Gut Feelings: The Intelligence of the Unconscious - Gerd Gigerenzer (2007)
Part 2. GUT FEELINGS IN ACTION
A man can be short and dumpy and getting bald but if he has fire, women will like him.
8. ONE GOOD REASON IS ENOUGH
Who would ever base an important decision on only one reason? If anything unites the various tribes of rationality, it is the dictum that one should search for all relevant information, weigh it, and add it up to reach a final judgment. Yet, defying the official guidelines, people often base their intuitive judgments on what I call one-reason decision making.1 Keenly aware of this tendency, so do many advertising campaigns. What did McDonald’s do when Burger King and Wendy’s began to rival its top-ranked name recognition? It launched a campaign that provided the one reason to choose McDonald’s: “It’s an easy way to feel like a good parent.” As an internal memo explained the underlying psychology, parents want their kids to love them, and taking their children to McDonald’s seems to accomplish this, making them feel like good parents.2 Wouldn’t a few more reasons make a more convincing case? There is a proverb that a man with too many good excuses shouldn’t be trusted.
In this chapter, I will deal with intuitive judgments that are based on recall memory. Recall goes beyond mere recognition; it retrieves episodes, facts, or reasons from memory. I use the term reasons to refer to cues or signals that help make decisions. Let’s first take a look at how evolution creates minds and social environments in which the use of one good reason spreads.
In most species of birds of paradise, the colorful males display, and the plain females choose. The males assemble in leks, that is, communal areas in which several of them stand in line or in groups and perform courtship displays, while the females stroll from candidate to candidate, scrutinizing them. How do the females decide on a mate? Most seem to rely on one reason only:
Look over a sample of males, and go for the one with the longest tail.
Choosing a mate for only one reason may sound peculiar, but there are two theories to explain the practice.3 The first is Darwin’s theory of sexual selection elaborated by the statistician Sir Ronald A. Fisher. Females may have originally had a preference for a slightly longer tail because it allowed the male to fly and so get around better. If there is some genetic contribution to the natural variation in tail length, then a runaway process toward longer tails can be set in motion. Every female that deviated from the rule and chose a small-tailed male would be penalized, because if she did not produce long-tailed sons, her sons would have a smaller chance of being regarded as attractive and being able to reproduce. Tails accordingly grew longer over generations and eventually became widely accepted as attractive by females. Thus, the process of sexual selection can produce one-reason decision making in the minds of animals and an environment of long tails, bright colors, and other extravagant secondary sexual characteristics.
Darwin considered two mechanisms underlying dazzling male features. The first was male-male competition, which had led to developments such as deer antlers and antelope horns. But battles between males could not account for the train of the peacock, so Darwin proposed a second mechanism, the power of female choice. He believed that females have a sense of beauty and are excited by the extravagant ornaments displayed by males. Darwin’s theory of sexual selection was almost completely ignored for nearly a hundred years.4 His male contemporaries could not be convinced by the idea that birds or deer would have a sense of beauty, and even less, that female taste could influence the evolution of male bodily features. Men close to Darwin, such as Thomas Henry Huxley, known as Darwin’s bulldog, tried to persuade him to abandon the theory of sexual selection.5 Today, this theory is a vigorously pursued branch of biology, and one might speculate whether its acceptance has been facilitated by the rising public role of women in Western societies. Yet we are only beginning to understand the connection between sexual selection and one-reason decision making. Just as the theory of sexual selection was rejected for a long time in biology, so the theory that one good reason is a viable strategy is still controversial in decision theory. But there is hope, as science itself is evolving.
The second theory that accounts for the tail of the bird of paradise and similar features is Amotz Zahavi’s handicap principle. Whereas in the runaway theory of sexual selection the male may or may not be of good quality (and once the tail size escalates, the female is no longer choosing on grounds of quality), according to the handicap principle, he actually is of good quality. Birds of paradise’s tails, just like those of peacocks, evolved precisely because they are handicaps. A male bird shows off his tail because it advertises that he can survive in spite of it. In this theory, the one good reason—the big handicap—is truly a good one. In the runaway selection theory, the one good reason is a deceptive one, an initially good reason that grew out of control. Despite their differences in interpretation, both theories explain how one-reason decision making can spread.
