Secretary Problem
Explores optimal stopping in the classic Secretary Problem where N applicants are evaluated one by one.
Free theory articleExplores optimal stopping in the classic Secretary Problem where N applicants are evaluated one by one.
Concept & interpretation
The Secretary Problem explores the mathematics of optimal stopping. Imagine evaluating a sequence of N applicants for a position. You observe them one by one in uniformly random rank order, with rank N being the absolute best. You can only choose to accept or reject an applicant immediately after their interview. Once rejected, an applicant cannot be recalled. The strategy is to reject the first r applicants to set a baseline record, and then hire the next applicant who is strictly better than all previous applicants.
Experiment
To see this in action using the interactive Secretary Problem module:
- Set the Applicants N slider to 4.
- Set the Rejected prefix r slider to 1.
- Set the Displayed order dropdown to Ascending. Notice that you select the 2nd applicant (rank 2), which is not the best.
- With N=4 and r=1, change Displayed order to Middle peak. The order is [1,2,4,3], so rank 2 is still hired at position 2. The rule stops before seeing the later peak.
- The aggregate remains 11/24 when only the displayed order changes. Set Applicants N to 3, keep r=1 and Middle peak: the order [1,3,2] selects rank 3 at position 2, with aggregate success probability 1/2.