C Different Meanings of Rationality; Different Solutions to Problems

At this point we have two conflicting accounts of heuristics and biases: the fast-and-frugal program of the Gigerenzer school and the Prospect Theory of Kahneman and Tversky. How do their competing worldviews affect our under­standing of hypothesis-based scientific thinking and practice?

Most of us readily concede that we're not fully economically rational and, considering the personality traits of purely rational economic agents, we're glad that we're not.

Gigerenzer argues that the pragmatic, achievable standard of ecological ration­ality is the appropriate benchmark for human behavior; ecological rationality is what works, what produces beneficial results in the real world. Its effective­ness follows from its evolutionary origins. Ecologically rational heuristics have worked for millions of years, and, when viewed in this light, they makes perfect sense even when they are at odds with the textbook standard. Ecological ration­ality is close to what in everyday terms would be considered “reasonable” and is not necessarily rigorously “logical.”

I’m going to argue that scientists should have a clear idea of when to apply which standard ofrationality, especially when it comes to the topics ofhypothesis- based thinking and biases. This is a focal point of the discussion, and, to try to avoid any ambiguity I’ll review a few classic cognitive problems in the next sec­tion and compare how the two schools approach them.

12. C.1 The Linda Problem

You remember that we had a description of Linda, 31, single, outspoken, very bright, a college philosophy major deeply concerned with issues of discrimina­tion and social justice who participated in anti-nuclear demonstrations. We were asked whether it was more probable (or “more likely”) that Linda was (A) a bank teller or (B) a bank teller who was active in the feminist movement. Most people choose (B).

As Kahneman and Tversky point out that, logically, this answer is incorrect. The reason is that all feminist bank tellers are, first and foremost, bank tellers. It must be the case that Linda, or any random person, is mathematically more likely to be a bank teller—period—than a bank teller with any kind of qualifying pro­perty. Think of a Venn diagram with two overlapping circles: one labeled “bank tellers” and one labeled “feminists.” Each circle indicates the probability of being either a bank teller or a feminist.

The area where the circles overlap represents “feminist bank tellers,” and it must be smaller than either of the two main circles.¹⁸ In other words, the proba­bility of being a feminist bank teller must be smaller than being just a bank teller or just a feminist. Indeed, if you think about the large number of female bank tellers in the United States¹⁹ and the complexity of human nature, you'll prob­ably agree that there must be some bank tellers with all of Linda's characteris­tics except for being feminists, and furthermore, that the total group of bank tellers also includes males. By the rules of probability logic, the answer favored by Prospect Theory has to be right and, as a corollary, selecting answer (B) has to be irrational.

Gigerenzer says the Prospect Theory argument is irrelevant. When it comes to real people's reasoning in this case, the conventional logical rules don't apply.

In addition, as pointed out by the philosopher H. P. Grice, there are conver­sational rules that govern our interpersonal communications.²⁰ For instance, we assume that people are giving us relevant and important information when they communicate with us (and we occasionally get annoyed—“What's your point?”—when they don't seem to be). In fact, we are adept at picking up the unspoken message (implicature) of what we hear (e.g., we know that the ques­tion “Do you really want to go?” sometimes means, “I really don't want to go”). Gigerenzer and colleagues don't accept the interpretation that we fall for cogni­tive illusions; rather, the semantic content of a statement puts us into a social di­mension where perceptive discourse requires sensitivity to underlying intentions along with (or instead of) robotic transmission of data. We are not incapable of being strictly logical; it is just that when obvious word meanings and their con­text command our attention, then we go with them. Most subjects who are given the Linda Problem do not see it as a puzzle for their abstract reasoning abilities; they understand it as a request for their best guess about Linda's character.