The handicap principle was also rejected outright by the scientific community. Not until 1990 did this verdict change.6 Around that time, experiments with peacocks (who also assemble in leks, where they display their ornamented trains to visiting females) indicated that peahens also base their choice on one reason. The only factor correlated with mating success was the number of eyespots a male had on his feathers. But this correlation could be due to other factors; strong males might have more eyespots. If males were left the same in every other way but had fewer eyespots, would the females no longer choose them? In an ingenious experiment, British researchers cut away 20 of around 150 eyespots from half of the males under study, and handled the other half in the same stressful way without actually removing the spots. They reported a sharp decline in the mating success of those with a reduced number of eyespots compared to that of the previous season and to those who still had their full number of spots. Moreover, the researchers did not observe a single peahen that mated with the first male that courted her; rather, peahens sampled on average three males before they chose. In almost all cases, the peahen chose the male with the highest number of eyespots in her sample.7 It is likely that the peahen’s one good reason is genetically coded.
Thus, both sexual selection and the handicap principle can produce one-reason decisions in both minds and their environments. The simultaneous evolution of genes (coding decision rules) and environment is called coevolution. We might find the minimalism of the bird of paradise’s mate choice amusing. However, it seems to have worked for millennia, and in fact, seems to exist in humans. The one good reason is often social, such as when a woman desires a man and primarily falls in love with him because he is desired by other women. This one reason virtually guarantees that a woman’s peer group will accept and admire the choice she has made.
The eyespots on a peacock’s tail are a powerful cue for the peahen. In general, environments are populated by more or less irresistible cues that control animal, including human, behavior. As already mentioned, some cuckoos leave their eggs in the nests of other birds, which hatch and feed the cuckoo chicks. In one species, a single irresistible cue, a patch on the cuckoo chick’s wing that flutters and simulates the gaping mouths of many hungry chicks, fools the foster parents into feeding them. The behavior of the host birds is sometimes cited as evidence that they cannot discriminate between the cuckoo chicks and their own because of cognitive limitations. But a little girl cuddling baby dolls has no problem in distinguishing between them and human babies; the dolls’ cuteness simply elicits her maternal instincts. Similarly, a man who squanders his time looking at porn magazines is captivated by the photos of nude women though he knows they’re not the real thing.
Irresistible cues can be the product of cultural transmission as well as of evolution. Voting is a case in point. The scheme of political Left-Right is a simple cultural cue that provides many of us with an emotional guide for what is right and wrong in politics. It is so emotionally overwhelming that it can also structure what is politically acceptable in our everyday lives. People who think of themselves as politically left-wing may not want to be friends or even talk with someone who is politically right-wing. Similarly, for some conservatives, a socialist or communist is almost an alien life-form. Let us have a closer look at this overpowering cue that shapes our identity.
THE ONE-DIMENSIONAL VOTER
With the collapse of the Soviet Union, democracy has become universally praised as the preeminent form of government in Europe and North America. Its institutions guarantee us advantages that our grandmothers and grandfathers were willing to risk their lives for: freedom of speech, freedom of the press, equality of citizens, and constitutional assurances of due process, among others. Yet there is a paradox. Philip Converse’s seminal study, The Nature of Belief Systems in Mass Publics, revealed that American citizens as a rule are badly informed about political choices, have not thought through the issues, and can be easily blown from one side of an issue to the other.8 It’s not that people know nothing; it’s just that they know nothing about politics. The most widely known fact about George H. W. Bush in the presidential elections of 1992 was that he hated broccoli. And almost all Americans knew that the Bushes’ dog was named Millie, while only 15 percent knew that both Bush and Clinton favored the death penalty.9 Converse was not the first to notice this shocking degree of ignorance. The existence of chronic, often opinionated know-nothings was noted in Europe as well. Karl Marx spoke of the lumpenproletariat, people he felt were easily propagandized, manipulated, and mobilized to act against the interests of the working classes. Marx was explicit about what he thought of the makeup of this bottom stratum of society:
Vagabonds, discharged soldiers, discharged jailbirds, escaped galley slaves, swindlers, mountebanks, lazzaroni, pickpockets, tricksters, gamblers, procurers, brothel keepers, porters, literati, organ grinders, rag pickers, knife grinders, tinkers, beggars—in short, the whole indefinite, disintegrated mass, thrown hither and thither.10
More than a century later, in the 1978 gubernatorial race in Georgia, the candidate Nick Belluso broadcast a television ad. The candidate’s consultants seemed to think the American public’s opinion was just as moldable as that of Marx’s lumpenproletariat. Here is the commercial:
Candidate: This is Nick Belluso. In the next ten seconds you will be hit with a tremendously hypnotic force. You may wish to turn away. Without further ado let me introduce to you the hypnogenecist of mass hypnosis, the Reverend James G. Masters. Take us away, James.
