The Dating Problem
- Thirty-seven percent Rule
How many people should you date before truly finding the “one” or deciding to settle down with? It’s a tricky question, and as with many tricky questions, math has an answer of some sort, which tells you It's 37% of the way through your search!
This answer has its origin in a famous puzzle in mathematics known as ‘The Secretary Problem’. The strategy is, say you’re interviewing a group of applicants for a position, how do you maximize the chances of hiring the single best applicant in the pool. This problem became popular when it was first published in a scientific journal (Scientific American) in 1960.
The process is a manager interviewing applicants for the position of secretary. The applicants will be interviewed in random order, one at a time. A decision about each applicant is to be made immediately following each interview, If rejected, the applicant leaves the room after the interview, and he or she is not recalled again. Any applicant will accept the job if asked, effectively ending the search.
The crucial problem here is not who would you choose but how many options would you consider before choosing. What if you choose too early and miss the best applicant that follows? What if you stop looking too late and the best applicant already left? At what point do you stop and select the best candidate? When do you stop and just make the decision?
The problem has an elegant solution using a method called Optimal Stopping. The answer with the highest probability of success is to reject the first 37% of applicants, then when the next best applicant comes along and is found better than the first 37, you stop and hire! This gives you the best chance of ending the interview with the best candidate.
Optimal stopping deals with the problem of choosing a time to take a specific action, in order to maximize an expected reward or minimize an expected cost. The logic in this method helps decide on when to look and when to leap. Secretary Problem is a key example of the optimal stopping theory.
Now, this strategy requires you would have to set the benchmark required for comparison, meaning the best of the first 37 applicants, you actually got to interview them, the best of them will set your benchmark so can make the comparison after you have gone past the tipping point, that is after you have gone past the 37% of applicants. So the sample will be rejected and will only be used for setting the benchmark.
In case of n candidates, the optimal stopping rule prescribes always rejecting the first (~n/e) applicants that are interviewed (where e is the base of the natural logarithm) and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs).
Optimal stopping can be found in areas of statistics, economics, and finance. It has also been explored within fields like experimental psychology in order to simulate and understand real-world decision-making.
1/e law of Optimal Strategy
This strategy is also called the 1/e stopping rule because the probability of stopping at the best applicant with this strategy is about 1/e for moderate values of n. One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.
If you are interested to learn more about Optimal Stopping theory, check out these research papers:
