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Israel Journal of Mathematics

, Volume 2, Issue 2, pp 81–90 | Cite as

Optimal selection based on relative rank (the “secretary problem”)

  • Y. S. Chow
  • S. Moriguti
  • H. Robbins
  • S. M. Samuels
Article

Abstract

n rankable persons appear sequentially in random order. At theith stage we observe the relative ranks of the firsti persons to appear, and must either select theith person, in which case the process stops, or pass on to the next stage. For that stopping rule which minimizes the expectation of the absolute rank of the person selected, it is shown that asn → ∞ this tends to the value
$$\prod\limits_{j = 1}^\infty {(\tfrac{{j + 2}}{j})^{1/j + 1} } \cong 3.8695$$
.

Keywords

Random Order Selection Strategy Direct Proof Recursion Formula Relative Rank 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Reference

  1. 1.
    D. V. Lindley,Dynamic programming and decision theory, Applied Statistics10 (1961), 39–51.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1964

Authors and Affiliations

  • Y. S. Chow
    • 1
    • 2
    • 3
  • S. Moriguti
    • 1
    • 2
    • 3
  • H. Robbins
    • 1
    • 2
    • 3
  • S. M. Samuels
    • 1
    • 2
    • 3
  1. 1.Purdue UniversityUSA
  2. 2.University of TokyoJapan
  3. 3.Columbia UniversityUSA

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