Hypnotist (in strange garb, surrounded by mist): Do not be afraid. I am placing the name of Nick Belluso in your subconscious mind. You will remember this. You will vote on Election Day. You will vote Nick Belluso for governor. You will remember this. You will vote on Election Day. You will vote Nick Belluso for governor.11
Perhaps because most TV stations refused to run the ad (some fearing the effects of hypnosis on the viewer), the ad was a flop; Belluso lost the vote and went on to run unsuccessfully for a number of positions, including president in 1980. Many political ads are equally edifying, if less amusing, when it comes to the candidate. Few ads in modern democracies provide information about the issues; most rely on increasing name recognition by means of repetition, on creating negative emotions toward the opponent, or simply on one-liners, laughter, and the politics of entertainment. How can citizens have an opinion about parties if they know so little about them? In deference to Herbert Simon, this mystery is known as Simon’s puzzle.12 It is the paradox of mass politics.
In 1980, something unique took place in the history of German democracy. A new party, the Greens, competed in the federal election, challenging the established system. This event marked the beginning of a swift career from a citizens’ initiative against nuclear power to a partnership in the federal government by the end of the twentieth century. A successful new party is a rare affair and poses a new twist to Simon’s puzzle: how can citizens have an opinion about a new party when they barely know anything about the old ones?
Let’s first look at the time before the Greens emerged. Back then, six parties occupied the German political landscape. Scores of issues divided them: religious versus secular orientation, economic policies, social welfare orientation, family and immigrant politics, and moral issues, including abortion. Citizens knew about most of these issues, but their preferences showed no such complexity. Rather, most voters’ preferences for the six parties were based on only one reason: where the parties fall in the continuum of Right and Left. Voters perceived the parties like six pearls on a string (Figure 8-1). This string of pearls has served as a model for political life in France, Italy, the United Kingdom, and the United States as well. In the United States, where the political Left in the European sense is almost nonexistent, it has also been called liberal versus conservative. Voters agree where the parties are located in the one-dimensional landscape, but they disagree on which ones they like and hate.
Helga Q. Public’s “ideal point” on the string is close to her favorite party, say, the Liberals. Can one predict how she ranks the other parties? Yes, and quite simply. Helga “picks up” the string at her ideal point, which leaves both ends hanging down in parallel strings.13 She does not have to know anything about the other parties beyond Left-Right, but she can nevertheless “read off” her preferences for a new (or old) party by relying on what I call the string heuristic:
Figure 8-1: The string heuristic. Voters tend to reduce the complexity of the political landscape to one dimension: Left-Right. Parties are mentally arranged like pearls on a string. By picking up the string at one’s ideal point, a voter can ``read off ’’ his or her preferences for the other parties. Shown are six political parties in Germany (Socialists = Social Democratic Party; Liberals = Free Democratic Party; Nationalists = National Democratic Party).
The closer a party is to your ideal point on the continuum of Left-Right, the higher your preference.
The string heuristic determines the party preferences within each of the two “ends” in Figure 8-1. For instance, Helga Q. prefers the Socialists to the Communists, the Christian Democrats to the Christian Socialists, and both to the Nationalists. If she preferred the Communists to the Socialists, or the Nationalists to the Christian Socialists, each of these preferences would contradict the hypothesis that she uses the string heuristic. How many voters actually rely on it? For the classical six-party system, 92 percent of all voters I studied followed this simple rule of thumb.14 This is how consistent preferences are formed, even when the voter is fairly uninformed.