Furthermore, the meanings of words are rarely as clear-cut as they'd have to be to support a valid critique of subjects' solutions to the Linda Problem as being logically deficient. In contrast to the crisp denotation of “more probable” that Kahneman and Tversky took for granted, many investigators point out the plethora of synonyms for “probable” that you’ll find in the Oxford English Dictionary, which include the more flexible “to be expected, anticipated, foresee­able, potential, credible, quite possible” and informal “a good bet, a reasonable bet.” Once again, someone working from an imprecise definition could answer the Linda Problem and be both socially rational and inconsistent with the rules of probability logic. Hertwig and Gigerenzer²¹ blame the wording of the Linda Problem for the troubles that people have with it and demonstrate that if you rewrite the problem in a way that encourages subjects to see it as a test of logic then “erroneous,” socially sensitive answers decrease significantly (though not all researchers find as much support for this “linguistic ambiguity hypothesis”²²). Evidence like this confirms that people can be analytical when they understand that the context calls for it. This isn’t what you’d expect based on Prospect Theory’s pessimistic view that people are either rational or, more often, irrational; that our ability to reason abstractly doesn’t hinge on the specific words used. This raises the question: Do words matter as much in the overtly quantitative realm, or are we simply hopeless when it comes to numbers?

12. C.2 Probability Versus Frequency

Consider this problem: you know that 10% of the people in a particular town always lie and that 80% of the liars have a red nose; 10% of the people who don’t lie also have a red nose.

Now, recast the problem like this: eliminate the intimidating and multifaceted word “probability” and replace it with the evolutionarily friendly and numeri­cally evocative concept of “frequency.” You get something like this: in a certain town, 10 out of every 100 people that you meet always lie, and 8 of the 10 people who always lie have red noses. Of the 90 people who don’t lie, 9 also have red noses. Now the question: If you meet a group of people with red noses, how many will be liars? Right away you can see that a total of 8 + 9 = 17 of every 100 people have red noses. Therefore, if you meet a group of red-nosed people, you can ex­pect that 8 out of every 17 of them will be liars. In these terms, with actual num­bers rather than probabilities, many children and most adults (~76%) get the solution.

Kahneman believes that many of us flail around when confronted with a mys­tery such as the red nose problem because we suffer from an intellectual malady called base-rate neglect. Essentially, we don't know how to incorporate the crucial information about the prevalence of red noses in the town population as a whole into our calculation, and so we pay no attention to it. In contrast, Gigerenzer believes that the real barrier to success is the problem's abstract terms; we need the context of the natural frequencies that we normally deal with. Natural fre­quencies, countable things, exist in the world, “probabilities” do not. Hence, the form in which the problem was presented was at fault, not the subjects' minds. Whereas Kahneman tends to be fatalistic when contemplating our in­herent intellectual limitations, Gigerenzer is quite optimistic about the potential for improving our performance through education and policy changes in how information is presented to us.

12. C.3 The Wason Selection Task

The notorious Wason Selection Task, invented by psychologist Peter Wason,²³ highlights another distinction between logical and ecological rationality. In this task there are four cards in front of you, marked D, F, 3, and 7, you're told that each card has a number on one side and a letter on the other. You're supposed to test the “hypothesis” that “all cards with D on one side have 3 on the reverse side.” The question is: What cards must you turn over to test the hypothesis? If you've never seen this one, try it before going on.

Ready? The minimal correct answer is that you must turn over the D and 7 cards.²⁴ How'd you do? The great majority of test takers (~75%) don't get it right. The reasoning goes like this: obviously, you have to turn over the D card, but turning over the 3 is pointless; the instructions we're given don't state that only D's are associated with 3's, so you learn nothing if the 3 card doesn't have a D on the back. And even if there is a D on the back, the proposed hypothesis could still be false. The acid test is the 7 card; if it has a D on the other side, the hypothesis is toast, yet if there is a different letter on the other side, then you have no reason to reject it. Again, Kahneman's conclusion is that people who don't do well on the task are irrational.

This is all well and good, but Gigerenzer and colleagues point out that if you change the labels on the cards, you can get a problem that is formally identical to the original but that almost everybody gets right. For example, imagine that the cocktail lounge that you own is going to lose its liquor license if anyone un­derage is caught drinking alcohol in it, and you resolve to check the customers carefully. You go to a booth where there are four customers with cards in front of them, and one side of each card identifies the beverage the customer is drinking while the other side lists his or her age. The cards are marked: Beer, Coke, 25, and 16. Which ones must you turn over to find out whether or not you’re in trouble?

