Thursday, January 30, 2014

When should I get married?

Secretary Problem (Background Information)

[from Wikipedia]

The basic form of the problem is the following: imagine an administrator willing to hire the best secretary out of n rankable applicants for a position. The applicants are interviewed one-by-one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator can rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy to maximize the probability of selecting the best applicant. 

The optimal stopping rule prescribes to reject about n/e applicants after the interview (where e is the base of the natural logarithm) without choice then stop at the first applicant who is better than every applicant interviewed so far (or proceed to the last applicant if this never occurs)

This strategy selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.

My Case
  • Years to live: 60
  • Average number of marriage candidates met every day: 2
  • Total number of candidates to be met: 43'800
  • Eliminate all without thinking until no. 16'113
  • Years to wait: 22.07 (at least)