The questions posted in the previous blog were designed to highlight the two systems of thought (the intuitive and the rational) that operate in our brain (see references for confirmation of this outlandish statement!) The degree to which an individual monitors their intuitive thoughts with their rational mind is a profound indicator of other significant personal characteristics.
Question one asked: A bat and a base-ball cost $1.10 together. The bat costs $1.00 more than the base-ball. How much do the bat and the base-ball cost individually? (Did you give it a go?)
Almost everyone who is asked this question reports that the answer that immediately comes to mind is that the bat costs $1.00 and the base-ball costs $0.10. However, if you ‘think’ about the question for more than a moment it becomes clear that this cannot be right as it would result in the bat costing $0.90 more than the base-ball.
Academic Shane Fredericks (2005) found that many intelligent people yield to their first impression and give the wrong result to this question. In one study of Princeton University students 50 per cent gave the wrong answer and in another study of University of Michigan students 56 per cent!
The correct answer is that the bat costs $1.05 and the base-ball costs $0.05.
This question highlights how lax we can be in our conscious monitoring, and how easily we trust a plausible judgement that comes quickly to mind. Generally these intuitive ‘answers’ are based on implicit assumptions. The wide-spread lack of mental monitoring is kinda scary when we move away from questions of base-ball prices and address questions of racism, sexism and the many areas of life where our decisions are guided by implicit assumptions.
The next two questions were in the same theme.
Question two asked: If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
The answer is 5 minutes, but many people respond by saying 100 minutes. It seems right at an intuitive level.
Question three asked: There is a lake suffering from a blue-green algae bloom. Every day the size of the bloom doubles. If it takes 48 days for the bloom to cover the entire lake, how long would it take for the patch to cover half the lake?
The intuitive answer tends to be 24 days. It is wrong.
The correct answer is 47 days.
Fredericks also found that people’s answers to these questions were highly correlated with certain behavioural traits. For instance, people who answered all three questions right tended to be more patient and more willing to wait to be rewarded. Fredericks’ subjects were asked another question: would you rather $3,400 this month or $3,800 next month?
The students who got all three questions wrong then 65 per cent went for the $3,400 this month. In contrast, of those who got all three answers right, 60 per cent decided to wait a month and take $3,800. The two different amounts equate to an implied discount rate (the interest rate a bank would have to pay you on $3,400 to make it worth $3,800 in a month) of 280 per cent!
How did you go with these simple questions? Should I lend you some money for the month? (You wouldn’t happen to have $3,400 sitting around would you?)
Frederick, S., 2005, Cognitive reflection and decision making, Journal of Economic Perspectives, Volume 19, Number 4.
Epstein, S., 1994, Integration of the cognitive and psychodynamic unconscious, American Psychologist, 49, 709-724.
Chaiken, S., and Trope, Y., (Eds) 1999, Dual-process theories in social psychology, New York: Guilford Press.
Kahneman, D., 8 December 2002, Maps of bounded rationality: A perspective on intuitive judgement and choice, Noble Prize Lecture.