Probably, like most (~75%) subjects, you got this one right—you flipped over the cards marked Beer and 16. What happened? The problem has gone from being from an abstract, mechanical reasoning puzzle to one that is mean­ingful to human social circumstance. It’s obvious that you don’t care about how old the Coke-drinker is or what the 25-year-old is having. The evolutionary psychologists Leda Cosmides and John Tooby²⁵ see the improved performance on this form of the Selection Task as evidence of a built-in “cheating detector” that humans have evolved to ensure that members of a society obey its rules. Although not all psychologists are comfortable with that interpretation²⁶ many do agree that how you perform on the Wason Selection task depends on whether it is presented in terms that you care about; basically, its ecological rationality. Since our thinking abilities are adapted to our ancient ancestors’ needs, it appears that instilling the ability to solve abstract, content-free problems was not high up on evolution’s to-do list.

12. C.4 Framing Effects or Efficient Choosing

Imagine the following, admittedly pretty unrealistic, scenarios:

Scenario 1: You’re given $1,000 by a well-funded (!) researcher; now choose between:

A. getting an additional $500 for sure.

B. taking a 50% chance to win an additional $1,000, otherwise getting nothing more.

Scenario 2: You’re given $2,000 by the same well-funded researcher; now choose between:

C. losing $500 for sure.

D. taking a 50% chance to lose $1,000, otherwise losing nothing at all.

In Scenario 1 most of us choose the sure thing, choice A, get $500 for sure, and, in Scenario 2, the gamble, choice D, a 50% chance of losing $1,000.

The punch-line is that our choice pattern violates the rules of Expected Utility Theory, which only looks at the overall value (utility) of what we have. In con­trast, we humans pay attention to the way in which the choices are expressed; that is, how they are framed by the wording. Choices A and Care sure things; they guarantee that we'll walk away with $1500. Choices B and D are risky bets; they both offer the chance of having either $1,000 or $2,000 at the end. If we were logically consistent, we'd pick either choices A and C, or B and D, but most of us mix things up. Our behavior conforms to a general rule, however: we are risk-averse when outcomes are framed as potential gains, as in Scenario 1; that is, we play it safe when we stand to gain and prefer the guaranteed money over the chance of having more money (“a bird in the hand... ”). When outcomes are framed as potential losses, as in Scenario 2, we become risk-seeking; we prefer to risk losing even more money rather than to voluntarily give up a smaller amount. This pattern of choices counts as irrational behavior in the world of Prospect Theory.

The fast- and-frugal heuristics program accounts for the pattern of choices that most of us made in Scenarios 1 and 2 in terms of adaptive strategies—quantified as mathematical process models—that predict when people will choose to stand pat and when they will take a chance. The fast-and-frugal advocates think it is absurd to imagine that we ordinarily go through an involved, Utility Theory- compliant, quantitative calculation when facing such choices. Instead, we can use a priority heuristic²⁷ that makes a few simple comparisons to judge the rel­ative benefits of a choice. We needn't go into the details here, but, in brief, the scheme starts with a priority rule that looks at the minimum possible gain of each alternative, the chance of minimum gain, and the maximum possible gain, and incorporates a stopping rule that says when to quit and decide. The heuristic adheres to the principle of satisficing (aiming for an outcome that is good enough without trying to maximize returns). The net result is that, using the priority heuristic, you can, in principle, reproduce the apparently anomalous pattern— risk-avoiding for gains, risk-seeking for losses—in a plausible way that does not imply that you're behaving irrationally.

Which account of human behavior—P rospect Theory or the priority heuristic—is the right one? Although a definitive answer is not available, in head- to-head comparisons where computer programs representing the two theories compete to see which one can best predict or postdict some forms of human choice behavior, the priority heuristic often comes out on top. Still, knowing that a heuristic process could account for behavior is not the same as saying that people do rely on it when making choices.

