-paradoxes in "quantum" decision theory: Apparent effects of observation on probability and utility. Theory and Decision, 35, 55-76.
46. Merryfield, K. G., Viet, N., & Watson, S. (1997). The wallet paradox. The American Mathematical Monthly, 104, 647-649.
47. Mixon, W. (1995). Comment on Brams and Kilgour (1995) (and editor's response). Mathematics Magazine, 68, 322-323.
48. Mosteller, F. (1965). Fifty challenging problems in probability with solutions. Reading. MA: Addison-Wesley.
49. Nalebuff, B. (1988). Puzzles: Cider in your ear, continuing dilemma, the last shall be first, and more. Journal of Economic Perspectives, 2, 149-156.
50. Nalebuff, B. (1989). Puzzles: The other person's envelope is always greener. Journal of Economic Perspectives, 3, 171-181.
51. Nickerson, R. S. (1996). Ambiguities and unstated assumptions in probabilistic reasoning. Psychological Bulletin, 120, 410-433.
52. Nickerson, R. S. (2000). Null hypothesis significance testing: A review of an old and continuing controversy. Psychological Methods, 5, 241-301.
53. Nickerson, R. S. (2004). Cognition and chance: The psychology of probabilistic reasoning. Mahwah, NJ: Lawrence Erlbaum Associates Inc.
54. Norton, J. D. (1998). When the sum of our expectations fails us: The exchange paradox. Pacific Philosophical Quarterly, 79, 34-58.
55. Portnoy, S. (1994). A Lewis Carroll pillow problem: Probability of an obtuse triangle. Statistical Science, 9, 279-284.
56. Rapoport, A. (1967). Escape from paradox. Scientific American, 217(1), 50-56.
57. Rawling, P. (1994). A note on the two envelopes problem. Theory and Decision, 36, 97-102.
58. Rawling, P. (1997). Perspectives on a pair of envelopes. Theory and Decision, 43, 253-277.
59. Roch, S. G., Lane, J. A. S., Samuelson, C. D., Allison, S. T., & Dent, J. L. (2000). Cognitive load and the equality heuristic: A two-stage model of resource overconsumption in small groups. Organizational Behaviour and Human Decision Processes, 83(2), 185-212.
60. Ross, S. M. (1994). Comment on Christensen and Utts (1992). The American Statistician, 48, 267.
61. Samet, D., Samet, I., & Schmeidler, D. (2004). One observation behind two-envelope puzzles. American Mathematical Monthly, 111, 347-351.
62. Schechter, B. (1998). My brain is open: The mathematical journeys of Paul Erdös. New York: Simon & Schuster.
63. Shaughnessy, J. M., & Dick, T. (1992). Monty's revenge. In Readers' Reflections, The Mathematics Teacher, 85(2), 91.
64. Shimojo, S., & Ichikawa, S. (1989). Intuitive reasoning about probability: Theoretical and experimental analyses of the "problem of three prisoners". Cognition, 32, 1-24.
65. Sobel, J. H. (1994). Two envelopes. Theory and Decision, 36, 69-96.
66. Stigler, S. M. (1986). The history of statistics: The measurement of uncertainty before 1900. Cambridge, MA: Harvard University Press.
67. SzÕkely, G. J. (1986). Paradoxes in probability theory and mathematical statistics. Dordrecht, the Netherlands: Reidel.
68. Todhunter, I. (2001). A history of the mathematical theory of probability from the time of Pascal to that of Laplace. Bristol, UK: Thoemmes Press. [Originally published in 1865.]
69. vos Savant, M. (1991). Ask Marilyn. Parade Magazine, February 17, p. 12.
70. Zabell, S. L. (1988a). Discussion of a paper by B. M. Hill. In J. M. Bernardo, M. H. Degroot, D. V. Lindley, & A. F. M. Smith (Eds.), Bayesian Statistics 3: Proceedings of the Third Valencia International Meeting (pp. 233-236). Oxford: Clarendon Press.
71. Zabell, S. L. (1988b). Symmetry and its discontents. In B. Skyrms & W. L. Harper (Eds.), Causation, chance, and credence (Vol. I, pp. 155-190). Dordrecht, the Netherlands: Kluwer Academic Publishers.