Before we go any further, please take a
look at this problem.
Table 1 |
The problem requires correctly
interpreting a contingency table. Even bright college students often
get it wrong. When deciding whether the skin cream works, some
people only compare the numbers in the top row—the number of people
who used the skin cream who get better or worse. But this ignores
important information from the control group that didn't take the
skin cream. Other people only compare the numbers in the left
column—the number of people getting better who took the skin cream
or didn't. But this ignores the fact that many more people took the
skin cream than didn't. To correctly answer this question, you have
to consider all four cells of the table. You must compare the
percentage of people who used the skin cream who got better to the
percentage of people who didn't use the skin cream who got better.
Of the 298 people who used the skin cream, 223, or 75% of them, got
better. Of the 128 people who didn't use it, 107, or 84% of them,
got better. The correct answer is that the skin cream is
ineffective.
Why is this problem so difficult? In
part, it's because Dan Kahan and his colleagues—who did the study I'm about to report—put their thumb on the scales. They chose data
such that, if you use either of the two shortcuts I
mentioned—comparing only the numbers in the top row or the left
column—you'll get the wrong answer. Fifty-nine percent of the
participants in this study answered the problem incorrectly.
This problem illustrates the difference
between System 1 and System 2 thinking, the central metaphor of this blog. According to Daniel Kahnemann, in his book Thinking, Fast and Slow, we have two cognitive
systems. System 1 is automatic and effortless. We simply say and do
what feels right. The System 1 response to this problem is to say
that the skin cream works, because that's what it looks like at first
glance. System 2 is deliberate and effortful. It comes into play
when we take the time to analyze a situation carefully. It can be
used to correct the errors that System 1 is prone to making. In this
case, System 2 requires that you do the math.
As
difficult as this problem is, it has one thing going for it. We
don't have any emotional investment in whether this skin cream works.
But what if the issue were one about which we had a prior
hypothesis? In this case, System 1 could lead us to a second source
of error, confirmatory bias—the
tendency the interpret new information in a way that is consistent
with our prior beliefs and ideological biases. Compare the problem
in Table 1 to these three other problems.
Does a city-wide
ban on concealed weapons increase or decrease crime? Conservatives
would probably expect crime to increase (since people can no longer
use their concealed weapons to shoot bad guys), and would be
resistant to information suggesting that gun control actually works.
Of course, the opposite is true for liberals. Kahan expected
political ideology to affect participants' responses to the gun
control questions, but not the skin cream questions.
Now
let's introduce another variable into the mix—numeracy.
(I realize this is getting complicated, but please bear with me.
It's worth it.) Numeracy—analogous to literacy—refers to
mathematical competence and a tendency to use quantitative reasoning
in appropriate ways. You would expect numerate people to do better
when making judgments of contingency, at least when evaluating skin
creams. But what happens when numerate people encounter data
contradict that their political views?
We
know that liberals and conservatives clash over scientific issues
such as gun control and global warming. Kahan suggests two theories
to explain these political impasses. The science-comprehension
thesis suggests that people
don't have enough training in science and math. With better
education, people would be capable of correctly interpreting the
results of empirical studies. The identity-protective
cognition thesis is more
pessimistic. It argues that our ideological polarization is so great
that it cancels out even the ability of well-educated people to
utilize their math and science skills. If the confirmatory bias
trumps numeracy, Kahan believes that this raises serious questions
about whether Americans are capable of enlightened self-government.
We may have to turn over important decisions to committees of
experts. (But who will choose the experts?)
What do you think?
The answer provided by Kahan's research comes in Part 2.
You may also be interested in reading:
Is Democracy Possible? Part 2
Is Democracy Possible? Appendix
Climate of Mistrust
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