WHY GOOD INTUITIONS SHOULDN’T BE LOGICAL - UNCONSCIOUS INTELLIGENCE - Gut Feelings: The Intelligence of the Unconscious - Gerd Gigerenzer

Gut Feelings: The Intelligence of the Unconscious - Gerd Gigerenzer (2007)


We live in a dappled world, a world rich in different things, with different natures, behaving in different ways. The laws that describe this world are a patchwork, not a pyramid. They do not take after the simple, elegant and abstract structure of a system of axioms and theorems.

—Nancy Cartwright1


Imagine you are asked to participate in a psychological experiment. The experimenter gives you the following problem:

Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy. As a student she was deeply concerned with issues of discrimination and social justice and participated in antinuclear demonstrations.

Which of the following two alternatives is more probable?

Linda is a bank teller

Linda is a bank teller and active in the feminist movement

Which one did you choose? If your intuitions work like those of most people, you picked the second alternative. Amos Tversky and Nobel laureate Daniel Kahneman, however, argued that this is the false answer, because it violates logic. A conjunction of two events (Linda is a bank teller and active in the feminist movement) cannot be more probable than only one of them (Linda is a bank teller). In other words, a subset can never be larger than the set itself. “Like it or not, A cannot be less probable than (A&B), and a belief to the contrary is fallacious.”2 They labeled the intuition shared by most people the conjunction fallacy. The Linda problem has been used to argue that human beings are fundamentally illogical and has been invoked to explain various economic and human disasters, including U.S. security policy, John Q. Public’s fear of nuclear reactor failures, and his imprudent spending on insurance. The evolutionary biologist Stephen Jay Gould wrote,

I am particularly fond of [the Linda] example, because I know that the [conjunction] is least probable, yet a little homunculus in my head continues to jump up and down, shouting at me— “but she can’t just be a bank teller: read the description.”…Why do we consistently make this simple logical error? Tversky and Kahneman argue, correctly I think, that our minds are not built (for whatever reason) to work by the rules of probability.3

Gould should have trusted the gut feeling of his homunculus, rather than his conscious reflections. Academics who agree with the conjunction fallacy believe that mathematical logic is the basis for determining whether judgments are rational or irrational. In the Linda problem, all that counts for the logical definition of rational reasoning are the English terms and and probable, which are assumed to have only one correct meaning: the logical AND (that we use, for example, in search machines) and mathematical probability (a comparison of the number of favorable outcomes to the number of possible outcomes). I call such logical norms content-blind because they ignore the content and the goals of thinking. Rigid logical norms overlook that intelligence has to operate in an uncertain world, not in the artificial certainty of a logical system, and needs to go beyond the information given. One major source of uncertainty in the Linda problem is the meaning of the terms probable and and. Each of these terms has several meanings, as any good English dictionary or its equivalent in other languages will reveal. Consider the meanings of probable. A few, such as “what happens frequently,” correspond to mathematical probability, but most do not, including “what is plausible,” “what is believable,” and “whether there is evidence.” As we have seen in chapter 3, perception solves this problem of ambiguity by using intelligent rules of thumb, and, I argue, so does higher-order cognition. One of these unconscious rules that our minds appear to use to understand the meaning of language is the conversational maxim of relevance.4

Assume that the speaker follows the principle “Be relevant.”

The unconscious inference is thus: if the experimenter reads to me the description of Linda, it is most likely relevant for what he expects me to do. Yet the description would be totally irrelevant if one understood the term probable as mathematical probability. Therefore, the relevance rule suggests that probable must mean something that makes the description relevant, such as whether it is plausible. Read the description—Gould’s homunculus understood this point.

Is most people’s answer to the Linda problem based on a reasoning fallacy or on an intelligent conversational intuition? To decide between these alternatives, Ralph Hertwig and I asked people to paraphrase the Linda task for a person who is not a native speaker and does not know the meaning of probable. Most people used nonmathematical meanings such as whether it is possible, conceivable, plausible, reasonable, and typical. Only very few used “frequent” or other mathematical meanings. This suggests that conversational intuition rather than logical error is at issue, specifically the ability to infer the meaning of ambiguous statements by means of conversational rules. As a further test of this hypothesis, we changed the ambiguous phrase probable into a clear how many?

There are a hundred persons who fit the description above(i.e., Linda’s). How many of them are

bank tellers?

bank tellers and active in the feminist movement?

