In the decades since the secretary problem was first introduced

Both Kepler and Trick—in opposite ways—experienced
firsthand some of the ways that the secretary problem
oversimplifies the search for love. In the classical secretary
problem, applicants always accept the position, preventing
the rejection experienced by Trick. And they cannot be
“recalled” once passed over, contrary to the strategy
followed by Kepler.
In the decades since the secretary problem was first
introduced, a Wide range of variants on the scenario have
been studied, with strategies for optimal stopping worked
out under a number of different conditions. The possibility
of rejection, for instance, has a straightforward
mathematical solution: propose early and often. If you
have, say, a 50/50 chance of being rejected, then the same
kind of mathematical analysis that yielded the 37% Rule
says you should start making offers after just a quarter of
your search. If turned down, keep making offers to every
best-yet person you see until somebody accepts. With such
a strategy, your chance of overall success—that is,
proposing and being accepted by the best applicant in the
pool—will also be 25%. Not such terrible odds, perhaps, for
a scenario that combines the obstacle of rejection with the
general difficulty of establishing one’s standards in the
first place.

Kepler, for his part, decried the “restlessness and
doubtfulness” that pushed him to keep on searching. “Was
there no other way for my uneasy heart to be content with
its fate,” he bemoaned in a letter to a confidante, “than by
realizing the impossibility of the fulfillment of so many
other desires?” Here, again, optimal stopping theory
provides some measure of consolation. Rather than being
signs of moral or psychological degeneracy, restlessness
and doubtfulness actually turn out to be part of the best
strategy for scenarios where second chances are possible.
If you can recall previous applicants, the optimal
algorithm puts a twist on the familiar Look-Then-Leap
Rule: a longer noncommittal period, and a fallback plan.
For example, assume an immediate proposal is a sure
thing but belated proposals are rejected half the time.
Then the math says you should keep looking
noncommittally until you’ve seen 61% of applicants, and
then only leap if someone in the remaining 39% of the pool
proves to be the best yet.
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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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