How did voters react to the new party? The platform of the Greens did not easily fit into the old Left-Right scheme. The Greens brought together issues such as the protection of the forest and the closing down of nuclear power plants, which united both conservative forest workers and left-wing intellectuals who feared worldwide radioactive pollution following a nuclear meltdown. Would the party be assimilated into the old Left-Right scheme, or would the scheme be extended to new issues, such as environmentalism? To answer this question, I studied a group of 150 university student voters. Among them, 37 percent voted for the Greens. Although voters located the Greens all over the Left-Right continuum, each individual voter’s preferences were consistent and stable over time. Their party preferences continued to follow the string heuristic, only now the string had one more pearl. But what happened to the ecological dimension? From all we know, ecological orientation has little to do with the Left or Right, as it has been a key issue for neither. In fact, voters’ perception of how ecologically oriented a party was could be derived from its orientation toward the Left or Right. When one picked up the string at the point where a voter had located the Greens, the two ends revealed this voter’s rankings of the parties’ ecological orientation. Yet none of the voters appeared to be conscious of its mechanisms.
Einstein is reported to have said, “Politics is more difficult than physics.”15 That may be true, but to the degree we understand the cognitive processes involved, Simon’s puzzle can be resolved, piece by piece. The string heuristic explains how politically uninformed people get a feeling for where parties stand on issues and allows these voters to form consistent opinions. In a two-party system, such as in the United States, this mechanism is even simpler. When is the string heuristic reasonable? It seems to work in systems where political institutions present themselves along the Left-Right divide, arranging and polarizing their issues accordingly. An issue that is initially only loosely associated with a party, such as a stance in favor of abortion or against the death penalty, will become more and more attached to it as political opponents take the opposite stance. When this happens, voters can indeed read off from Left to Right where parties stand on the issues, even when the stance is often little more than historical accident. Consistent with this hypothesis, political campaigns and media reports use the Left-Right vocabulary, and political scientists construct their research instruments accordingly.16 Wherever the string heuristic and party politics coevolve in this way, the heuristic becomes helpful. The one-dimensional voter is able to “know” where parties stand without actually knowing.
Both the peacock’s tail and the political Left-Right scheme are irresistible cues. Yet one single cue is not sufficient for all situations. There is another class of intuitive judgments in which one or more cues are looked up in memory, although again only one of them determines the final decision. A process in which one first considers one cue, and, if it does not allow a decision, considers another, and so forth, is called sequential decision making. Put yourself in the following situation.
Around midnight, your child is short of breath, coughing and wheezing. You desperately look for an available doctor. In your phone book there are two entries for local after-hours primary health care. One is a general practitioner who would come to your home within twenty minutes. You know him from your health center, and he never listens to what you have to say. The other entry is an emergency center sixty minutes away, run by general practitioners. You don’t know these doctors, but you’ve heard that they listen to parents. Whom do you call? And why?
In the United Kingdom, parents of children under thirteen were asked this and similar questions.17 The pairs of consultations described were variations of four reasons that earlier studies had identified to be of primary concern for British parents: where their child was seen, by whom, the time taken between call and treatment (waiting time), and whether the doctor listened to them. Many seemed to carefully weigh each of the four reasons and combine them into their decision. However, almost every second parent had one dominant reason that made their decision. For the largest group, over a thousand parents, it was whether or not the doctor listened to what they were saying—even if it meant waiting forty minutes longer. These parents were more likely to be female, well educated, and have more children. For about 350 parents, the dominant reason was waiting time. Fifty parents needed to see a physician they knew, whether or not the doctor listened and no matter how long the waiting time would be. The fourth reason—whether the child was seen at home or in an emergency center—by contrast, was not a dominant reason for any of the parents.
How can we understand these parents’ intuitions? Assume that the order of importance is from top to bottom: the doctor’s tendency to listen, waiting time, familiarity, and location. Now consider the choice between primary health care A and B, available in one night:
Since the first reason already allows for a decision, the search for further information is stopped, all other potential reasons are ignored, and the parents go for alternative A. On another night, the choice may be more complicated:
In the second situation, neither the first nor the second reason allows for a decision. The third one does, and the parents therefore go for alternative D, using the Take the Best heuristic, which we encountered in the context of predicting dropout rates in high schools. It consists of three building blocks:
Search rule: Look up reasons in the order of importance.
Stopping rule: Stop search as soon as the alternatives for one reason differ.
Decision rule: Choose the alternative that this reason suggests.
