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On Generalized Secretary Problems

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Uncertainty and Risk

Part of the book series: Theory and Decision Library C ((TDLC,volume 41))

Abstract

This paper is composed of two related parts. In the first, we present a dynamic programming procedure for finding optimal policies for a class of sequential search problems that includes the well-known “secretary problem”. In the second, we propose a stochastic model of choice behavior for this class of problems and test the model with two extant data sets. We conclude that the previously reported bias for decision makers to terminate their search too early can, in part, be accounted for by a stochastic component of their search policies.

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References

  • Bearden, J.N., Rapoport, A., Murphy, R.O. (2004), Sequential oberservation and selection with rank-dependent payoffs: An experimental test. Unpublished manuscript.

    Google Scholar 

  • Bearden, J.N., Wallsten, T.S., Fox, C.R. (2004), A stochastic model of subadditivity. Unpublished manuscript.

    Google Scholar 

  • Bock, R.D., Jones, L.V. (1968), The Measurement and Prediction of Judgment and Choice. San Francisco: Holden-Day.

    Google Scholar 

  • Corbin, R.M., Olson, C.R., Abbondanza, M. (1975), Context effects in optimal stopping rules. Behavior and Human Performance, 14, 207–216.

    Article  Google Scholar 

  • Erev, I., Wallsten, T.S., Budescu, D.V. (1994), Simulataneous over-and under-confidence: The role of error in judgment processes. Psychological Review, 101, 519–528.

    Article  Google Scholar 

  • Ferguson, T.S. (1989), Who solved the secretary problem? Statistical Science, 4, 282–296.

    Google Scholar 

  • Freeman, P.R. (1983), The secretary problem and its extensions: A review. International Statistical Review, 51, 189–206.

    Article  Google Scholar 

  • Gilbert, J., Mosteller, F. (1966), Recognizing the maximum of a sequence. Journal of the American Statistical Association, 61, 35–73.

    Article  Google Scholar 

  • Hey, J.D. (1981), Are optimal search rules reasonable? And vice versa? Journal of Economic Behavior and Organization, 2, 47–70.

    Article  Google Scholar 

  • Hey, J.D. (1982), Search for rules of search. Journal of Economic Behavior and Organization, 3, 65–81.

    Article  Google Scholar 

  • Hey, J.D. (1987), Still searching. Journal of Economic Behavior and Organization, 8, 137–144.

    Article  Google Scholar 

  • Juslin, P., Olsson, H., Björkman, M. (1997), Brunswikian and Thurstonian origins of bias in probability assessment: On the interpretation of stochastic components of judgment. Journal of Behavioral Decision Making, 10, 189–209.

    Article  Google Scholar 

  • Lindley, D.V. (1961), Dynamic programming and decision theory. Applied Statistics, 10, 39–51.

    Article  Google Scholar 

  • Luce, R.D. (1977), Thurstone’s discriminable process fifty years later. Psychometrika, 42, 461–489.

    Article  Google Scholar 

  • Luce, R.D. (1994), Thurstone and sensory scaling: Then and now. Psychological Review, 101, 271–277.

    Article  Google Scholar 

  • Moriguti, S. (1993), Basic theory of selection by relative rank with cost. Journal of the Operations Research Society of Japan, 36, 46–61.

    Google Scholar 

  • Mucci, A.G. (1973), Differential equations and optimal choice problems. Annals of Statistics, 1, 104–113.

    Google Scholar 

  • Pfeifer, P.E. (1994), Are we overconfident in the belief that probability forecasters are overconfident. Organizational Behavior and Human Decision Processes, 58, 203–213.

    Article  Google Scholar 

  • Ratchford, B.T., Srinivasan, N. (1993), An empirical investigation of return to search. Marketing Science, 12, 73–87.

    Article  Google Scholar 

  • Rottenstreich, Y., Tversky, A. (1997), Unpacking, repacking, and anchoring: Advances in support theory. Psychological Review, 104, 406–415.

    Article  Google Scholar 

  • Seale, D.A., Rapoport, A. (1997), Sequential decision making with relative ranks: An experimental investigation of the secretary problem. Organizational Behavior and Human Decision Processes, 69, 221–236.

    Article  Google Scholar 

  • Seale, D.A., Rapoport, A. (2000), Optimal stopping behavior with relative ranks: The secretary problem with unknown population size. Journal of Behavioral Decision Making, 13, 391–411.

    Article  Google Scholar 

  • Stein, W.E., Seale, D.A., Rapoport, A. (2003), Analysis of heuristic solutions to the best choice problem. European Journal of Operational Research, 51, 140–152.

    Article  Google Scholar 

  • Soll, J.B. (1996), Determinants of overconfidence and miscalibration: The roles of random error and ecological structure. Organizational Behavior and Human Decision Processes, 65, 117–137.

    Article  Google Scholar 

  • Stigler, G.L. (1961), The economics of information. Journal of Political Ecnonomy, 69, 213–225.

    Article  Google Scholar 

  • Thurstone, L.L. (1927a), A law of comparative judgment. Psychological Review, 34, 273–286.

    Article  Google Scholar 

  • Thurstone, L.L. (1927b), Psychophysical analysis. American Journal of Psychology, 38, 368–389.

    Article  Google Scholar 

  • Tversky, A., Koehler, D. (1994), Support theory: A nonextensional representation of subjective probability. Psychological Review, 101, 547–567.

    Article  Google Scholar 

  • Yeo, A.J., Yeo, G.F. (1994), Selecting satisfactory secretaries. Australian Journal of Statistics, 36, 185–198.

    Article  Google Scholar 

  • Zwick, R., Rapoport, A., Lo, A.K.C., Muthukrishnan, A.V. (2003), Consumer sequential search: Not enough or too much? Marketing Science, 22, 503–519.

    Article  Google Scholar 

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Bearden, J.N., Murphy, R.O. (2007). On Generalized Secretary Problems. In: Abdellaoui, M., Luce, R.D., Machina, M.J., Munier, B. (eds) Uncertainty and Risk. Theory and Decision Library C, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48935-1_11

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