Fooled by Randomness (22 page)

Buridan’s Donkey or the Good Side of Randomness

Nonlinearity in random outcomes is sometimes used as a tool to break stalemates. Consider the problem of the nonlinear nudge. Imagine a donkey equally hungry and thirsty placed at exactly equal distance from sources of food and water. In such a framework, he would die of both thirst and hunger as he would be unable to decide which one to get to first. Now inject some randomness in the picture, by randomly nudging the donkey, causing him to get closer to one source, no matter which, and accordingly away from the other. The impasse would be instantly broken and our happy donkey will be either in turn well fed then well hydrated, or well hydrated then well fed.

The reader no doubt has played a version of Buridan’s donkey, by “flipping a coin” to break some of the minor stalemates in life where one lets randomness help with the decision process. Let Lady Fortuna make the decision and gladly submit. I often use Buridan’s donkey (under its mathematical name) when my computer goes into a freeze between two possibilities (to be technical, these “randomizations” are frequently done during optimization problems, when one needs to perturbate a function).

Note that Buridan’s donkey was named after the fourteenth-century philosopher Jean Buridan. Buridan had an interesting death (he was thrown in the Seine tied in a bag and died drowning). This tale was considered an example of sophistry by his contemporaries who missed the import of randomization—Buridan was clearly ahead of his time.

WHEN IT RAINS, IT POURS

As I am writing these lines, I am suddenly realizing that the world’s bipolarity is hitting me very hard. Either one succeeds wildly, by attracting all the cash, or fails to draw a single penny. Likewise with books. Either everyone wants to publish it, or nobody is interested in returning telephone calls (in the latter case my discipline is to delete the name from my address book). I am also realizing the nonlinear effect behind success in anything: It is better to have a handful of enthusiastic advocates than hordes of people who appreciate your work—better to be loved by a dozen than liked by the hundreds. This applies to the sales of books, the spread of ideas, and success in general and runs counter to conventional logic. The information age is worsening this effect. This is making me, with my profound and antiquated Mediterranean sense of
metron
(measure), extremely uncomfortable, even queasy. Too much success is the enemy (think of the punishment meted out on the rich and famous); too much failure is demoralizing. I would like the option of having neither.

Eleven

•

RANDOMNESS AND OUR MIND: WE ARE PROBABILITY BLIND

PARIS OR THE BAHAMAS?

Y
ou have two options for your next brief vacation in March. The first is to fly to Paris; the second is to go to the Caribbean. You expressed indifference between the two options; your spouse will tip the decision one way or the other. Two distinct and separate images come to you when you think of the possibilities. In the first one, you see yourself standing at the Musée d’Orsay in front of some Pissaro painting depicting a cloudy sky—the gray Parisian wintry sky. You are carrying an umbrella under your arm. In the second image, you are lying on a towel with a stack of books by your favorite authors next to you (Tom Clancy and Ammianus Marcellinus), and an obsequious waiter serving you a banana daiquiri. You know that the two states are mutually exclusive (you can only be in one place at one time), but exhaustive (there is a 100% probability that you will be in one of them). They are equiprobable, with, in your opinion, 50% probability assigned to each.

You derive great pleasure thinking about your vacation; it motivates you and makes your daily commute more bearable. But the adequate way to visualize yourself, according to rational behavior under uncertainty, is 50% in one of the vacation spots and 50% in the other—what is mathematically called a
linear combination
of the two states. Can your brain handle that? How desirable would it be to have your feet in the Caribbean waters and your head exposed to the Parisian rain? Our brain can properly handle one and only one state at once—unless you have personality troubles of a deeply pathological nature. Now try to imagine an 85%/15% combination. Any luck?

Consider a bet you make with a colleague for the amount of $1,000, which, in your opinion, is exactly fair. Tomorrow night you will have zero or $2,000 in your pocket, each with a 50% probability. In purely mathematical terms, the fair value of a bet is the linear combination of the states, here called the
mathematical expectation,
i.e., the probabilities of each payoff multiplied by the dollar values at stake (50% multiplied by 0 and 50% multiplied by $2,000 =$1,000). Can you
imagine
(that is visualize, not compute mathematically) the value being $1,000? We can conjure up one
and only one
state at a given time, i.e., either 0 or $2,000. Left to our own devices, we are likely to bet in an irrational way, as one of the states would dominate the picture—the fear of ending with nothing or the excitement of an extra $1,000.

