Against the Gods: The Remarkable Story of Risk (37 page)

The trick is to be flexible enough to recognize that regression to
the mean is only a tool; it is not a religion with immutable dogma and
ceremonies. Used to make mechanical extrapolations of the past, as President Hoover or my older associates used it, regression to the
mean is little more than mumbo jumbo. Never depend upon it to
come into play without constantly questioning the relevance of the
assumptions that support the procedure. Francis Galton spoke wisely
when he urged us to "revel in more comprehensive views" than the
average.

'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.