The Secretary Problem: Use this algorithm to determine exactly how many people you should assess before making a new hire or choosing a life partner.

Use This Algorithm to Determine Exactly How Many People to Date Before Getting Married

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Dec. 17 2014 9:21 AM

The Secretary Problem

An algorithm for deciding who to marry, and other tough choices.

Finding a life partner is a delicate balance. When you first start dating people, you don’t know, on average, how romantically well matched other people could be to you, and without that baseline you cannot ascertain if someone is an above average catch and someone you should settle down with. This makes permanently partnering up with the first person you date a bit of a gamble: You should date a few people to get the lay of the land. That said, if you take too long dating people, you run the risk of missing your ideal partner and being forced to make do with whoever is available at the end. It’s a tricky one. The ideal thing to do would be to date just the right number of people to gain the best sense of your options while leaving the highest probability of not missing your ideal partner.

Luckily, math has made it easy for us: That right number of people is the square root of the total number of people you could date in your life. How you estimate the size of your possible dating population is entirely up to your statistical skills and the level of your self-confidence, as is how you then collect your sample. A “voluntary response sample” is generally regarded as socially acceptable, whereas a “stratified random sample” can land you in jail.

Putting that aside, here is the recipe for finding optimal love:

Step 1: Estimate how many people you could date in your life, n.

Step 2: Calculate the square root of that number, √n.

Step 3: Date and reject the first √n people; the best of them will set your benchmark.

Step 4: Continue dating people and settle down with the first person to exceed the benchmark set by the initial √n dates.

Who knew it could be so easy? Problems like deciding who to settle down with have the mildly disturbing math name of “optimal stopping problems.” The original optimal stopping problem was known as the secretary problem, and here it is as originally framed.

You’re hiring a new personal assistant and the company’s human resources department has put out an advertisement following the guidelines laid down in its official diversity policies. There is now a queue of potential candidates outside your office, spanning a wide range of genders and ethnicities, all ready to be interviewed for the job. Each of the 10 candidates will come into your office individually for you to assess their qualifications for the role. After you have interviewed each candidate you need to decide on the spot if you want to hire them for the job or move on to the next interview. If you dismiss someone without a job offer, they’ll be snapped up by a rival company: You cannot go back to them later and offer them the job.

You’re in an interesting position. Logic suggests that you shouldn’t offer the job to the first person you interview, because you have no idea what the general caliber of the candidates is. Nor do you want to wait until the 10th person, because if they’re the only one left you’re going to be forced to offer them the job regardless of how well suited to it they are. Somewhere in the middle there must be an ideal place to stop interviewing more candidates just to see what they’re like, and hurry up and choose a good one. This is the optimal place to stop. It’s exactly the same constraint as dating to find a life partner; if you break up with someone you later realize was an ideal candidate, you can rarely go back to re-interview them.