'p to now, our story has focused on theories about probability and on ingenious ways of measuring it: Pascal's Triangle, Jacob Bernoulli's search for moral certainty in his jar of black and white balls, Bayes's billiard table, Gauss's bell curve, and Galton's Quincunx. Even Daniel Bernoulli, delving for perhaps the first time into the psychology of choice, was confident that what he called utility could be measured.

Now we turn to an exploration of a different sort: Which risks should we take, which risks should we hedge, what information is relevant? How confidently do we hold our beliefs about the future? In short, how do we introduce management into dealing with risk?

Under conditions of uncertainty, both rationality and measurement are essential to decision-making. Rational people process information objectively: whatever errors they make in forecasting the future are random errors rather than the result of a stubborn bias toward either optimism or pessimism. They respond to new information on the basis of a clearly defined set of preferences. They know what they want, and they use the information in ways that support their preferences.

Preference means liking one thing better than another: tradeoff is implicit in the concept. That is a useful idea, but a method of measuring preferences would make it more palpable.

That was what Daniel Bernoulli had in mind when he wrote his remarkable paper in 1738, boasting, "It would be wrong to neglect [his ideas] as abstractions resting upon precarious hypotheses." Bernoulli introduced utility as the unit for measuring preferences-for calculating how much we like one thing more than another. The world is full of desirable things, he said, but the amount that people are willing to pay for them differs from one person to another. And the more we have of something, the less we are willing to pay to get more.1

Bernoulli's concept of utility was an impressive innovation, but his handling of it was one-dimensional. Today, we recognize that the desire to keep up with the Joneses may lead us to want more and more even when, by any objective standard of measurement, we already have enough. Moreover, Bernoulli built his case on a game in which Paul wins the first time Peter's coin comes up heads, but Paul loses nothing when Peter's coin comes up tails. The word "loss" does not appear in Bernoulli's paper, nor did it appear in works on utility theory for another two hundred years. Once it had appeared, however, utility theory became the paradigm of choice in defining how much risk people will take in the hope of achieving some desired but uncertain gain.

Still, the power of Bernoulli's concept of utility is evident in the way his insights into "the nature of man" continue to resonate. Every advance in decision-making theory and in risk evaluation owes something to his efforts to provide definition, quantification, and guides to rational decisions.

One might expect, as a result, that the history of utility theory and decision-making would be dominated by Bernoullians, especially since Daniel Bernoulli was such a well-known scientist. Yet such is not the case: most later developments in utility theory were new discoveries rather than extensions of Bernoulli's original formulations.

Was the fact that Bernoulli wrote in Latin a problem? Kenneth Arrow has pointed out that Bernoulli's paper on a new theory of measuring risk was not translated into German until 1896, and that the first English translation appeared in an American scholarly journal as late as 1954. Yet Latin was still in common usage in mathematics well into the nineteenth century; and the use of Latin by Gauss was surely no barrier to the attention that his ideas commanded. Still, Bernoulli's choice of Latin may help explain why his accomplishments have received greater notice from mathematicians than from economists and students of human behavior.

Arrow suggests a more substantive issue. Bernoulli dealt with utility in terms of numbers, whereas later writers preferred to think of it as a preference-setter: saying "I like this better than that" is not the same as saying "This is worth x utils to me."

Utility theory was rediscovered toward the end of the eighteenth century by Jeremy Bentham, a popular English philosopher who lived from 1748 to 1832. You can still see him on special occasions at University College, London, where, under the terms of his will, his mummified body sits in a glass case with a wax head to replace the original and with his hat between his feet.

His major work, The Principles of Morals and Legislation, published in 1789, was fully in the spirit of the Enlightenment:

Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do, as well as to determine what we shall do.... The principle of utility recognizes this subjection, and assumes it for the foundation of that system, the object of which is to rear the fabric of felicity by the hands of reason and law.2

Bentham then explains what he means by utility: "... that property in any object, whereby it tends to produce benefit, advantage, pleasure, good, or happiness .... when the tendency it has to augment the happiness of the community is greater than any it has to diminish it."

Here Bentham was talking about life in general. But the economists of the nineteenth century fastened onto utility as a tool for discovering how prices result from interactive decisions by buyers and sellers. That detour led directly to the law of supply and demand.

According to the mainstream economists of the nineteenth century, the future stands still while buyers and sellers contemplate the opportunities open to them. The focus was on whether one opportunity was superior to another. The possibility of loss was not a consideration. Consequently the distractions of uncertainty and the business cycle did not appear in the script. Instead, these economists spent their time analyzing the psychological and subjective factors that motivate people to pay such-and-such an amount for a loaf of bread or for a bottle of port-or for a tenth bottle of port. The idea that someone might not have the money to buy even one bottle of port was unthinkable. Alfred Marshall, the pre-eminent economist of the Victorian age, once remarked, "No one should have an occupation which tends to make him anything less than a gentleman."3

William Stanley Jevons, a card-carrying Benthamite with a fondness for mathematics, was one of the prime contributors to this body of thought. Born in Liverpool in 1837, he grew up wanting to be a scientist. Financial difficulties, however, prompted him to take a job as assayer in the Royal Mint in Sydney, Australia, a gold-rush boom town with a population rapidly approaching 100,000. Jevons returned to London ten years later to study economics and spent most of his life there as Professor of Political Economy at University College; he was the first economist since William Petty to be elected to the Royal Society. Despite his academic title, Jevons was among the first to suggest dropping the word "political" from the phrase "political economy." In so doing, he revealed the level of abstraction toward which the discipline was moving.

