From Priceonomics:
By all accounts, Marilyn vos Savant was a child prodigy.
Born
in St. Louis, Missouri in 1946, the young savant quickly developed an
aptitude for math and science. At age 10, she was given two intelligence
tests -- the Stanford-Binet, and the Mega Test -- both of which placed
her mental capacity at that of a 23-year-old. She went on to be listed
in the Guinness Book of World Records for having the “World’s Highest IQ,” and, as a result, gained international fame.
Despite her status as the "world’s smartest woman,” vos Savant maintained
that attempts to measure intelligence were “useless,” and she rejected
IQ tests as unreliable. In the mid-1980s, with free rein to choose a
career path, she packed her bags and moved to New York City to be a
writer.
Here, she caught a break: when Parade Magazine
wrote a profile on her, readers responded with so many letters that the
publication offered her a full-time job. Shortly thereafter, she
established “Ask Marilyn,” a now-famous weekly column in which she
answered (and continues to answer, to this day) a variety of academic
questions and logic puzzles. It was in the body of one of these columns
that vos Savant ignited one of the most heated statistical battles of
the 21st century.
When vos Savant politely responded to
a reader’s inquiry on the Monty Hall Problem, a then-relatively-unknown
probability puzzle, she never could’ve imagined what would unfold:
though her answer was correct, she received over 10,000 letters, many
from noted scholars and Ph.Ds, informing her that she was a hare-brained
idiot.
What ensued for vos Savant was a nightmarish
journey, rife with name-calling, gender-based assumptions, and academic
persecution.
The Monty Hall Problem: A Brief History
Imagine
that you’re on a television game show and the host presents you with
three closed doors. Behind one of them, sits a sparkling, brand-new
Lincoln Continental; behind the other two, are smelly old goats. The
host implores you to pick a door, and you select door #1. Then, the
host, who is well-aware of what’s going on behind the scenes, opens door
#3, revealing one of the goats.
“Now,” he says, turning toward you, “do you want to keep door #1, or do you want to switch to door #2?”
Statistically,
which choice gets you the car: keeping your original door, or
switching? If you, like most people, posit that your odds are 50-50,
you’re wrong -- unless, of course, you like goats as much as you like
new cars, in which case you'll win 100% of the time.
Loosely based on the famous television game show Let’s Make a Deal,
the scenario presented above, better known as the “Monty Hall Problem,”
is a rather famous probability question. Despite its deceptive
simplicity, some of the world’s brightest minds -- MIT professors,
renowned mathematicians, and MacArthur “Genius” Fellows -- have had
trouble grasping its answer. For decades, it has sparked intense debates
in classrooms and lecture halls.
Historically, the Monty Hall Problem was predated by several very similar puzzles.
In Joseph Bertrand’s box paradox
(1889), three boxes are presented -- one containing two gold coins, one
containing two silver coins, and the final containing one of each.
Assuming the participant draws one gold coin from a box, the problem
then asks what the probability is that the other coin in that box is
gold. Bertrand, who concluded that the probability was ⅔, was lauded for
his ability to look beyond the obvious.
A second iteration of this paradox, the Three Prisoners Problem
(1959), presents a statistically identical scenario, with the same
outcome. “[It’s] a wonderfully confusing little problem," its creator, Scientific American columnist Martin Gardner, later wrote, smugly. "In no other branch of mathematics is it so easy for experts to blunder as in probability theory."
First presented in a letter to the editor of The American Statistician
in 1975, the Monty Hall Problem was also counterintuitive. In this
letter, Steve Selvin, a University of California, Berkeley professor,
splayed out the situation in the intro of this article, and contended
that switching doors yields a ⅔ chance of winning the car, whereas
keeping the original door results in winning only ⅓ of the time.
Over the next decade or so, the Monty Hall Problem made several appearances, first in a Journal of Economics Perspectives puzzle by Barry Nalebuff, and subsequently in a 1989 issue of Bridge Today, by Phillip Martin. Neither man’s logic was refuted, and the problem generated relatively little attention.
Then,
after 15 years without incident, the Monty Hall Problem was resurrected
by Marilyn vos Savant -- and an absolute shit-storm ensued....
....MUCH MORE