This process is also described as lexicographic—when one looks up words in a lexicon, one has to look up the first letter first, then the second, and so on. Dozens of experimental studies have shown that people’s judgments tend to follow Take the Best, and identified conditions where this likely happens.18 Intuitions that rely on Take the Best may need to search through several reasons, but finally rely on just one to make the decision.
To now, we have seen how parents made this important decision, but we do not know how good their preferences would be. Many authorities on rational decision making would be appalled to hear how these parents dealt with such a life-and-death issue, given their low esteem of lexicographic rules such as Take the Best:
We examine an approach that we believe is more widely adopted in practice than it deserves to be: lexicographical ordering. However, it is simple and it can easily be administered. Our objection is that it is naively simple…. Again, we feel that such an ordering procedure, if carefully scrutinized, will rarely pass a test of “reasonableness.”19
This message is from two eminent figures in rational decision making, who seemed so sure about their verdict that they did not bother to conduct the test themselves. In order to test how “reasonable” sequential decision making is, we need to look at a situation where a clear-cut outcome exists. What would be better than sports?
Take the Best
Over one thousand matches were played in the National Basketball Association’s (NBA’s) 1996-97 season. Undergraduate students from New York University were asked to predict which team would win in a random sample of all games from that season. They were given only two clues: the number of games won in the season (the base rate), and the score at halftime of the game. In order to prevent other information from influencing the predictions, the names of the teams were not given. In more than 80 percent of the cases, the intuitive judgments were found to be consistent with Take the Best. Here is the theory of how it worked. The first clue was the number of games won. If both teams differed by more than fifteen games, then search was stopped and the person guessed that the team with the higher amount would win that game. The following NBA match is an illustration.
Since the first clue allowed for a decision, the information about the halftime result was ignored, and the prediction was that team A would win. If the difference in games won was smaller than fifteen, the second clue, the score at halftime, was considered:
Since team D was ahead at halftime (here the difference in scores didn’t matter), the prediction was that it would win.
But how accurate are intuitions based on only one reason? As mentioned above, according to traditional theories of rationality, these intuitions are doomed to failure. One should never ignore reasons, but combine number of games won and halftime score. In this view, hunches that rely on Take the Best commit one of two “sins.” If, as in the first example, an intuitive judgment relies solely on the base rate information (the number of games won) and ignores the halftime score, it commits what has been called conservatism. Conservatism means that only the old information is taken into consideration and the new information, the halftime result, is ignored. If, as in the second example, intuition is instead based on the halftime score only, this “sin” has been labeled the base-rate fallacy.20
These alleged sins are presented in virtually every psychology textbook as verdicts against intuition: people may use simple rules as a shortcut, but it’s naive to do so. Yet, as I discussed earlier, Take the Best can predict school dropout rates faster and more accurately than a complex version of Franklin’s rule does. The NBA study provided another test of Take the Best, this time against Bayes’s rule, the Goliath of rational strategies.21 Bayes’s rule does not waste information. It always uses base rates and halftime score, as well as the actual difference in scores at halftime, whereas Take the Best either ignores halftime or simply considers who is ahead in a match. The question is, if people followed the rational Bayes’s rule, how much more accurate would they be in predicting the outcomes of all 1,187 NBA games than if their intuitions followed the simple Take the Best heuristic?
The test showed by way of computer simulation that if people used Bayes’s rule, they would be able to predict 78 percent of the winners correctly. Take the Best, in spite of committing alleged sins against rationality, predicted exactly the same percentage of winners, yet more quickly and with less information and computation.
Something must be wrong, it seems, with this result. Yet it held in soccer as well. A student of mine replicated the result with soccer matches in the German major league, the Bundesliga, for the seasons 1998-2000. Take the Best used the same order of reasons. For both seasons, it predicted the outcomes of more than four hundred games as well as or better than Bayes’s rule did.22 The advantage of the simple rule was most pronounced when the base rates (the games won) were two years old rather than from the previous season, that is, when the problem was most difficult. In each case, Take the Best embodied the intuition that if one team had been considerably more successful than its opponent in a previous season, it would likely win again; otherwise, the team that led at halftime would win. The complex calculations could not beat this intuition.
When Is One Good Reason Better Than Many?
