The Problem With The 37% Rule

In The 37 Percent Rule, the basic idea is that you have a series of candidates you are interviewing for the role of secretary (this thought experiment originated in the 1950s). You interview each candidate one by one and must decide on the spot if you will stop your search there and hire the candidate. If you decide to move to the next candidate, the previous candidate is gone forever.

The algorithm suggests that to maximize your probability of finding the best secretary, you should interview 37% of the candidates without making a decision, and then hire the next candidate who is the best one so far. This rule gives, by coincidence, a 37% chance of ending up with the best candidate.

The 37% rule isn’t just recommended for hiring secretaries, many books have suggested that you use it for other decisions in life, like finding a mate.

But that may not be such a great idea, as Gerd Gigerenzer points out in Simple Heuristics That Make Us Smart.

Through his analyses, Gigerenzer and his team discover that even for a simple cost-free, non-mutual (one-sided) search like secretary problem, the 37% rule is outperformed by heuristics that sample much fewer prospects. Simple Heuristics that make us Smart, Gerd Gigerenzer (P. 291–294)

In real life, women and men searching for a mate, especially in modern Western cultures, don’t encounter idealized scenarios given in support of the 37% rule. The modern search for a mate requires a sequential search through successive potential mates in which each is evaluated and decided on ( a process that can take minutes, hours, or years). The decision here can be thought of as whether to settle down and start a family, but other definitions are possible.

There are costs associated with checking out each person during this search, not to mention that it is difficult, if not impossible, to return to a mate that has been abandoned.

To make things more complicated, no one can know ahead of time what the range of potential mates may be. It is not possible to know, the first time one falls in love, whether someone else will be able to incite even deeper feelings if they search more. It is not possible to know whether a future prospect will accept their decision. It is not even possible to know how many mates one will encounter.

Since these limitations exist, the task of finding a mate looks like a daunting problem. And the 37% rule, a simplistic mathematical algorithm that ignores the complexities of the real world, should be taken with many grains of salt.

Gigerenzer provides another example to illustrate this point, that is more precise than the secretary problem when it comes to mate choice. It is known as the “dowry problem.”

A sultan wishes to test the wisdom of his chief advisor, to decide if the advisor should retain his cabinet position. The chief advisor is seeking a wife, so the sultan takes this opportunity to judge his wisdom. The sultan arranges to have 100 women from the kingdom brought before the advisor in succession, and all the advisor has to do to retain his post is to choose the woman with the highest dowry (marriage gift from her family). If he chooses correctly, he gets to marry that woman and keep his post; if not, the chief executioner chops off his head, and worse, he remains single. Simple Heuristics that make us Smart, Gerd Gigerenzer (P. 291–294)

Like the secretary problem, the advisor can see one woman at a time and ask her dowry, then must instantly decide if she is the one with the highest dowry out of 100 women. Otherwise, he will let her pass by and go on to the next woman. He cannot return to a woman he has seen before. And the advisor does not know the range of dowries before he starts ewing the women. What strategy can he use to give him the best chance of choosing the woman with the highest dowry?

It turns out that the algorithm that gives the advisor the best chance of choosing correctly is the 37% rule. That is, he should look at the first 37 women, letting each one pass, but taking note of the highest dowry (call it “D”) from that group. Then, starting with the 38th woman, he should choose the first woman with a woman with a dowry higher than D.

This algorithm outperformed the rest — it finds the highest value more often than any other algorithm (coincidentally, 37 percent of the time).

With this rule, the advisor has slightly better than a one in three shot at picking the right woman and keeping his head. The other two-thirds of the time, the sultan has to look for another advisor. Simple Heuristics that make us Smart, Gerd Gigerenzer (P. 291–294)

But the problem with this example is that it does not reflect real life mate selection, since it is one-sided. It reduces search to one dimension rather than consider the many facets that go into the way we judge one another. And it denies the possibility of comparing prospects at the same time, or returning to those who were previously seen. But it’s a reasonable starting point that one can build on.

Another major difference between the dowry problem and the real world is that mating decisions are not so dramatic. We get to live with whatever choice we make — there is no Sultan threatening to chop off our heads if we make the wrong decision.

But to a population of individuals all using such an algorithm to choose their mates, what this rule does the other 63% of the time would matter a lot. For instance, if applied to a set of 100 dowries covering all integer values from 1 to 100, the 37% rule returns an average value of about 81 (i.e., the mean of all dowries chosen by this rule).

Simple Heuristics that make us Smart, Gerd Gigerenzer (P. 291–294)

The idea here is that if you rank order each person with a number (from 1–100), and then you apply the 37% rule, you would end up with a mate with an average value of 81. Only 67% of the individuals selected by this rule would be in the top 10 percent, and 9 percent would be in the bottom 25 percent.

So, if your priority was to choose a mate in the top 10 percent, you would miss out a third of the time. And if you wanted to avoid a mate who was in the bottom 25 percent, you would fail a tenth of the time.

If you were risk averse, and had more realistic aspirations, you should look at different stopping rules. For example, if your priority was to choose someone in the top 10 percent, you should look at the first 14% of candidates and choose the next candidate that is better than the previous ones. That would give you an 83% chance of a top 10% candidate (as opposed to 67%).

You can apply a different rule if you are okay with settling for someone in the top 25% — only look at the first 7%, this will give you a 92% chance of getting someone in the top quartile.

What if the population was very large? Say 1000 people? You would need to look at only 3% of the candidates (a 97% probability of finding a top 10%). For a top 25% mate, check only 1 to 2%.

Unless you, like the Sultan’s advisor, want to maximize the chance of getting the best mate, and ignore all the other potential outcomes, you would be advised against using the 37% rule.

That is not to say that you can never benefit from the 37% rule. One day, you may find yourself in a position like the Sultan’s advisor, where you must choose the best candidate, or else…

Originally published at http://unearnedwisdom.com.

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