Imagine a future cat-topia where both
cats and people are applying to the physics and
在天文系 2只猫被录取 2只没有
In astronomy, 2 cats are accepted and 2 are rejected,
while 1 human is accepted and 1
在物理系 1只猫咪被录取 2只被拒绝
In physics 1 cat gets in and 2 don’t,
while 2 humans get in 4 don’t. So,
overall at the university,
3 cats are accepted and 4 rejected for a 43 % acceptance rate,
while 3 humans are accepted and 5 rejected
for a 38 % acceptance rate.
Is the university discriminating against humansin its application process?
That’s because if each department reviews its own applications,
then the numbers show
that the astronomy department lets in 50 %
of cats and 50 % of humans, which seems fair,
and the physics department lets in 33 %
of cats and 33 % of humans, which again seems
The reason, then,
for the apparent unfairness at the university level is the imbalance in
how many cats and humans apply to each department:
more of the cats applied to the astronomy department,
which happened to let in moreapplicants (regardless of species), while
more of the humans applied to physics, which let in fewer applicants.
This situation is another illustration ofSimpson’s statistical paradox, and something
like it actually happened at Berkeley in the 1970s,
which realized it was letting in 44 %
of men applying to the graduate school, but only 35 % of women.
Careful analysis was able to show
that women tended to apply more to departments that had
less funding and fewer places, like English,
and men tended to apply more to less competitive departments,
Thus within each department ( which was the level
at which applications were evaluated ),
there wasn ’ t obvious evidence
of gender discrimination among applicants – if anything,
women were favored.
And yet, the unequal distribution
of women and men across departments resulted in an
unequal distribution of women and men at theuniversity overall.
The question, then,
is what caused the unequal distribution of women and men to begin with?
One can of course imagine a sinister institution
knowing how Simpson’s paradox works, wanting
to discriminate against a particular group,
and thus advertising smaller, more competitive
departments more heavily to that group,
and vice-versa for groups they want to promote .
certain departments or fields may have reputations for being unwelcoming
and unsupportive towards women even if they let them in fairly,
and it ’ s also possible
that aspects of a university itself
attract applicants who are more likely to follow gendered
但是最终 正如伯克利所说 更大更社会的问题是
But ultimately, as the Berkeley study concluded,the problem is a bigger, societal, one: “Women
女生被其它的学科领域吸引了 这些学科通常更多在学者 更少的学位输出 更少的资金 而且往往就业前景较为不理想
are shunted towards fields of study that aregenerally more crowded, less productive of completed degrees, less well funded, and that
frequently offer poorer professional employment prospects…
The absence of a demonstrable bias
in the admissions system does not give grounds for
concluding that there must be no
bias anywhere else in the educational
process.” Those words were written in a statistics paperin 1975.
And more recent statistics tell us that they still remain true today –
which is unfortunate
if you think women and men should have
equal opportunities and/or be paid equally for equal
So the paradox isn ’ t really in the statistics,
since after careful analysis, the statistics
tell us we’re biased and even hint at wherethose biases are (or aren’t) coming into
the paradox is that we ’ ve remained so reluctant to fight our biases,
even when they ’ re
put in plain sight.
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