If people don’t understand that a set cannot be smaller than a subset, and consistently make this logical blunder, then this new version should produce the same results as the old one. If on the other hand, there is no blunder but people make intelligent unconscious inferences about what meanings of probable make the description of Linda relevant, these meanings are now excluded and the so-called fallacy should largely disappear. And this indeed is what happened (Figure 6-1).5 The result is consistent with earlier research by the Swiss psychologists Bärbel Inhelder and Jean Piaget, who performed similar experiments with children (“Are there more flowers or more primulas?”) and reported that by the age of eight, a majority gave responses consistent with class inclusion. Note that children were asked how many, not how probable. It would be very strange if later in life adults could no longer understand what eight-year-olds can. Logic is not a sensible norm for understanding the question “Which alternative is more probable?” in the Linda problem. Human intuition is much richer and can make reasonable guesses under uncertainty.

The Linda problem—and the hundreds of studies it has generated to find out what conditions make people reason more or less logically—illustrates how the fascination with logic leads researchers to pose the wrong questions and miss the interesting, psychological ones. The question is not whether people’s intuitions follow the laws of logic, but rather, what unconscious rules of thumb underlie intuitions about meaning. Let us take a closer look at natural language comprehension.


Figure 6-1: Is Linda a bank teller?

Peggy and Paul

In first-order logic, the particle AND is commutative, that is, a AND b is equivalent to b AND a. Yet again, this is not how we understand natural language. For instance, consider the following two sentences:

Peggy and Paul married and Peggy became pregnant.

Peggy became pregnant and Peggy and Paul married.

We know intuitively that the two sentences convey different messages. The first suggests that pregnancy followed marriage, whereas the second implies that pregnancy came first and was possibly the reason for marriage. If our intuition worked logically and treated the English term and as the logical AND, we wouldn’t notice the difference. And can refer to a chronological or causal relation, neither of which is commutative. Here are two more pairs:

Mark got angry and Mary left.

Mary left and Mark got angry.

Verona is in Italy and Valencia is in Spain.

Valencia is in Spain and Verona is in Italy.

We understand in a blink that the first pair of sentences conveys opposite causal messages, whereas the second pair is identical in meaning. Only in the last pair is the and used in the sense of the logical AND. Even more surprising, we also know without thinking when and should be interpreted as the logical OR, as in the sentence

We invited friends and colleagues.

This sentence refers to the joint set of friends and colleagues, not to their intersection. Not everyone is both a friend and a colleague; many are either or. Once again, intuitive understanding violates the conjunction rule, but this is not an error of judgment. Rather it is an indication that natural language is more sophisticated than logic.

How do our minds infer at one glance what and means in each context? These inferences have the three characteristics of intuitions: I know the meaning, I act on it, but I do not know how I know it. Since a single sentence is sufficient as context, the clues must come from the content of the sentence. To this day, linguists are still working on spelling out the rules of thumb that underlie this remarkably intelligent intuition. No computer program can decode the meaning of an and sentence as well as we can. These are the interesting unconscious processes that we only partly understand, but which our intuition masters in the blink of an eye.


Framing is defined as the expression of logically equivalent information (whether numerical or verbal) in different ways. For example, your mother has to decide whether she will have a difficult operation and is struggling with the decision. Her physician says that she has a 10 percent chance of dying from the operation. That same day another patient asks about the same operation. He is told that he has a 90 percent chance of surviving.

Logic does not make a difference between either of these statements, and consequently, logically minded psychologists have argued that human intuition should be indifferent, too. They claim that one should ignore whether one’s doctor describes the outcome of a possible operation as a 90 percent chance of survival (a positive frame) or a 10 percent chance of dying (a negative frame). But patients pay attention and try to read between the lines. By using a positive frame, the doctor might signal to the patient that the operation is the best choice. In fact, patients accept the treatment more often if doctors choose a positive frame.6 Kahneman and Tversky, however, interpret attention to framing to mean that people are incapable of retranslating the two versions of the doctors’ answer into a common abstract form and are convinced that “in their stubborn appeal, framing effects resemble perceptual illusions more than computational errors.”7

I disagree. Framing can communicate information that is overlooked by mere logic. Consider the most famous of all framing examples:

The glass is half full.

The glass is half empty.

According to the logical norm, people’s choices should not be affected by the two formulations. Is the description in fact irrelevant? In an experiment, a full glass of water and an empty glass are put on a table.8The experimenter asks the participant to pour half of the water into the other glass, and to place the half-empty glass at the edge of the table. Which one does the participant pick? Most people chose the previously full glass. When other participants were asked to move the half-full glass, most of them chose the previously empty one. This experiment reveals that the framing of a request helps people extract surplus information concerning the dynamics or history of the situation and helps them to guess what it means. Once again, intuition is richer than logic. Of course, one can mislead people by framing a choice accordingly. But that possibility does not mean that attending to framing is irrational. Any communication tool, from language to percentages, can be exploited.

