Against the Gods: The Remarkable Story of Risk Page 24
Ideas came to Keynes in such a rush and in such volume that he often found himself at odds with something he had said or written earlier. That did not disturb him. "When somebody persuades me that I am wrong," he wrote, "I change my mind. What do you do?"19
In 1921, Keynes completed a book titled A Treatise on Probability. He had begun work on it shortly after graduating from Cambridge and had worked on it fitfully for about fifteen years; he even took it with him on his travels abroad, including a trip on horseback through Greece with the painter Duncan Grant. He struggled to convey novel ideas with the clarity he prized. He never quite broke away from his training in philosophy at Cambridge, where, he later reminisced, "`What exactly do you mean?' was the phrase most frequently on our lips. If it appeared under cross-examination that you did not mean exactly anything, you lay under a strong suspicion of meaning nothing whatever. "20
A Treatise on Probability is a brilliant exploration of the meaning and applications of probability, much of it a critique of the work of earlier writers, many of whom have made their appearance in the earlier pages of this book. Unlike Knight, Keynes does not distinguish categorically between risk and uncertainty; in less precise fashion, he contrasts what is definable from what is undefinable when we contemplate the future. Like Knight, however, Keynes has little patience with decisions based on the frequency of past occurrences: He felt that Galton's peapod analogy was applicable to nature but irrelevant to human beings. He rejects analyses based on events but welcomes predictions based on propositions. His preferred expression is "degrees of belief-or the a priori probabilities, as they used to be called."21
Keynes begins the book with an attack on traditional views of probability; many of our old friends are victims, including Gauss, Pascal, Quetelet, and Laplace. He declares that probability theory has little relevance to real-life situations, especially when applied with the "incautious methods and exaggerated claims of the school of Laplace."22
An objective probability of some future event does exist-"it is not, that is to say, subject to human caprice"-but our ignorance denies us the certainty of knowing what that probability is; we can only fall back on estimates. "There is little likelihood," Keynes suggests, "of our discovering a method of recognizing particular probabilities, without any assistance whatever from intuition or direct judgment.... A proposition is not probable because we think it so."23
Keynes suggests that "we pass from the opinions of theorists to the experience of practical men." He pokes fun at the seat-of-the-pants method that most insurance companies use in calculating their premiums. He doubts that two equally intelligent brokers would consistently arrive at the same result: "It is sufficient if the premium he names exceeds the probable risk."24 He cites the odds quoted by Lloyd's on August 23, 1912, on the three-way race for the presidency of the United States; the odds added up to 110%! The reinsurance rates in the insurance market on the Waratagh, a ship that disappeared off South Africa, varied from hour to hour as bits of wreckage were discovered and as a rumor spread that under similar circumstances a vessel had stayed afloat, not seriously damaged, for two months before being dis covered. Yet the probability that the Waratagh had sunk remained constant even while the market's evaluation of that probability fluctuated wildly.
Keynes was scornful of what he refers to as "The Law of Great Numbers." Simply because similar events have been observed repeatedly in the past is a poor excuse for believing that they will probably occur in the future. Rather, our confidence in an outcome should be strengthened only when we can discover "a situation where each new series differs in some significant fashion from the others."25
He heaps scorn on the arithmetic mean, "a very inadequate axiom." Instead of adding up a series of observations and then dividing the sum by the total number of observations, "Equal suppositions would have equal consideration, if the ... estimates had been multiplied together instead of added. "26 Granted, the arithmetic mean is simple to use, but Keynes quotes a French mathematician who had pointed out that nature is not troubled by difficulties of analysis, nor should humanity be so troubled.
Keynes rejects the term "events" as used by his predecessors in probability theory, because it implies that forecasts must depend on the mathematical frequencies of past occurrences. He preferred the term "proposition," which reflects degrees of belief about the probability of future events. Bradley Bateman, an economist who teaches at Grinnell College, has observed that probability to Keynes is the basis on which we analyze and evaluate propositions. 27
If Keynes believed that probability reflects degrees of belief about the future, and that past events are only a modest part of the input, we might conclude that he regarded probability as a subjective concept. Not so. Modern though he is in so many ways, he occasionally revealed his Victorian background. At the time he wrote A Treatise on Probability, he believed that all rational people would in time come to recognize the correct probability of a certain outcome and would hold identical degrees of belief. "When once the facts are given which determine our knowledge, what is probable or improbable in these circumstances has been fixed objectively and is independent of our opinion."28
Yielding to criticism of this unrealistic view, Keynes later began to focus increasingly on how uncertainty influences decisions and, in turn, the world economy. At one point in the Treatise he declares, "Perception of probability, weight, and risk are all highly dependent on judgment," and "the basis of our degrees of belief is part of our human outfit."29 Charles Lange, a statistician and an old friend, once remarked that he was pleased that "Maynard does not prefer algebra to earth."
