Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-07T23:29:29.403Z Has data issue: false hasContentIssue false
  • English
  • Français

Kings and Prisoners (and Aces)

Published online by Cambridge University Press:  28 February 2022

Jordan Howard Sobel
Jordan Howard Sobel*
Affiliation:
University of Toronto
Get access Rights & Permissions [Opens in a new window]

Extract

What we make of information we come to have should take into account that we have come to have it, and how we think we have come to have it

I relate this homily to several puzzles. In one, three cards, of which I know one is a king, lie face-down. After I select, without inspecting, a card and bet that it is a king, you reveal that a certain other card is not a king. I wonder what this does to my chances on that bet. In another puzzle I am one of three prisoners and learn that one of us will be released. Then I learn that a certain other prisoner will not be released. Again I wonder what this does to my chances.

Type
Part VI. Decision Theory
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1992 , Issue 1: Volume One: Contributed Papers 1992 , 1992 , pp. 203 - 216
Copyright
Copyright © 1992 by the Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bar-Hillel, M. (1989), “How to Solve Probability Teasers”, Philosophy of Science 56:348-58.CrossRefGoogle Scholar
Burks, A.W. (1977),Chance, Cause, Reason: An Inquiry into the Nature of Scientific Evidence, Chicago: University of Chicago Press.Google Scholar
Faber, R. (1976), “Discussion: Re-encountering a Counter-intuitive Probability”, Philosophy of Science 43:283-85.CrossRefGoogle Scholar
Freund, J.E. (1965), “Puzzle or Paradox”, The American Statistician 19:29-44. (See letters in 20 (1,2,5) and 21 (2,3,4).)Google Scholar
Gridgeman, N.T. (1963), “The Pit of Paradox”, The New Scientist 20:462-65.Google Scholar
Kemeny, J.G., Snell, J.L., Thompson, G.L. (1979),Introduction to Finite Mathematics, Third Edition, New York: Prentice Hall.Google Scholar
Schrodinger, E. (1947), “The Foundation of the Theory of Probability—I,” Proceedings of the Royal Irish Academy 51:51-66.Google Scholar
Shafer, G. (1983), “Conditional Probability”, International Statistical Review 53, 1985:261-77.Google Scholar
Sobel, J.H. (1961), “What If Everyone Did That?”, Ann Arbor, Michigan: University Microfilms, Inc.Google Scholar
Sobel, J.H. (1990), “Conditional Probabilities, Conditionalization, and Dutch Books,” PSA 1990: Proceedings of the 1990 Biennial Meeting of the Philosophy of Science Association, Volume One, Contributed Papers, edited by Fine, A. , Forbes, M. & Wessels, L. , East Lansing, Michigan: 503-516.Google Scholar
Sobel, J.H. (1992), “On Conditional Probabilities,” manuscript.Google Scholar
Zabell, S.L., “The Probabilistic Analysis of Testimony,” Journal of Statistical Planning and Inference, 1988: 327-54.CrossRefGoogle Scholar