SOME ARCHITECTURAL CONSIDERATIONS

Time to reveal Nero’s secret. It was a black swan. He was then thirty-five. Although prewar buildings in New York can have a pleasant front, their architecture seen from the back offers a stark contrast by being completely bland. The doctor’s examination room had a window overlooking the backyard of one such Upper East Side street, and Nero will always remember how bland that backyard was in comparison with the front, even if he were to live another half century. He will always remember the view of the ugly pink backyard from the leaden window panes, and the medical diploma on the wall that he read a dozen times as he was waiting for the doctor to come into the room (half an eternity, for Nero suspected that something was wrong). The news was then delivered (grave voice), “I have some . . . I got the pathology report . . . It’s . . . It is not as bad as it sounds . . . It’s . . . It’scancer.” The declaration caused his body to be hit by an electric discharge, running through his back down to his knees. Nero tried to yell “What?” but no sound came out of his mouth. What scared him was not so much the news as the sight of the doctor. Somehow the news reached his body before his mind. There was too much fear in the doctor’s eyes and Nero immediately suspected that the news was even worse than what he was being told (it was).

The night of the diagnosis, at the medical library where he sat, drenched wet from walking for hours in the rain without noticing it and making a puddle of water around him (he was yelled at by an attendant but could not concentrate on what she was saying so she shrugged her shoulders and walked away); later he read the sentence “72% 5-year actuarially adjusted survival rate.” It meant that 72 people out of 100 make it. It takes between three and five years for the body without clinical manifestations of the disease for the patient to be pronounced cured (closer to three at his age). He then felt in his guts quite certain that he was going to make it.

Now the reader might wonder about the mathematical difference between a 28% chance of death and a 72% chance of survival over the next five years. Clearly, there is none, but we are not made for mathematics. In Nero’s mind a 28% chance of death meant the image of himself dead, and thoughts of the cumbersome details of his funeral. A 72% chance of survival put him in a cheerful mood; his mind was planning the result of a cured Nero skiing in the Alps. At no point during his ordeal did Nero think of himself as 72% alive and 28% dead.

Just as Nero cannot “think” in complicated shades, consumers consider a 75% fat-free hamburger to be different from a 25% fat one. Likewise with statistical significance. Even specialists tend to infer too fast from data in accepting or rejecting things. Recall the dentist whose emotional well-being depends on the recent performance of his portfolio. Why? Because as we will see, rule-determined behavior does not require nuances. Either you kill your neighbor or you don’t. Intermediate sentiments (leading, say, to only half his killing) are either useless or downright dangerous when you do things. The emotional apparatus that jolts us into action does not understand such nuances—it is not efficient to understand things. The rest of this chapter will rapidly illustrate some manifestations of such blindness, with a cursory exposition of the research in that area (only what connects to the topics in this book).

BEWARE THE PHILOSOPHER BUREAUCRAT

For a long time we had the wrong product specifications when we thought of ourselves. We humans have been under the belief that we were endowed with a beautiful machine for thinking and understanding things. However, among the factory specifications for us is the lack of awareness of the true factory specifications (why complicate things?). The problem with thinking is that it causes you to develop illusions. And thinking may be such a waste of energy! Who needs it!

Consider that you are standing in front of a government clerk in a heavily socialist country where being a bureaucrat is held to be what respectable people do for a living. You are there to get your papers stamped by him so you can export some of their lovely chocolate candies to the New Jersey area, where you think the local population would have a great taste for them. What do you think his function is? Do you think for a minute that he cares about the general economic theory behind the transaction? His job is just to verify that you have the twelve or so signatures from the right departments, true/false; then stamp your papers and let you go. General considerations of economic growth or balance of trade are none of his interests. In fact you are lucky that he doesn’t spend any time meditating about these things: Consider how long the procedure would take if he had to solve balance of trade equations. He just has a rulebook and, over a career spanning forty to forty-five years, he will just stamp documents, be mildly rude, and go home to drink nonpasteurized beer and watch soccer games. If you gave him Paul Krugman’s book on international economics he would either sell it in the black market or give it to his nephew.

Accordingly, rules have their value. We just follow them not because they are the best but because they are useful and they save time and effort. Consider that those who started theorizing upon seeing a tiger on whether the tiger was of this or that taxonomic variety, and the degree of danger it represented, ended up being eaten by it. Others who just ran away at the smallest presumption and were not slowed down by the smallest amount of thinking ended up either outchasing the tiger or outchasing their cousin who ended up being eaten by it.

