The 37 Percent Rule, or When to Stop Looking

The search for an ideal usually ends in marriage to the first person who turns up.

— An ironic aphorism

The mathematically perfect search for a partner starts with unwelcome news: the first candidates have to be rejected no matter how good they are. Picture a hundred closed doors. Behind each one is a candidate, and you can only open the doors in order. After a viewing you either choose that person forever or refuse forever. There is no going back. At the end you must choose someone. All candidates share a single ranking, which you learn on meeting them. Their order is random. Under those rules the optimal strategy is elegant. The first thirty-seven doors or so are used for reconnaissance. You pick nobody, but you remember the best level seen. Then you take the first person who beats everyone seen so far. The probability of getting the absolute best turns out to be about the same 37 percent.

This is the secretary problem. In popular retellings it became an instruction manual for love.

The number 1/e

The exploration share r gives a neat maximum at r = 1/e, roughly 0.368. The best candidate has to appear after the exploration stretch; you manage to choose them when the best of the earlier ones fell inside that stretch and set the threshold. Summing over the possible positions leads to the famous number. The setup matters more: a known number of options in advance, random order, irreversible refusal, a single ranking and the goal of getting the absolute maximum. The percentage belongs to that game, not to the human mind.

Change one rule and the strategy changes.

People stop earlier

In laboratory versions of the problem, participants saw a sequence of relative ranks and each time decided whether to stop or to gamble on what they had already seen. Without prompting they quickly found the general shape of the strategy: first gather a benchmark, then decide. People grasped the two-phase logic more easily than the exact boundary between the phases.

In the experiments by Daniel Seale and Amnon Rapoport, stopping usually happened earlier than the mathematical optimum. In the classical setup a viewing has no separate cost: the participant pays only with the risk of missing the best option and ending up with nothing. The laboratory human also bears attention, time and the subjective price of continuing. Once those costs are included, stopping early stops looking like a plain mistake and becomes the solution to a different problem.

The neighbourhood of the optimum is also fairly flat: a small shift in the threshold barely changes the probability of success. The popular version presents 37 percent as a safe combination in which a few extra candidates wreck your fate. The mathematics is strict about its conditions but comparatively tolerant of neighbouring strategies.

The lab separates the principle from its price. People understand the move “learn first, then choose,” and set the length of learning by their own costs. In dating those costs vary a lot: a meeting can be exhausting, expensive, unsafe or pleasant regardless of the outcome. Optimal exploration depends on the cost of search no less than on the chance of meeting the maximum.

Real dating breaks almost every initial condition. The number of future candidates is unknown, the order is sorted by school, profession, neighbourhood and friends, there is no single ranking, sometimes you can go back to someone you rejected, and they are choosing too. Usually people are not looking for the objectively best of all humans but for a good enough mutual union. The secretary problem assumes the rejected disappear forever; perhaps that is why it describes hiring a secretary more accurately than the lives of people who know how to keep phone numbers.

The possibility of returning gives early options an option value. Candidates who change over time cannot be ranked once. And when the quality of a relationship is partly created after the choice, no absolute ranking exists before the choice at all. The 37 percent rule as life advice does not survive the transfer.

Once the sacred percentage is gone, the two-phase logic remains. At the start a person knows neither the distribution of options nor their own reactions well. A few meetings calibrate expectations: what is common, which requirements are rare, what turns out to matter in person. Later the returns on exploration fall. Yet another similar meeting barely changes the picture of the market and increasingly serves to postpone the decision.

Here the mathematical problem keeps a heuristic meaning: exploring first is useful, then you have to switch to choosing. Without exploration, expectations are arbitrary; without the switch to choosing, the search becomes a way of life.

The goal changes the strategy

The strategy changes along with the goal. Looking for any candidate in the top ten percent ends sooner than hunting for the single best. A high price for ending up with nobody lowers the threshold, the possibility of returning softens the rejection of early options, expensive meetings shorten exploration, and a systematically changing environment cancels random order. Instead of one percentage, six variables remain:

roughly how many opportunities are expected;

what counts as an acceptable outcome;

whether you can go back;

what continuing the search costs;

how much new meetings still change your understanding of the distribution;

what is lost by choosing too late.

The answers will not produce a number that is the same for everyone. They will produce a decision tied to a particular horizon.

The strategy needs only relative comparisons: a new option is set against the best of those already met. This protects against a bad absolute scale and makes the decision depend on the quality of the exploration sample. A narrow environment forms a low threshold and passes it off as rational; a few rare strong acquaintances can push expectations too high. A threshold only learns from the market it was shown.

A threshold starts with checking how varied the exploration was, not with counting percentages. Ten identical acquaintances give less information than five from different social circles. It makes sense to build it on an understanding of the range of options, your own constraints and the cost of continuing, rather than on the number of people rejected. After such a check the exact number becomes secondary.

A threshold that has to update

An updating threshold is more useful than a fixed 37 percent. At twenty a person can explore a wide range and learn their own taste; later they have more data but different deadlines and goals. A move requires new calibration. A run of bad relationships calls for a check of the scale itself, not an automatic lowering of requirements. Mutuality is part of the threshold too: a person who takes first place and does not want to continue is absent from the available options.

The 37 percent rule remains fine mathematics. It shows that searching and choosing are different modes, and that endless exploration has a price. The percentage simply belongs to a world where all the doors are counted in advance, people stand in a random queue and nobody calls back.

Main sources

Ferguson, T. S. (1989). Who solved the secretary problem? Statistical Science, 4(3), 282–289.

Seale, D. A., & Rapoport, A. (1997). Sequential decision making with relative ranks: An experimental investigation of the secretary problem. Organizational Behavior and Human Decision Processes, 69(3), 221–236.

Gilbert, J. P., & Mosteller, F. (1966). Recognizing the maximum of a sequence. Journal of the American Statistical Association, 61(313), 35–73.

Freeman, P. R. (1983). The secretary problem and its extensions: A review. International Statistical Review, 51(2), 189–206.