See if you can solve the following problem:
A bat and a ball cost $1.10. The bat costs $1.00 more than the ball. How much does the ball cost?
Most people are tempted to say that the ball costs 10 cents. If that was your answer, think again. A few people resist the initial temptation, do some calculation, and discover that the ball in fact costs 5 cents. But however you answered, take comfort. Even at elite universities, most people get this question wrong.
What’s going on here? It’s not that the question is particularly difficult. Here is a tougher version of the original problem:
A banana and a bagel cost 37 cents. The banana costs 13 cents more than the bagel. How much does the bagel cost?
Most people get this question right. What is so challenging about bats and balls?
The answer to that question is easy. We are tempted to solve the bat-and-ball problem by attribute substitution, mentally replacing `$1.00 more than’ with `$1.00’. The modified problem reads:
A bat and a ball cost $1.10. The bat costs $1.00. How much does the ball cost?
This substitution biases our answers. When we solve the modified problem, we wrongly conclude that the ball costs 10 cents.
We’re not tempted to do make any such substitution in the banana-and-bagel problem. It’s not tempting in the slightest to substitute 13 cents for the cost of the banana. For this reason, we get the banana-and-bagel problem right. But why would we ever make an erroneous substitution in the first place?
One answer is that humans are lazy and irrational reasoners. More specifically, we’re cognitive misers, spending as little cognitive effort as we can get away with. And in particular, we’re lax monitors of our own cognitive processes. We didn’t catch the illicit attribute substitution because we weren’t paying attention.
New evidence suggests that humans are neither as miserly nor as lax as we may appear. We do not flunk the bat-and-ball problem because we are lazy. Taking longer to solve the problem does not improve most people’s answers. Nor do we give the wrong answer because we are not paying attention. When solving the bat-and-ball problem we are less confident in our answers, take longer to respond, and feel more strongly that we have made an error than in solving the banana-and-bagel problem. This suggests that we were paying attention to the fact that we have made a risky substitution, even if we ultimately took the risk.
These results are no accident. Recent studies suggest that humans have a remarkable capacity to monitor and detect our own biases. We respond to a range of biases with decreased confidence, increased response time, and increased feelings of having made an error. Even as we make biased judgments, we are sensitive to the presence of bias.
How do we detect our own biases without explicitly discovering and correcting them? They jury is still out on this question. Perhaps we were reasoning through the bat-and-ball problem in several ways at once. Even as one line of reasoning tempted us to respond incorrectly, we were thinking through the problem using another, more correct strategy. That correct strategy influenced our confidence, feelings, and response time. Or perhaps we simply judged or felt the likelihood that we had made a mistake. We knew we had done something risky in solving the banana-and-bagel problem but decided to take the risk anyways.
What does all of this tell us about human rationality? It seems a stretch to say that biased reasoners are thinking rationally, particularly when it is well within our abilities to do better. More plausibly, our sensitivity to bias suggests that rationality is not an all-or-nothing affair. Even as we reason irrationally, we often recognize and respond to the potential for bias. That is not as much rationality as we might have hoped for, but it is an awful lot better than nothing.
