A general counsel faced with twenty candidates for an open position, or two dozen firms of which one can be retained, might despair at the time drain. Do you have to see them all or is there a golden number? Cheer up! Mathematicians have figured out how many you should interview. John D. Barrow, 100 Essential Things You Didn’t Know You Didn’t Know: Math Explains Your World (Norton 2008) at 86, describes the reasoning.
The bottom line is that with 100 candidates, “The optimal strategy is to see 37 of them and then pick the next one that we see who is better than any of them and then see no one else.” You need to know how many total candidates you might see. And you must keep score of those you see up to the tipping point. For all such sequential choice problems, the right point is to see 37 percent of the candidates and then select then next one that is better than any that preceded.
By the way, the book by Barrow has been fertile (See my post of April 15, 2011: to calculate how many documents were not found; April 28, 2011: geometric means; April 28, 2011: a trick to help a weak candidate win; and April 29, 2011: statistical error.).