Monet, Taylor Swift, ‘Moana’: What Got Readers Through Their Grief

You will no doubt be familiar with the ball and bat problem;

• A bat and a ball cost $1.10 in total.
• The bat costs $1.00 more than the ball.
• How much does the ball cost? ____ cents.

In a paper in Cognition, Meyer and Fredrick test multiple versions of the ball and bat and related problems to try to uncover where people’s intuitions go wrong. The most remarkable two versions of which are shown below:

• A bat and a ball cost $110 in total.
• The bat costs $100 more than the ball.
• How much does the ball cost?
• Before responding, consider whether the answer could be $5.
•  $_____

———–

• A bat and a ball cost $110 in total.
• The bat costs $100 more than the ball.
• How much does the ball cost?
• The answer is $5.
• Please enter the number 5 in the blank below.
•  $_____

Remarkably, even when told to consider $5, most people continue to answer $10. Even more shockingly, most people get the answer right when they are explicitly told the answer and instructed to enter it, yet 23% still get the answer wrong! Wow.

The authors conclude:

…this “hinted” procedure serves to partition respondents into three groups: the reflective (who reject the common intuitive error and solve the problem on the first try), the careless (who answer 10, but revise to 5 when told they are wrong), and the hopeless (who are unable or unwilling to compute the correct response, even after being told that 10 is incorrect)

…many respondents maintain the erroneous response in the face of facts that plainly falsify it, even after their attention has been directed to those facts….the remarkable durability of that error paints a more pessimistic picture of human reasoning than we were initially inclined to accept; those whose thoughts most require additional deliberation benefit little from whatever additional deliberation can be induced.

As an economist, I would have liked to see an incentivized version (maybe some people are pulling the authors legs) but I don’t actually think that explains the results. Quite a few people are indeed hopeless.

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