The odds if we hire at random are one-third, or 33%?

Add a third applicant, and all of a sudden things get
interesting. The odds if we hire at random are one-third,
or 33%. With two applicants we could do no better than
chance; with three, can we? It turns out we can, and it all
comes down to what we do with the second interviewee.
V\7hen we see the first applicant, we have no information-
she’ll always appear to be the best yet. V\Then we see the
third applicant, we have no ageucy—we have to make an
offer to the final applicant, since we’ve dismissed the
others. But when we see the second applicant, we have a
little bit of both: we know whether she’s better or worse
than the first, and we have the freedom to either hire or
dismiss her. V\7hat happens when we just hire her if she’s
better than the first applicant, and dismiss her if she’s not?
This turns out to be the best possible strategy when facing
three applicants; using this approach it’s possible,
surprisingly, to do just as well in the three-applicant
problem as with two, choosing the best applicant exactly
half the time.f
Enumerating these scenarios for four applicants tells us
that we should still begin to leap as soon as the second
applicant; with five applicants in the pool, we shouldn’t
leap before the third.
As the applicant pool grows, the exact place to draw the
line between looking and leaping settles to 37% of the pool,
yielding the 37% Rule: look at the first 37% of the
applicants: choosing none, then be ready to leap for
anyone better than all those you’ve seen so far.

the strategy itself and its chance of success work out to the
very same number. The table above shows the optimal
strategy for the secretary problem with different numbers
of applicants, demonstrating how the chance of success-
like the point to switch from looking to leaping—converges
on 37% as the number of applicants increases.
A 63% failure rate, when following the best possible
strategy, is a sobering fact. Even when we act optimally in
the secretary problem, we will still fail most of the time-
that is, we won’t end up with the single best applicant in
the pool. This is bad news for those of us who would frame
romance as a search for “the one.” But here’s the silver
lining. Intuition would suggest that our chances of picking
the single best applicant should steadily decrease as the
applicant pool grows. If we were hiring at random, for
instance, then in a pool of a hundred applicants we’d have
a 1% chance of success, and in a pool of a million
applicants we’d have a 0.0001% chance. Yet remarkably,
the math of the secretary problem doesn’t change. If you’re
stopping optimally, your chance of finding the single best
applicant in a pool of a hundred is 37%. And in a pool of a
million, believe it or not, your chance is still 37%.
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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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