Keynes's view of economics ultimately revolves around uncertaintyuncertainty as to how much a family will save or spend, uncertainty as to what portion of its accumulated savings a family will spend in the future (and when it will spend that portion), and, most important, uncertainty as to how much profit any given outlay on capital goods will produce. The decisions business firms make on how much to spend (and when to spend it) on new buildings, new machinery, new technology, and new forms of production constitute a dynamic force in the economy. The fact that those decisions are essentially irreversible, however, makes them extremely risky given the absence of any objective guide to the probability that they will turn out as planned.
As Frank Knight observed fifteen years before Keynes published The General Theory, "At the bottom of the uncertainty problem in economics is the forward-looking character of the economic process itself."" Because the economic environment is constantly changing, all economic data are specific to their own time period. Consequently they provide only a frail basis for generalizations. Real time matters more than time in the abstract, and samples drawn from the past have little relevance. What was 75% probable yesterday has an unknown probability tomorrow. A system that cannot rely on the frequency distribution of past events is peculiarly vulnerable to surprise and is inherently volatile.
Keynes had no use for a hypothetical economy in which past, present, and future are merged by an impersonal time machine into a single moment. Involuntary unemployment and disappointing profits occur too frequently for an economy to work as the classical economists had assumed it would. If people decide to save more and spend less, consumer spending will fall and investment will decline. The inter est rate in any case might fail to fall in response to the higher propensity to save. Keynes argued that interest is a reward for parting with liquidity, not for refraining from consumption. Even if the interest rate does decline, it may not decline enough to encourage business managers to risk investing further capital in an economic environment in which animal spirits are lacking and in which shifting to a new set of decisions is costly. Decisions, once made, create a new environment with no opportunity to replay the old.
Another reason for a decline in investment spending may be that business firms have exhausted all opportunities for earning a profit. Keynes once remarked, "The Middle Ages built cathedrals and sang dirges.... [T]wo masses for the dead are
twice as good as one; but not so two railways from London to York. 113' That same idea had appeared in a song popular during the Great Depression, "Brother, Can You Spare a Dime?" "Once I built a building, now it's done./Once I built a railroad, made it run."
Keynes and his followers focused on money and contracts to demonstrate that uncertainty rather than mathematical probability is the ruling paradigm in the real world. The desire for liquidity and the urge to cement future arrangements by legally enforceable agreements testify to the dominance of uncertainty in our decision-making. We are no longer willing to accept the guidance that the mathematical frequency of past events might provide.
Keynes rejected theories that ignored uncertainty. The "signal failure of [the classical doctrine] for the purposes of scientific prediction," he observed, "has greatly impaired, in the course of time, the prestige of its practitioners."32 The classical economists, he charged, had reached a state where they were looked upon as "Candides, who ... having left this world for the cultivation of their gardens, teach that all is for the best in the best of all possible worlds, provided we will let well alone."33
Impatient with Candide-based theories, Keynes proposed a course of action that was diametrically opposed to laissez-faire: a more active role for the government, not just in order to substitute government demand for waning private demand, but to reduce the uncertainties abroad in the economy. We have discovered over time that Keynes's cure has on occasion been worse than the disease and that his analysis has other, less visible, faults. Yet none of that can detract from his primary contribution to economic theory and the understanding of risk.
At the end of the single-paragraph first chapter of The General Theory, Keynes wrote: "[T]he characteristics ... assumed by the classical theory happen not to be those of the economic society in which we actually live, with the result that its teaching is misleading and disastrous if we attempt to apply it to the facts of experience."34 Given the state of the world in 1936, Keynes could hardly have concluded otherwise. Uncertainty must provide the core of the new economic theory.
In 1937, in response to criticisms of The General Theory, Keynes summed up his views:
By "uncertain" knowledge ... I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty.... The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention.... About these matters, there is no scientific basis on which to form any calculable probability whatever. We simply do not know!3s
A tremendous idea lies buried in the notion that we simply do not know. Rather than frightening us, Keynes's words bring great news: we are not prisoners of an inevitable future. Uncertainty makes us free.
Consider the alternative. All the thinkers from Pascal to Galton told us that the laws of probability work because we have no control over the next throw of the dice, or where our next error in measurement will occur, or the influence of a static normality to which matters ultimately revert. In this context, everything in life is like Jacob Bernoulli's jar: we are free to pull out any pebble, but we cannot choose its color. As Laplace reminded us, "All events, even those which on account of their insignificance do not seem to follow the great laws of nature, are a result of it just as necessarily as the revolutions of the sun."36
This is, in short, a story of the inevitable. Where everything works according to the laws of probability, we are like primitive people-or gamblers-who have no recourse but to recite incantations to their gods. Nothing that we do, no judgment that we make, no response to our animal spirits, is going to have the slightest influence on the final result. It may appear to be a well-ordered world in which the probabilities yield to careful mathematical analysis, but each of us might just as well retire to a windowless prison cell-a fate that the flutter of a butterfly's wings billions of years ago may have ordained in any case.
