Sorry, the first 36.8% of candidates, you’re out

It’s great that life can be expressed in hard and fast numbers, isn’t it? Whatever would we do if the world were a damn sight more difficult to fathom?

But recently we learnt that the best number of people to have in a meeting is seven. Specifically, that for contestant number 8 and each person thereafter, the group’s effectiveness is reduced by something like 10%. I am as wary of bandying numbers about as you are, so let me just point you at that story: Sorry, Snow White, You’re Out

Now there’s more. Specifically this: don’t hire anybody from the first 36.8% of candidates you interview. Seriously.

America’s National Public Radio (via Lifehacker) describes what’s reportedly known as either the Marriage Problem or the Secretary Problem. It’s a thing. It’s been a thing from sometime in the Stone Age where these two issues were considered to boil down to the same thing: how a man (always a man) should choose the perfect woman (always a girl) for him and nuts to whether she’s got her own sliderule equation about him.

NPR’s story is based on a tale told by author Alex Bellos in The Grapes of Math (UK edition, US edition) – his new and so-gorgeously-titled book that I’m going to buy it right after we’re done.

Alex writes: “Imagine that you are interviewing 20 people to be your secretary [or your spouse or your garage mechanic] with the rule that you must decide at the end of each interview whether or not to give that applicant the job.” If you offer the job to somebody, game’s up. You can’t go on and meet the others. “If you haven’t chosen anyone by the time you see the last candidate, you must offer the job to her,” Alex writes (not assuming that all secretaries are female — he’s just adapting the attitudes of the early ’60s).

So remember: At the end of each interview, you either make an offer or you move on.

If you don’t make an offer, no going back. Once you make an offer, the game stops.

According to Martin Gardner, who in 1960 described the formula (partly worked out earlier by others), the best way to proceed is to interview (or date) the first 36.8 percent of the candidates. Don’t hire (or marry) any of them, but as soon as you meet a candidate who’s better than the best of that first group — that’s the one you choose! Yes, the Very Best Candidate might show up in that first 36.8 percent — in which case you’ll be stuck with second best, but still, if you like favorable odds, this is the best way to go.

How To Marry The Right Girl: A Mathematical Solution – Robert Krulwich, NPR (15 May 2014)

It’s easy to mock the way men think there’s logic to dating, so let’s.

But the 36.8% figure has some solid reasoning and also an interesting mathematical history. So do read NPR’s article for more and then do buy Bellos’s book (UK edition, US edition).

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