Skip to main content

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

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

$$\prod\limits_{j = 1}^\infty {(\tfrac{{j + 2}}{j})^{1/j + 1} } \cong 3.8695$$

.

This is a preview of subscription content, access via your institution.

Reference

  1. 1.

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

    MATH  Article  MathSciNet  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Y. S. Chow.

Additional information

Research supported by Office of Naval Research and Aerospace Research Laboratories. Reproduction in whole or in part is permitted for any purpose of the United States Government.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chow, Y.S., Moriguti, S., Robbins, H. et al. Optimal selection based on relative rank (the “secretary problem”). Israel J. Math. 2, 81–90 (1964). https://doi.org/10.1007/BF02759948

Download citation

Keywords

  • Random Order
  • Selection Strategy
  • Direct Proof
  • Recursion Formula
  • Relative Rank