Friday, January 20, 2006

Back-Door Paternalism

Shane Frederick, an assistant professor at MIT's Sloan School of Management, suggests (in so many words) that the "best and brightest" should make decisions for the rest of us. He makes his case in "On the Ball: Cognitive Reflection and Decision Making." Frederick begins well enough, with premises that seem well supported:
  • Bright people have a lower time preference than less-bright people; that is, bright people are more likely than the less-bright to forgo current gratification in favor of greater future gratification (e.g., more income), where the attainment of the greater gratification is fairly certain.
  • In addition, bright people are more risk-tolerant than less-bright people, where there is the prospect of a gain; that is they are more willing than the less-bright to gamble a given amount of money for the prospect of winning an even larger amount of money.
Here are excerpts of the evidence adduced by Frederick:
People with higher cognitive ability (or “IQ”) differ from those with lower cognitive ability in a variety of important and unimportant ways. On average, they live longer, earn more, have larger working memories, faster reaction times, and are more susceptible to visual illusions. . . .

Despite the diversity of phenomena related to IQ, few have attempted to understand – or even describe – its influences on judgment and decision making. Studies on time preference, risk preference, probability weighting, ambiguity aversion, endowment effects, anchoring, and other widely researched topics rarely make any reference to the possible effects of cognitive abilities (or cognitive traits). . . .

Many researchers have emphasized the distinction between two types of cognitive processes: those executed quickly with little conscious deliberation [System 1] and those that are slower and more reflective [System 2]. . . . System 1 processes occur spontaneously, and do not require or consume much attention. Recognizing that the face of the person entering the classroom belongs to your math teacher involves System 1 processes – it occurs instantly and effortlessly, and is unaffected by intellect, alertness, motivation or the difficulty of the math problem being attempted at the time. Conversely, finding [the square root of] 19163 to two decimal places without a calculator involves System 2 processes – mental operations requiring effort, motivation, concentration, and the execution of learned rules. . . .

By contrast, consider the problem below:
A bat and a ball cost $1.10. The bat costs $1.00 more than the ball.
How much does the ball cost? ____ cents
Here, an intuitive answer does spring quickly to mind: “10 cents.” But this “impulsive” answer is wrong. . . .

In a study conducted at Princeton, which measured time preferences using both real and hypothetical rewards, those answering “10 cents” were found to be significantly less patient than those answering “5 cents.” Motivated by this result, two other problems found to yield impulsive erroneous responses were included with the “bat and ball” problem to form a simple, three item “Cognitive Reflection Test” (CRT), shown in Figure 1. The three items on the CRT are “easy” in the sense that their solution is easily understood when explained, yet reaching the correct answer often requires the suppression of an erroneous answer that springs “impulsively” to mind.
Figure 1. The Cognitive Reflection Test (CRT)

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

(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100
machines to make 100 widgets?
____ minutes

(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 of the lake?
____ days
Over a 26-month period beginning in January, 2003, the CRT was administered to 3,428 respondents in 35 separate studies that also measured various decision making characteristics, like time and risk preferences. . . .

The notion that more intelligent people are more patient – that they devalue or “discount” future rewards less steeply – has prevailed for some time. . . .

The widely presumed relation between cognitive ability and patience has been tested in several studies, although rather unsystematically. . . .

Collectively, these studies offer some support for the view that cognitive ability and time preference are somehow connected, though none has identified the types of intertemporal decisions over which cognitive ability exerts influence, nor explained why it does so. Toward this end, I examined the relation between CRT scores and a wide variety of items intended to measure various aspects of “time preference.” . . . .

As predicted, those who scored higher on the CRT were generally more “patient”; their decisions implied lower discount rates. For short term choices between monetary rewards, the high CRT group was much more inclined to choose the later larger reward. . . . However, for choices involving longer horizons . . . , temporal preferences were weakly related or unrelated to CRT scores.

A tentative explanation for these results is as follows: a thoughtful respondent can find good reasons for discounting future monetary outcomes – the promiser could default, one may be predictably wealthier in the future (with correspondingly diminished marginal utility for further wealth gains), interest rates could increase (which increases the opportunity cost of foregoing the immediate reward), and inflation could reduce the future rewards’ real value (if the stated amount is interpreted as being denominated in nominal units). . . . However, such reasons do not apply with the same force for short term options; they are not sufficiently compelling to justify choosing $3400 this month over $3800 next month (which implies an annual discount rate of 280%). Hence, for choices . . . where the careful deliberation associated with “System 2” ought to strongly oppose one’s intuitive “System 1” preference for the more immediate reward . . . one observes considerable differences between CRT groups. . . .

Thus, greater cognitive reflection seemingly fosters the recognition or appreciation of considerations (like interest rates) that may favor the later larger reward. . . .

To assess the relation between CRT and risk preferences, I included several measures of risk preferences in my questionnaires, including choices between a certain gain (or loss) and some probability of a larger gain (or loss). For some items, expected value was maximized by choosing the gamble, and for some it was maximized by choosing the certain outcome.