The idea that intuitions based on Take the Best could be as accurate as complex decision making is hard to swallow. When I presented the first results to international groups of experts, I asked them to estimate how closely Take the Best would match the accuracy of a sophisticated modern version of Franklin’s rule (multiple regression). Not a single one expected that the simple rule could be as accurate, let alone that it could be better, and most estimated that Take the Best would fail by 5 to 10 percentage points or more. To their surprise, across twenty studies, using Take the Best produced more accurate decisions. Since then, we have shown the power of one good reason in a broad range of real-world situations.23
These results are important in demonstrating that intuitions based on one good reason not only are efficient but can also be highly accurate. In fact, even if a mind were able to compute the most sophisticated artificial intelligence strategies available today, it would not always do better. The lesson is to trust your intuition when thinking about things that are difficult to predict and when there is little information.
Recall that in an uncertain world, a complex strategy can fail exactly because it explains too much in hindsight. Only part of the information is valuable for the future. A simple rule that focuses only on the best reason and ignores the rest has a good chance of hitting at the most useful information.
Imagine a plot with 365 points representing the daily temperature in New York for one year. The values are low in January, rise through spring and summer, and then decrease again. The pattern is quite jagged. If you are mathematically sophisticated, you can find a complex curve that fits the points almost perfectly. But this curve is not likely to predict next year’s temperatures as well. After the fact, a good fit is, by itself, worth little. By trying to find the perfect fit, one fits irrelevant effects that do not generalize to the future. A simpler curve will give better predictions for next year’s temperature, even though it does not match the existing data as well. Figure 5-2 illustrates exactly this principle. The more complex strategy is better than the simple one in hindsight, but not in predictions. In general:
Intuitions based on only one good reason tend to be accurate when one has to predict the future (or some unknown present state of affairs), when the future is difficult to foresee, and when one has only limited information. They are also more efficient in using time and information. Complex analysis, by contrast, pays when one has to explain the past, when the future is highly predictable, or when there are large amounts of information.24
DESIGNING OUR WORLD
Evolution appears to have designed various animal minds to rely on sequential cue assessment.25 For instance, female sage grouse first assess males in a lek on the basis of their songs and visit only those who pass this first test for a closer inspection. Such a sequential process of mate choice seems to be widespread and has also been observed in food choice and navigation. Honeybees trained in experiments to identify model flowers rely on a set order of cues, with odor on the top. They decide on the basis of color only if the odor of two flowers matches and on the basis of shape only if odor and color match. Yet the cue that is consulted first is not always the most valid one; in some cases the order is determined by how far a sense can reach out into the world. In an environment in which trees and bushes block vision, acoustic cues tend to be available before visual and other cues. For instance, a deer stag estimates the strength of a rival first by the deepness of its roar, and only later by vision. If these two reasons were not enough to make it run off scared, it will experience the most authoritative signals of its opponent’s strength when they begin fighting.
Sequential decisions based on one good reason, however, are not animals’ only adaptive strategies. Adding and averaging of two or more cues seem to occur with individual differences between young and old, experienced and inexperienced. For instance, older female garter snakes appear to demand males that are good on two cues, whereas either cue alone satisfies younger snakes.
As we have seen before, intuition, like evolution, takes advantage of one good reason. We humans can also consciously take advantage of it in designing our world. Sequential decisions can make the environment safer, more transparent, and less confusing.
Playing in the World Cup tournament is the ultimate dream of every national soccer team. In the first round, groups of four teams compete. The two best teams in each group move on to the next round. But how to determine who is the “best”? The FIFA (International Federation of Football Associations) considers six aspects of performance to be relevant.
1. Total points in all matches (three for a win, one for a tie)
2. Points in the direct competition matches
3. Difference in number of goals in the direct competitions
4. Number of goals in the direct competitions
5. Difference in number of goals in all matches
6. Number of goals in all matches
Let’s look first at the ideal of making trade-offs, that is, weighing and adding. A committee of international experts could come up with a weighing scheme. For instance, one could give the first aspect a weight factor of 6, the second a weight of 5, and so on. That, one might argue, would be fairer and allow a more comprehensive evaluation of performance than would simply judging teams on one of these aspects. Designing such a scheme, however, clearly invites endless discussion; the American Bowl Championship Series formula that ranks college football teams by complex weighing and adding sparked a wave of complaints. An equally worrisome problem is that a weighing scheme is not intuitively transparent. Coaches, players, reporters, and fans alike would be busier calculating the final score results than enjoying the game.