The potential of framing is now being recognized in many disciplines. The renowned physicist Richard Feynman emphasized the importance of deriving different formulations for the same physical law, even if they are mathematically equivalent. “Psychologically they are different because they are completely unequivalent when you are trying to guess new laws.”9 Playing with different representations of the same information helped Feynman to make new discoveries, and his famous diagrams embody the emphasis he placed on presentation. Yet psychologists themselves are in danger of discarding psychology for mere logic.


Reinhard Selten is a Nobel laureate in economics who made the “chain store problem” famous by proving that an aggressive policy against competitors is futile. Here is the problem:

A chain store called Paradise has branches in twenty cities. A competitor, Nirvana, plans to open a similar chain of stores and decide one by one whether or not to enter the market in each of these cities. Whenever a local challenger enters the market, Paradise can respond either with aggressive predatory pricing, which causes both sides to lose money, or with cooperative pricing, which will result in sharing profits 50-50 with the challenger. How should Paradise react when the first Nirvana store enters the market? Aggression or cooperation?

One might think that Paradise should react aggressively to early challengers, in order to deter others from entering the market. Yet using a logical argument, Selten proved that the best answer is cooperation. His argument is known as backward induction, because one argues backward from the end to the beginning. When the twentieth challenger enters the market, there is no reason for aggression, because there is no future competitor to deter and so no reason to sacrifice money. Given that the chain store will decide to be cooperative to the last competitor, there is no reason to be aggressive to the nineteenth competitor either, because everyone knows that the final challenger cannot be deterred. Thus, it is rational for Paradise to cooperate with the next-to-last challenger, too. The same argument applies to the eighteenth challenger, and so on, back to the first. Selten’s proof by backward induction implies that the chain store should always respond cooperatively, in every city, from the first to the last challenger.

But that is not the end of the story. Seeing his result, Selten found his logically correct proof intuitively unconvincing and indicated that he would rather follow his gut feeling to be aggressive in order to deter others from entering the market.

I would be very surprised if it failed to work. From my discussion with friends and colleagues, I get the impression that most people share this inclination. In fact, up to now I met nobody who said that he would behave according to [backward] induction theory. My experience suggests that mathematically trained persons recognize the logical validity of the induction argument, but they refuse to accept it as a guide to practical behavior.10

Those who don’t know Reinhard Selten might suspect that he is an overly aggressive person whose impulses overwhelm his thinking, but he is not. The clash between Selten’s logic and his intuitions have nothing to do with a preference for aggressive action. As we have seen repeatedly, logical arguments may conflict with intuition. And as we have also seen, intuition is often the better guide in the real world.


Artificial intelligence (AI) has spent some of its history building disembodied intelligences that carry out abstract activities, such as chess playing, where the only interaction with the world is by means of a screen or printer. This suggests that the nature of thinking is logical, not psychological. Logic is the ideal of a disembodied system, the proper yardstick for deductive arguments that concern the truth of propositions, such as in a mathematical proof. Few logicians, however, would argue that logic provides the yardstick for all kinds of thinking. Similarly, a century ago Wilhelm Wundt, who has been called the father of experimental psychology, pointed out the difference between the laws of logic and the process of thinking.11

At first it was thought that the surest way would be to take as a foundation for the psychological analysis of the thought-processes the laws of logical thinking, as they had been laid down from the time of Aristotle by the science of logic. These norms only apply to a small part of the thought-processes. Any attempt to explain, out of these norms, thought in the psychological sense of the word can only lead to an entanglement of the real facts in a net of logical reflections. We can in fact say of such attempts, that measured by the results they have been absolutely fruitless. They have disregarded the psychological processes themselves.

I could not agree more with Wundt. Nevertheless, as we have seen, many psychologists have treated forms of logic as a universal calculus of cognition, and many economists use it as a universal calculus of rational action. The work of Piaget, for instance, is concerned with the growth of all knowledge, from the intellectual growth of one child to human intellectual history. For him, the development of cognition was fundamentally the development of logical structures, from prelogical thought to abstract formal reasoning.12 The ideal of logic is so embedded in our culture that even those who criticize Piaget’s claim as empirically wrong often maintain it as the universal standard of good reasoning. Those who violate that standard are diagnosed as having cognitive illusions, such as the conjunction fallacy.

Generations of students in the social sciences have been exposed to entertaining lectures that point out how dumb everyone else is, constantly wandering off the path of logic and getting lost in the fog of intuition. Yet logical norms are blind to content and culture, ignoring evolved capacities and environmental structure. Often what looks like a reasoning error from a purely logical perspective turns out to be a highly intelligent social judgment in the real world. Good intuitions must go beyond the information given, and therefore, beyond logic.