Satisficing

It is a fact that our brains would not be able to operate without such shortcuts. The first thinker who figured it out was Herbert Simon, an interesting fellow in intellectual history. He started out as a political scientist (but he was a formal thinker, not the literary variety of political scientists who write about Afghanistan in
Foreign Affairs
); he was an artificial-intelligence pioneer, taught computer science and psychology, did research in cognitive science, philosophy, and applied mathematics, and received the Bank of Sweden Prize for Economics in honor of Alfred Nobel. His idea is that if we were to optimize at every step in life, then it would cost us an infinite amount of time and energy. Accordingly, there has to be in us an approximation process that stops somewhere. Clearly he got his intuitions from computer science—he spent his entire career at Carnegie-Mellon University in Pittsburgh, which has a reputation as a computer science center. “Satisficing” was his idea (the melding together of
satisfy
and
suffice
): You stop when you get a near-satisfactory solution. Otherwise it may take you an eternity to reach the smallest conclusion or perform the smallest act. We are therefore rational, but in a limited way: “boundedly rational.” He believed that our brains were a large optimizing machine that had built-in rules to stop somewhere.

Not quite so, perhaps. It may not be just a rough approximation. For two (initially) Israeli researchers on human nature, how we behave seemed to be a completely different process from the optimizing machine presented by Simon. The two sat down introspecting in Jerusalem looking at aspects of their own thinking, compared it to rational models, and noticed
qualitative
differences. Whenever they both seemed to make the same mistake of reasoning they ran empirical tests on subjects, mostly students, and discovered very surprising results on the relation between thinking and rationality. It is to their discovery that we turn next.

FLAWED, NOT JUST IMPERFECT

Kahneman and Tversky

Who has exerted the most influence on economic thinking over the past two centuries? No, it is not John Maynard Keynes, not Alfred Marshall, not Paul Samuelson, and certainly not Milton Friedman. The answer is two noneconomists: Daniel Kahneman and Amos Tversky, the two Israeli introspectors, and their specialty was to uncover areas where human beings are not endowed with rational probabilistic thinking and optimal behavior under uncertainty. Strangely, economists studied uncertainty for a long time and did not figure out much—if anything, they thought they knew something and were fooled by it. Aside from some penetrating minds like Keynes, Knight, and Shackle, economists did not even figure out that they had no clue about uncertainty—the discussions on risk by their idols show that
they did not know how much they did not know.
Psychologists, on the other hand, looked at the problem and came out with solid results. Note that, unlike economists, they conducted experiments, true controlled experiments of a repeatable nature, that can be done in Ulan Bator, Mongolia, tomorrow if necessary. Conventional economists do not have this luxury as they observe the past and make lengthy and mathematical comments, then bicker with each other about them.

Kahneman and Tversky went in a completely different direction than Simon and started figuring out rules in humans that did not make them rational—but things went beyond the shortcut. For them, these rules, which are called
heuristics,
were not merely a simplification of rational models, but were different in methodology and category. They called them “quick and dirty” heuristics. There is a dirty part: These shortcuts came with side effects, these effects being the biases, most of which I discussed previously throughout the text (such as the inability to accept anything abstract as risk). This started an empirical research tradition called the “heuristics and biases” tradition that attempted to catalogue them—it is impressive because of its empiricism and the experimental aspect of the methods used.

Since the Kahneman and Tversky results, an entire discipline called behavioral finance and economics has flourished. It is in open contradiction with the orthodox so-called neoclassical economics taught in business schools and economics departments under the normative names of efficient markets, rational expectations, and other such concepts. It is worth stopping, at this juncture, and discussing the distinction between normative and positive sciences. A normative science (clearly a self-contradictory concept) offers prescriptive teachings; it studies how things
should
be. Some economists, for example those of the efficient-market religion, believe that our studies should be based on the hypothesis that humans are rational and act rationally because it is the best thing for them to do (it is mathematically “optimal”). The opposite is a positive science, which is based on how people actually are observed to behave. In spite of economists’ envy of physicists, physics is an inherently positive science while economics, particularly microeconomics and financial economics, is predominantly a normative one. Normative economics is like religion without the aesthetics.

Note that the experimental aspect of the research implies that Daniel Kahneman and the experimental ponytailed economist Vernon Smith were the first true scientists ever to bow in front of the Swedish king for the economics prize, something that should give credibility to the Nobel academy, particularly if, like many, one takes Daniel Kahneman far more seriously than a collection of serious-looking (and very human, hence fallible) Swedes. There is another hint of the scientific firmness of this research: It is extremely readable for someone outside of psychology, unlike papers in conventional economics and finance that even people in the field have difficulty reading (as the discussions are jargon-laden and heavily mathematical to give the illusion of science). A motivated reader can get concentrated in four volumes the collection of the major heuristics and biases papers.