Nevertheless, his masterwork, published in 1871, was titled The Theory of Political Economy.' Jevons opens his analysis by declaring that "value depends entirely upon utility." He goes on to say, "[W]e have only to trace out carefully the natural laws of the variation of utility, as depending upon the quantity of a commodity in our possession, in order to arrive at a satisfactory theory of exchange."

Here we have a restatement of Bernoulli's pivotal assertion that utility varies with the quantity of a commodity already in one's possession. Later in the book Jevons qualifies this generalization with a statement typical of a proper Victorian gentleman: "the more refined and intellectual our needs become, the less they are capable of satiety."

Jevons was confident that he had solved the question of value, claiming that the ability to express everything in quantitative terms had made irrelevant the vague generalities that had characterized economics up to that point. He brushed off the problem of uncertainty by announcing that we need simply apply the probabilities learned from past experience and observation: "The test of correct estimation of probabilities is that the calculations agree with the fact on the average. ... We make calculations of this kind more or less accurately in all the ordinary affairs of life."

Jevons takes many pages to describe earlier efforts to introduce mathematics into economics, though he makes no mention of Bernoulli. He leaves no doubt, however, about what he himself has achieved:

Previous to the time of Pascal, who would have thought of measuring doubt and belief? Who would have conceived that the investigation of petty games of chance would have led to the creation of perhaps the most sublime branch of mathematical science-the theory of probabilities?

Now there can be no doubt that pleasure, pain, labour, utility, value, wealth, money, capital, etc. are all notions admitting of quantity; nay, the whole of our actions in industry and trade certainly depend upon comparing quantities of advantage and disadvantage.

Jevons's pride in his achievements reflects the enthusiasm for measurement that characterized the Victorian era. Over time, more and more aspects of life succumbed to quantification. The explosion of scientific research in the service of the industrial revolution added a powerful impulse to that trend.

The first systematic population census in Britain had been carried out as early as 1801, and the insurance industry's use of statistics had grown more and more sophisticated throughout the century. Many right-thinking men and women turned to sociological measurement in the hope of relieving the ills of industrialization. They set out to improve life in the slums and to combat crime, illiteracy, and drunkenness among the newly poor.

Some of the suggestions for applying the measurement of utility to society were less than practical, however. Francis Edgeworth, a contemporary of Jevons and an innovative mathematical economist, went as far as to propose the development of a "hedonimeter." As late as the mid-1920s Frank Ramsay, a brilliant young Cambridge mathematician, was exploring the possibility of creating a "psychogalvanometer."

Some Victorians protested that the rush toward measurement smacked of materialism. In 1860, when Florence Nightingale, after consulting with Galton and others, offered to fund a chair in applied statistics at Oxford, her offer was flatly refused. Maurice Kendall, a great statistician and a historian of statistics, observed that "[I]t seems that our senior universities were still whispering from their towers the last enchantments of the Middle Ages... [A]fter thirty years of effort Florence gave it up."*s

But the movement to bring the social sciences to the same degree of quantification as the natural sciences grew stronger and stronger as time passed. The vocabulary of the natural sciences gradually found its way into economics. Jevons refers to the "mechanics" of utility and self-interest, for example. Concepts like equilibrium, momentum, pressure, and functions crossed from one field to the other. Today, people in the world of finance use terms like financial engineering, neural networks, and genetic algorithms.

One other aspect ofJevons's work as an economist deserves mention. As a man trained in the natural sciences, he could not avoid taking note of what was right in front of his face-the economy did fluctuate. In 1873, just two years after the publication of The Theory of Political Economy, a great economic boom that had lasted for over twenty years in Europe and the United States came to an end. Business activity fell steadily for three years, and recovery was slow to come. Industrial production in the United States in 1878 was only 6% higher than it had been in 1872. Over the next 23 years, the prices of U.S. goods and services fell almost uninterruptedly by some 40%, creating much hardship throughout western Europe and North America.

Did this devastating experience cause Jevons to question whether the economic system might be inherently stable at optimal levels of output and employment, as Ricardo and his followers had promised? Not in the least. Instead, he came up with a theory of business cycles based on the influence of sunspots on weather, of weather on harvests, and of harvests on prices, wages, and the level of employment. For Jevons, the trouble with the economy was in heaven and earth, not in its philosophy.

Theories of how people make decisions and choices seem to have become detached from everyday life in the real world. Yet those theo ries prevailed for nearly a hundred years. Even well into the Great Depression, the notion persisted that economic fluctuations were accidents of some kind rather than events inherent in an economic system driven by risk-taking. Hoover's promise in 1930 that prosperity was just around the corner reflected his belief that the Great Crash had been caused by a passing aberration rather than by some structural fault. In 1931, Keynes himself still exhibited the optimism of his Victorian upbringing when he expressed his "... profound conviction that the Economic Problem ... is nothing but a frightful muddle, a transitory and an unnecessary muddle."6 The italics are his.