The alternative is to dispense with weighing and adding, and to introduce Take the Best. That is what the FIFA uses. The aspects of performance are ordered as above, and if two teams differ on the first, the decision is made. Only when the teams are tied is the second aspect looked up, and so on. Everything else is ignored. Sequential decisions based on one good reason can be easily made and embody transparent justice.
Trade-offs may spoil the fun when it comes to ball games, but in other contexts would be downright dangerous. When determining which car has the right of way on a crossing, there are several potentially relevant factors.
1. The hand signals of the police officer regulating the traffic
2. The color of the traffic light
3. The traffic sign
4. Where the other car comes from (right or left)
5. Whether the other car is bigger
6. Whether the driver of the other car is older and deserves respect
Imagine a world in which traffic laws give each of these factors due consideration, because it is considered fair to make trade-offs between public signs and courtesy. Yet weighing and counting pros and cons would be unsafe, since drivers do not have the time and might make computational errors. Two cars may be close in size, and the age of the other driver may be difficult to assess. A safer design, and the one used in all the countries I know of, is sequential one-reason decision making. If there is a police officer who regulates the traffic, all other signals in the above list must be ignored by a driver approaching the crossing. If there is no police officer, only the traffic light counts. If there is no traffic light, then the traffic signs are decisive. One could of course imagine an alternative system in which all that counts is whether the other car is bigger, but this is fortunately not yet law and only practiced in isolated cases.
Traffic laws that make trade-offs would have a different structure. For instance, the police officer’s order to stop could be overruled if both a green traffic light and the traffic sign indicated otherwise. Or a green traffic light would be overruled if the traffic sign was a yield sign and the other car was bigger. Continually making trade-offs would turn our everyday world into a risky place by slowing down decisions that need to be made fast.
You enter a party and see a bunch of people. How many are there? An adult with no special training has a direct perception of up to only four people. That is, one immediately knows how many others are in the room, if they do not number more than four. Beyond that, humans have to count. This psychological capacity of four has become a building block of various cultural systems. Romans, for instance, gave ordinary names to the first four of their sons, but the fifth and every subsequent one was named by counting, that is, by a numeral: Quintus, Sixtus, Septimus, and so on. Similarly, in the original Roman calendar, the first four months had names, Martius, Aprilis, Maius, Junius; the fifth and all others were referred to by their order number: Quintilis, Sextilis, September, October, November, December.26
Various present-day cultures in Oceania, Asia, and Africa only have the words one, two, and many. But that does not mean that they cannot do arithmetic. People have designed various systems to count. Some cultures use wooden sticks to keep a tally; others tick things off with the parts of their bodies, matching numbers to a sequence of fingers, toes, elbows, knees, eyes, nose, and so on. Tally notches and marks have been found on animal bones and cave walls, probably twenty to thirty thousand years old. The tally system is the source of the Roman numbering system, where I is one, II is two, III is three, V is short for five, X for ten, C for hundred, D for five hundred, and M for thousand. Like the ancient Greek and Egyptian systems, the Roman numerals made calculation a pain. These cultures were locked up for centuries with tallying systems that were incoherent and unusable for most purposes except writing a number down.
The breakthrough came from Indian civilization, which gave us our modern “Arabic” system. Its genius lies in its introduction of a lexicographic system, which is inherent in the sequential rules discussed in this chapter. Take a quick look at the following two numbers, represented in the Roman system. Which one is larger?
Now look at these two numbers represented in the Arabic system.
One can see immediately that the first number is larger when represented in the Arabic, but not in the Roman system. Roman numerals represent magnitude neither by the length of the numeral nor by its order. In terms of length, MDCCCLXXX should be larger, but is not. In terms of order, from left to right, after the M (representing a thousand) there is a C (representing a hundred) in MCMXI, whereas there is a D (representing five hundred) in MDCCCLXXX. Nevertheless, the first number is larger. But the Arabic system is based strictly on order. If two numbers have the same length as in the example, one only needs to search from left to right for the first digit that is different. One can then stop searching and conclude that the number with the higher digit is the larger number. All other digits can be ignored. Putting order into our representations of the world can generate insight in our minds and simplify our lives.