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The Ups and Downs of the Hope Function In a Fruitless Search

On Bayesian updating of beliefs in sequentially searching a set of possibilities where failure is possible, such as waiting for a bus; the psychologically counterintuitive implication is that success on the next search increases even as the total probability of success decreases.

This transcript has been prepared from a scan of chapter 15, pages 353–377 in Subjective Probability 1994, edited by G. Wright & P. Ayton. All links are my own insertion; references have been inserted as footnotes at the first citation.

Note: to hide apparatus like the links, you can use reader-mode ().

  1. Bell, C.R. (1979) “Psychological aspects of probability and uncertainty”. In C.R. Bell (ed.), Uncertain Outcomes, MTP Press, Lancaster, England, pages 5–21.↩︎

  2. Jones, D.E.H. (1966) “On being blinded with science”. New Scientist, November, 465–7.↩︎

  3. Feller, W. (1957) An Introduction to Probability Theory and its Applications, Vol. 1 (2nd edition). Wiley, New York.↩︎

  4. Meshalkin, L.D. (1973) Collection of Problems in Probability Theory (L.F. Boron & B.A. Haworth, trans.) Noordhoff, Leyden, The Netherlands (Original work published 1963).↩︎

  5. Falk, R. (1993) Understanding Probability and Statistics: A Book of Problems. AK Peters, Wellesley, Ma.↩︎

  6. Gabriel, K.R. (1960) Nuptiality and Fertility in Israel. Doctoral dissertation (in Hebrew with English summary). The Hebrew University, Jerusalem.↩︎

  7. Tversky, A. & Kahneman, D. (1982) “Evidential impact of base rates”. In D. Kahneman, P. Slovic & A. Tversky (eds.), Judgement under Uncertainty: Heuristics and Biases. Cambridge University Press, Cambridge, pages 153–60.↩︎

  8. Falk, R. & Konold, C. (1992) “The psychology of learning probability”. In F.S. Gordon & S.P. Gordon (eds.), Statistics for the Twenty-First Century. The Mathematical Association of America, USA, pages 151–64.↩︎

  9. Konold, C., Lohmeier, J., Pollatsek, A., Well, A., Falk, R. & Lipson, A. (1991) “Novice views on randomness”. Proceedings of the 13th Annual Meeting of the International Group for the Psychology of mathematics Education—North American Chapter, 1, 167–73.↩︎

  10. Gigerenzer, G., Switjink, Z., Porter, T., Daston, L., Beatty, J. & Krueger, L. (1989) The Empire of Chance: How Probability Changed Science and Everyday Life. Cambridge University Press, Cambridge.↩︎

  11. Hacking, I. (1975) The Emergence of Probability. Cambridge University Press, Cambridge.↩︎

  12. Ennis, J. (1985) “Statistics, St Petersburg and Sellafield”. New Scientist, May, 26–28.↩︎

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