What a bore! But thank goodness, the world of pure probability does not exist except on paper or perhaps as a partial description of nature. It has nothing to do with breathing, sweating, anxious, and creative human beings struggling to find their way out of the darkness.
That is good news, not bad news. Once we understand that we are not obliged to accept the spin of the roulette wheel or the cards we are dealt, we are free souls. Our decisions matter. We can change the world. Keynes's economic prescriptions reveal that as we make decisions we do change the world.
Whether that change turns out to be for better or for worse is up to us. The spin of the roulette wheel has nothing to do with it.
e have just witnessed Frank Knight's determination to elevate uncertainty to a central role in the analysis of risk and decision-making and the energy and eloquence with which Keynes mounted his attack on the assumptions of the classical economists. Yet faith in the reality of rational behavior and in the power of measurement in risk management persisted throughout all the turmoil of the Depression and the Second World War. Theories on these matters now began to move along sharply divergent paths, one traveled by the followers of Keynes ("We simply do not know") and the other by the followers of Jevons ("Pleasure, pain, labour, utility, value, wealth, money, capital, etc. are all notions admitting of quantity.")
During the quarter-century that followed the publication of Keynes's General Theory, an important advance in the understanding of risk and uncertainty appeared in the guise of the theory of games of strategy. This was a practical paradigm rooted in the Victorian conviction that measurement is indispensable in interpreting human behavior. The theory focuses on decision-making, but bears little resemblance to the many other theories that originated in games of chance.
Despite its nineteenth-century forebears, game theory represents a dramatic break from earlier efforts to incorporate mathematical inevitability into decision-making. In the utility theories of both Daniel Bernoulli and Jevons, the individual makes choices in isolation, unaware of what others might be doing. In game theory, however, two or more people try to maximize their utility simultaneously, each aware of what the others are about.
Game theory brings a new meaning to uncertainty. Earlier theories accepted uncertainty as a fact of life and did little to identify its source. Game theory says that the true source of uncertainty lies in the intentions of others.
From the perspective of game theory, almost every decision we make is the result of a series of negotiations in which we try to reduce uncertainty by trading off what other people want in return for what we want ourselves. Like poker and chess, real life is a game of strategy, combined with contracts and handshakes to protect us from cheaters.
But unlike poker and chess, we can seldom expect to be a "winner" in these games. Choosing the alternative that we judge will bring us the highest payoff tends to be the riskiest decision, because it may provoke the strongest defense from players who stand to lose if we have our way. So we usually settle for compromise alternatives, which may require us to make the best of a bad bargain; game theory uses terms like "maximin" and "minimax" to describe such decisions. Think of seller-buyer, landlord-tenant, husband-wife, lender-borrower, GM-Ford, parentchild, President-Congress, driver-pedestrian, boss-employee, pitcherbatter, soloist-accompanist.
Game theory was invented by John von Neumann (1903-1957), a physicist of immense intellectual accomplishment.' Von Neumann was instrumental in the discovery of quantum mechanics in Berlin during the 1920s, and he played a major role in the creation of the first American atomic bomb and, later, the hydrogen bomb. He also invented the digital computer, was an accomplished meteorologist and mathematician, could multiply eight digits by eight digits in his head, and loved telling ribald jokes and reciting off-color limericks. In his work with the military, he preferred admirals to generals because ad mirals were the heavier drinkers. His biographer Norman Macrae describes him as "excessively polite to everybody except ... t
wo longsuffering wives," one of whom once remarked, "He can count everything except calories."2
A colleague interested in probability analysis once asked von Neumann to define certainty. Von Neumann said first design a house and make sure the living-room floor will not give way. To do that, he suggested, "Calculate the weight of a grand piano with six men huddling over it to sing. Then triple that weight." That will guarantee certainty.
Von Neumann was born in Budapest to a well-to-do, cultured, jolly family. Budapest at the time was the sixth-largest city in Europe, prosperous and growing, with the world's first underground subway. Its literacy rate was over 90%. More than 25% of the population was Jewish, including the von Neumanns, although John von Neumann paid little attention to his Jewishness except as a source of jokes.
He was by no means the only famous product of pre-World War I Budapest. Among his contemporaries were famous physicists like himself-Leo Szilard and Edward Teller-as well as celebrities from the world of entertainment-George Solti, Paul Lukas, Leslie Howard (born Lazlo Steiner), Adolph Zukor, Alexander Korda, and, perhaps most famous of all, ZsaZsa Gabor.
Von Neumann studied in Berlin at a leading scientific institution that had considered Einstein unqualified for a research grant.' He went on to Gottingen, where he met such distinguished scientists as Werner Heisenberg, Enrico Fermi, and Robert Oppenheimer. During his first visit to the United States, in 1929, von Neumann fell in love with the country and spent most of his subsequent career, except for extended periods working for the U.S. government, at the Institute for Advanced Study in Princeton. His starting salary at the Institute in 1937 was $10,000, the equivalent of over $100,000 in current purchasing power. When Einstein joined the Institute in 1933, he had asked for a salary of $3,000; he received $16,000.