. . . In the domain of gains, the high CRT group was more willing to gamble, particularly when the gamble had higher expected value . . . , but, notably, even when it did not. . . . This suggests that the correlation between cognitive ability and risk taking in gains is not due solely to a greater disposition to compute expected value or adopt that as the choice criterion. For items involving losses . . . , the higher CRT group was less riskseeking; they were more willing accept a sure loss to avoid playing a gamble with lower (more negative) expected value. . . .
Frederick then reinforces the connection between CRT and intelligence; for example:
[T]hough the CRT is intended to measure cognitive reflection, performance on it is surely aided by reading comprehension and mathematical skills (which the ACT [American College Test] and SAT [Scholastic Aptitude Test] also measure). Similarly, though Cacioppo et al. . . . claim that NFC [the "need for cognition scale] is “clearly separable” from intelligence, their list of ways in which those with high NFC were found to differ from those with low NFC sounds very much like the list one would create if people were sorted on any measure of cognitive ability. Namely, those with higher NFC were found to do better on arithmetic problems, anagrams, trivia tests, and college coursework, to be more knowledgeable, more influenced by the quality of an argument, to recall more of the information to which they are exposed, to generate more “task relevant thoughts” and to engage in greater “information-processing activity.”

The empirical and conceptual overlap between these tests suggests that they would all predict time and risk preferences. . . .
In his concluding discussion, Frederick jumps to the unwarranted implication that the "best and brightest" should make decisions for the rest of us; viz.:
[T]ime and risk preferences are sometime tied so strongly to measures of cognitive ability that they effectively function as such a measure themselves. For example, when a choice between a sure $500 and a 15% chance of $1,000,000 was presented to respondents (along with an eight item version of the CRT), only 25% of those who missed all eight problems chose the gamble, compared to 82% among those who solved them all. Should this result be interpreted to mean that choosing the gamble is the “correct” response for this item? . . .

. . . I suspect that if respondents were shown the respective test scores of those who chose the sure $500 vs. those who chose the 15% chance of $1,000,000, they would, in fact, feel more disposed to take the gamble; the correlation between cognitive ability and preference would hold some normative force for them. . . .

[A] relation between cognitive ability and preference does not, by itself, establish the correct choice for any particular individual. Two individuals with different cognitive abilities may experience outcomes differently, which may warrant different choices (for example, what magazines to read or movies to attend). But with respect to the example motivating this discussion, one must ask whether it is really plausible that people of differing cognitive abilities experience increments of wealth as differently as their choices suggest. It seems exceedingly unlikely that the low CRT group has a marked kink in their utility function around $W+500, beyond which an extra $999,500 confers little additional benefit. It seems more reasonable, instead, to override the conventional caveat about arguing with tastes . . . , and conclude that choosing the $500 is the “wrong answer” – much as 10 cents is the wrong answer in the “bat & ball” problem.

Whatever stance one adopts on the contentious normative issues of whether a preference can be “wrong” and whether more reflective people make “better” choices, respondents who score differently on the CRT make different choices, and this demands some explanation
Frederick, in effect, makes the following argument:
  • Bright people are good at getting right answers to questions for which there are right answers.
  • Bright people are good at evaluating prudent risks.
  • Bright people, therefore, are likely to be correct in all forms of risk-taking.
  • Thus all of us would do well to follow the instruction of bright people.
Frederick's logic fails, first, because he blurs the distinction between (a) the kind of prudent risk-taking that's involved in short-term financial transactions with fairly certain outcomes (which bright persons do well) and (b) straight-out gambling (for which bright persons seem to have a penchant). He compounds his confusion by treating gambling as a mere mathematical problem to which there is a right answer:
[C]hoosing the $500 is the "wrong answer" – much as 10 cents is the wrong answer in the "bat & ball" problem.
But getting the right answer to the "bat & ball" problem is trivial; it's a closed problem to which there can be only one right answer. Frederick seems to think that getting the "right" answer to the betting problem depends only on being able to calculate the "expected value" of the prize (value of the prize x probability of winning it). Well, when the expected value is $150,000 and one stands to lose "only" $500, it would be stupid to take the $500 instead gambling on the million. Right? Wrong:
  • Expected value is an artificial construct; one cannot win the expected value of anything.
  • If there's a 15% chance of winning the million, there's an 85% chance of not winning the million.
  • A person to whom $500 is a lot of money (a month's rent, for example) is stupid to gamble it with an 85% chance of losing it.
By Frederick's logic, bright jerks should be put in the position of gambling away other people's rent money. Or, to put it more generally, our affairs should be placed in the hands of the "best and brightest" -- empowered by government to regulate our lives. (Frederick doesn't come right out and say that, of course, but the subtext is clear.)

Actually, since the New Deal, successive Congresses, presidents, and Supreme Courts have been regulating our lives with the help of the "best and brightest" (a.k.a. the "brains trust"). And see where it has landed us.

In sum, Frederick's paper amounts to nothing more than a contrived justification of statist paternalism.

Related posts:

Fear of the Free Market -- Part I
Fear of the Free Market -- Part II
Fear of the Free Market -- Part III
The Rationality Fallacy
Socialist Calculation and the Turing Test
The Social Welfare Function
Libertarian Paternalism
A Libertarian Paternalist's Dream World
The Short Answer to Libertarian Paternalism
Second-Guessing, Paternalism, Parentalism, and Choice
Another Thought about Libertarian Paternalism
"The Private Sector Isn't Perfect"
Three Truths for Central Planners
Risk and Regulation