Saturday, May 17, 2014

NPR: How To Marry The Right Girl, A Mathematical Solution

"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.

Why 36.8 percent? The answer involves a number mathematicians call "e" – which, reduced to a fraction 1/e = 0.368 or 36.8 percent. For the specific details, check here, or Alex's book, but apparently this formula has proved itself over and over in all kinds of controlled situations. While it doesn't guarantee happiness or satisfaction, it does give you a 36.8 percent chance — which, in a field of 11 possible wives — is a pretty good success rate.
Also see Freeman Hunt's "Frank Advice for a Male Relative on Finding a Mate" Good Luck... and don't call me Frank ;)

17 comments:

edutcher said...

Can I call you Shirley?

Paddy O said...

I suspect that if someone is going about finding the right girl through the mathematical solution they're going to have a big problem with getting to requisite sample size in the first place.

Aridog said...

Huh?

I think I missed something. But I do have a pitch fork and access to a manure spreader.

Chip S. said...

Ari, the complete solution is here, in sec. 2.1, along w/ the necessary assumptions.

It works if: (1) your sole consideration is finding the best candidate, (2) you think all uninterviewed applicants are equally likely to be the best of that group, and (3) you can't go back to anyone you've already interviewed and passed over.

The basic idea is that you've got to be willing to "use up" some fraction of your applicant pool in order to calibrate the overall quality of the pool.

With more elaborate assumptions. or a different objective, you could get different results.

chickelit said...

I find the solution divisive. It multiplies a person's problems in finding a mate. In addition, it subtracts from the humanity of the whole thing. At its root, it's mean and pointless.

Sixty Grit said...

Those issues are imaginary and transcendental. Be constant, get her digits and don't be irrational.

Being divisive is also a factor.

Chip S. said...

Sixty is an exponent of using natural logs in bowl manufacturing.

chickelit said...

Titus expresses natural logs in bowls too.

bagoh20 said...

I have a friend who decided he wanted to get married and have kids. He devised a list of qualities that he must have in a wife and started dating women until he found one who fit all the qualities. He married her, they had 4 kids, and a very nice home. After about 15 years of marriage, she decided she was gay, and left him for a woman. There should be an extended warranty available, or he should have included that sexual preference thing in his selection criteria.

ricpic said...

This test assumes that it's all these girls and you're the one guy, but who's to say you're not just one more guy, perhaps at the 36% point on one girl's list, hmmm? Me and Fredo, smarter than yiz all tink!

MamaM said...

Factor in Humor. It saves posts, blogs and marriages.

Sixty Grit said...

Multiplying the complexity of the problem is as easy as pi. You might go around in cirlces depending on the degree of uncertainty and end up right where you started.

The first guy who figured out the diameter of the earth thought "Gee, Ah'm a tree!", as he was from southern Egypt. But that doesn't equate precisely with what CL was writing about.

Lydia said...

I'd rather go Bubbie's marriage-broker way in Crossing Delancey.

Lem said...

Chickl summed it up.

Aridog said...

Chip S ....I have tried and tried, to include using different browsers and even the elements features of Blogger, to open your link to Math/UCLA etc. Figured I might learn something. No luck. Won't open.

I think I get it however, but still question the utility of a system that samples from its own larger sample (inherent bias?)...the feature that means you might be discarding suitable candidates. I prefer a method that draws presumptions from prior sample of the over all universe....that determines the most likely successful candidate types.

I'd definitely not want to use this restricted theory in evaluation a woman I might want to fall in love with....halp! :-))

Chip S. said...

Ari, Try this one, which includes this useful caveat:

The last assumption, for example, that n is known, is more appropriate for the secretary interpretation than for the marriage interpretation.

To me, the worst assumption is that there's no value in choosing anyone other than the absolute best. Seems ridiculous, esp. if you don't know you've picked the second-best one.

Aridog said...

Okay, Chip S....that wore me out. I have to agree with you that selecting the "absolute best" may not be so...you'd just think it was, with the understanding that the true best was perhaps passed by in the sample phase. Maybe a means to select a functional partner in some endeavor, but no way to select a wife or lover. A need to do so would suggest you don't deserve either wife or lover.