Would You Take the Bird in the Hand, or a 75% Chance at the Two in the Bush?

The New York Times, "Economic Scene" , January 26, 2006

Would you rather have $1,000 for sure or a 90 percent chance of $5,000? A guaranteed $1,000 or a 75 percent chance of $4,000?

In economic theory, questions like these have no right or wrong answers. Even if a gamble is mathematically more valuable -- a 75 percent chance of $4,000 has an expected value of $3,000, for instance -- someone may still prefer a sure thing.

People have different tastes for risk, just as they have different tastes for ice cream or paint colors. The same is true for waiting: Would you rather have $400 now or $100 every year for 10 years? How about $3,400 this month or $3,800 next month? Different people will answer differently.

Economists generally accept those differences without further explanation, while decision researchers tend to focus on average behavior.

In decision research, individual differences ''are regarded as a nuisance -- as just another source of 'unexplained' variance,'' Shane Frederick, a management science professor at the Sloan School of Management at the Massachusetts Institute of Technology, wrote in ''Cognitive Reflection and Decision Making.'' The article is published in the Fall 2005 issue of The Journal of Economic Perspectives, which includes a special section of articles devoted to ''cognition, brain science and economics.'' (The article is available here.)

Professor Frederick discovered striking systematic patterns in how people answer questions about risk and patience, including those above. This short problem-solving test, he found, predicts a lot:

1) A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?

2) If it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets?

3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half the lake?

The test measures not just the ability to solve math problems but the willingness to reflect on and check your answers. (Scores have a 0.44 correlation with math SAT scores, where 1.00 would be exact.) The questions all have intuitive answers -- wrong ones.

Professor Frederick gave his ''cognitive reflection test'' to nearly 3,500 respondents, mostly students at universities including M.I.T., the University of Michigan and Bowling Green University. Participants also answered a survey about how they would choose between various financial payoffs, as well as time-oriented questions like how much they would pay to get a book delivered overnight.

Getting the math problems right predicts nothing about most tastes, including whether someone prefers apples or oranges, Coke or Pepsi, rap music or ballet. But high scorers -- those who get all the questions right -- do prefer taking risks.

''Even when it actually hurts you on average to take the gamble, the smart people, the high-scoring people, actually like it more,'' Professor Frederick said in an interview. Almost a third of high scorers preferred a 1 percent chance of $5,000 to a sure $60.

They are also more patient, particularly when the difference, and the implied interest rate, is large. Choosing $3,400 this month over $3,800 next month implies an annual discount rate of 280 percent. Yet only 35 percent of low scorers -- those who missed every question -- said they would wait, while 60 percent of high scorers preferred the later, bigger payoff.

Men and women also show different results. ''Expressed loosely,'' he writes, ''being smart makes women patient and makes men take more risks.''

High-scoring women show slightly more willingness to wait than high-scoring men, while the differences in risk-taking are much larger. High-scoring women are about as willing to gamble as low-scoring men, while low-scoring women are even more risk-averse.

For instance, 80 percent of high-scoring men would pick a 15 percent chance of $1 million over a sure $500, compared with only 38 percent of high-scoring women, 40 percent of low-scoring men and 25 percent of low-scoring women.

The connection between cognition and risk preferences challenges some of the ''prospect theory'' developed from the pioneering work of Daniel Kahneman and Amos Tversky. They observed that people would accept larger risks to avoid losses than to achieve gains, even when the two choices were mathematically equivalent. The same person might take a sure $100 instead of a 50 percent chance of $300, yet prefer a 50 percent chance of losing $300 rather than a sure $100 loss.

This result, which has implications for investment and insurance, is one of the major findings of behavioral economics. Although prospect theory ''is spectacularly true'' for the low-scoring group, Professor Frederick writes, high scorers treat potential gains and potential losses about the same.

Psychology studies often find that small differences in wording seem to produce large differences in survey answers. But since these experiments are usually done on college campuses using students, the real difference may lie elsewhere.

Maybe, suggested Professor Frederick in the interview, ''it's because one study was done at University of Toledo'' -- where the mean score on his test was 0.57 out of a possible 3 -- ''and one study was done at Princeton,'' where the mean was 1.63. The test groups may not really be the same.

''Most researchers are finding that subtle differences in framing cause different preferences,'' he said, ''but it might just be that these people are a whole lot smarter on average than these other people, and that's why you're getting these results.''

The correct answers, by the way, are 5 cents, 5 minutes, and 47 days.