It is worth noting that Prospect Theory and fast-and-frugal heuristics have en­tirely distinct perspectives on the role of emotion in shaping decisions. Prospect Theory sees emotions as a dominant force in driving irrational behavior. Indeed, “emotional” and “rational” are often used as antonyms in descriptions of people's behavior. While the fast-and-frugal school doesn't deny that we have emotions, it does downplay their significance. Members of this school want to know not so much what moves us to act, but what we do and why we do it, and their answer is that we act for adaptively sound reasons. Gigerenzer believes that the concept of emotion is patched into Prospect 'lheory and its successors as a sort of fudge factor to make up for the shortcomings in the classical economic Utility Theory. '1 hal is, since Prospect 'lheory is predicated on the same standard of rationality that underpins Expected Utility 'lheory, factoring in emotion is just a kludgy way to “repair” the classical theory.²⁸

12. C.5 Are Scientists Naturally Rational?

Do scientists, perhaps because of their nature or training, think differently, more logically than nonscientists? Maybe the insights regarding cognitive quirks simply don't apply to scientists? Data from two independent sources suggest otherwise. In one experiment, I gave 100 neuroscience students, postdocs, and faculty a modified version of a task that has been used to assess the effects of hidden influences on our thinking.²⁹ One group, roughly 50% of the subjects, randomly selected, received one form of a question and the rest of the subjects, another form. The process was anonymous, and I didn't know who answered, let alone how they answered. 'lhe task was a test of an occult “priming effect” in which simply seeing a completely meaningless number can influence people's responses to other. The first question was:

“Are there more than (x number) of windows in the US Presidential White House?” where “x” was “242” for one group and “56” for the other. 'lhe subjects checked “yes” or “no.”

The second question was identical for both groups:

“How many windows do you think there are in the US Presidential White House? Write your best guess here.” Eighty-one answers came in.

'lhe first question was a decoy—its purpose was to place two different num­bers before the subjects. Prospect 'lheory predicts that although the numbers in the first question were incorrect (the real number is 147) and entirely irrelevant to the second question, they would “prime” the guess in the second part. That is, people's answers to the second question would be influenced by the number that they saw in the first question. Indeed, the group that saw 56 guessed 115 ± 23 (n = 39) while the group that saw 242 guessed, 243 ± 21 (n = 42).

If the number in the first question did not affect the subjects, you'd expect that their answers to the second question would be random and indistinguish­able between the groups; as it was, their answers diverged significantly and systematically in the direction predicted by the theory. If you saw a low number in question one, you guessed a relatively low number for question two, and vice versa. The “anchoring index” (difference in group means/difference in group “anchors”) was (243 - 115)/(242 - 56) = 69%, typical for this kind of question.³⁰ It appears that these highly educated, presumably analytical thinkers were every bit as susceptible to this subtle cognitive influence as everybody else.

In an independent study, neuroscientist Raymond Dingledine posed four questions derived from Kahneman and Tversky's work to members of basic sci­ence departments at Emory University School of Medicine³¹ to test the hypo­thesis “that a scientifically literate population would respond more objectively to the survey questions originally posed in the 1960s and 1970s” (i.e., by Kahneman and Tversky). Dingledine's conclusion was succinct: “[The hypothesis] was wrong.” That is, modern biomedical scientists were no more objective in an­swering the questions than were the college students tested 50 years ago. In par­ticular, Dingledine identified believing in “the law of small numbers,” “intuitive pattern seeking,” and ignoring the “base rate” as cognitive errors that affected the scientists he tested.

Kahneman argues that the priming and anchoring effects show that we have a not always rational urge to attain “associative coherence” in our thinking. This is not the only possible explanation for these effects, and an alternative favors the ecological psychology interpretation: the anchoring-type problems are artifi­cial and nonrepresentative traps that we fall into because we normally and legiti­mately anticipate that people who ask us questions are not out to trick us. If they tell us some number, we expect it to be relevant. Under this interpretation, the priming and anchoring effects would have their own adaptive rationale.

The debate about how to interpret thinking that does not conform to the strict rules of logic goes on, but however you look at the debate, it seems that the hy­pothesis that scientists are inherently more rational (when rationality is defined by abstract systems of logic and Expected Utility Theory) than nonscientists has been falsified.

12.