Optimal Stopping: When To Stop Looking

An angst-ridden Brian went to his own college guidance
counselor his freshman year. His high-school girlfriend
had gone to a different college several states away, and
they struggled with the distance. They also struggled with
a stranger and more philosophical question: how good a
relationship did they have? They had no real benchmark of
other relationships by which to judge it. Brian’s counselor
recognized theirs as a classic freshman—year dilemma, and
was surprisingly nonchalant in her advice: “Gather data.”
The nature of serial monogamy, writ large, is that its
practitioners are confronted with a fundamental,
unavoidable problem. V\Then have you met enough people
to know who your best match is? And what if acquiring the
data costs you that very match? It seems the ultimate
Catch-22 of the heart.
As we have seen, this Catch—22, this angsty freshman cri
de coeur, is what mathematicians call an “optimal
stopping” problem, and it may actually have an answer:
Of course, it all depends on the assumptions you’re
willing to make about love.

In any optimal stopping problem, the crucial dilemma is
not which option to pick, but how many options to even
consider. These problems turn out to have implications
not only for lovers and renters, but also for drivers,
homeowners, burglars, and beyond.
The 37% Rulef derives from optimal stopping’s most
famous puzzle, which has come to be known as the
“secretary problem.” Its setup is much like the apartment
hunter’s dilemma that we considered earlier. Imagine
you’re interviewing a set of applicants for a position as a
secretary, and your goal is to maximize the chance of
hiring the single best applicant in the pool. V\Thile you have
no idea how to assign scores to individual applicants, you
can easily judge which one you prefer. (A mathematician
might say you have access only to the ordinal numbers-
the relative ranks of the applicants compared to each other
—but not to the cardinal numbers, their ratings on some
kind of general scale.) You interview the applicants in
random order, one at a time. You can decide to offer the
job to an applicant at any point and they are guaranteed to
accept, terminating the search. But if you pass over an

applicant, deciding not to hire them, they are gone forever.
The secretary problem is widely considered to have
made its first appearance in print—sans explicit mention
of secretaries—in the February 1960 issue of Scientific
American, as one of several puzzles posed in Martin
Gardner’s beloved column on recreational mathematics.
But the origins of the problem are surprisingly mysterious.
Our own initial search yielded little but speculation, before
turning into unexpectedly physical detective work: a road
trip down to the archive of Gardner’s papers at Stanford,
to haul out boxes of his midcentuiy correspondence.
Reading paper correspondence is a bit like eavesdropping
on someone who’s on the phone: you’re only hearing one
side of the exchange, and must infer the other. In our case,
we only had the replies to what was apparently Gardner’s
own search for the problem’s origins fiflysome years ago.
The more we read, the more tangled and unclear the stoiy
Harvard mathematician Frederick Mosteller recalled
hearing about the problem in 1955 from his colleague
Andrew Gleason, who had heard about it from somebody
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ZAKARIA AL BAZZAR, 19 yo, university student. love everything about new tech, and I'm sharing it with you :)
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