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.
psychology⁠, statistics⁠, survey⁠, Bayes⁠, insight-porn
by: Ruma Falk, Abigail Lipson, Clifford Konold 2012-07-012019-04-01 finished certainty: log importance: 4 backlinks


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.


  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 Thirteenth 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.↩︎