Against the Gods

The Remarkable Story of Risk

Peter L. Bernstein

• Publisher: Wiley
• Year: 2012
• Print ISBN: 9780471295631, 9780471121046
• eBook ISBN: 9780470534533
• Edition: 1
• Topic: Business
• Subtopic: Investments & Securities
• Index: Business

A Business Week, New York Times Business, and USA Today Bestseller "Ambitious and readable... an engaging introduction to the oddsmakers, whom Bernstein regards as true humanists helping to release mankind from the choke holds of superstition and fatalism."
— The New York Times "An extraordinarily entertaining and informative book."
— The Wall Street Journal "A lively panoramic book... Against the Gods sets up an ambitious premise and then delivers on it."
— Business Week "Deserves to be, and surely will be, widely read."
— The Economist "[A] challenging book, one that may change forever the way people think about the world."
— Worth "No one else could have written a book of such central importance with so much charm and excitement."
— Robert Heilbroner author, The Worldly Philosophers "With his wonderful knowledge of the history and current manifestations of risk, Peter Bernstein brings us Against the Gods. Nothing like it will come out of the financial world this year or ever. I speak carefully: no one should miss it."
— John Kenneth Galbraith Professor of Economics Emeritus, Harvard University In this unique exploration of the role of risk in our society, Peter Bernstein argues that the notion of bringing risk under control is one of the central ideas that distinguishes modern times from the distant past. Against the Gods chronicles the remarkable intellectual adventure that liberated humanity from oracles and soothsayers by means of the powerful tools of risk management that are available to us today. "An extremely readable history of risk."
— Barron's "Fascinating... this challenging volume will help you understand the uncertainties that every investor must face."
— Money "A singular achievement."
— Times Literary Supplement "There's a growing market for savants who can render the recondite intelligibly-witness Stephen Jay Gould (natural history), Oliver Sacks (disease), Richard Dawkins (heredity), James Gleick (physics), Paul Krugman (economics)-and Bernstein would mingle well in their company."
— The Australian

1700–1900: MEASUREMENT UNLIMITED

Chapter 6
Considering the Nature of Man

In just a few years the commanding mathematical achievements of Cardano and Pascal had been elevated into domains that neither had dreamed of. First Graunt, Petty, and Halley had applied the concept of probability to the analysis of raw data. At about the same time, the author of the Port-Royal Logic had blended measurement and subjective beliefs when he wrote, “Fear of harm ought to be proportional not merely to the gravity of the harm, but also to the probability of the event.”

In 1738, the Papers of the Imperial Academy of Sciences in St. Petersburg carried an essay with this central theme: “the value of an item must not be based on its price, but rather on the utility that it yields.”¹ The paper had originally been presented to the Academy in 1731, with the title Specimen Theoriae Novae de Mensura Sortis (Exposition of a New Theory on the Measurement of Risk); its author was fond of italics, and all three of the italicized words in the above quotation are his.^a So are all those in the quotations that follow.

It is pure conjecture on my part that the author of the 1738 article had read the Port-Royal Logic, but the intellectual linkage between the two is striking. Interest in Logic was widespread throughout western Europe during the eighteenth century.

Both authors build their arguments on the proposition that any decision relating to risk involves two distinct and yet inseparable elements: the objective facts and a subjective view about the desirability of what is to be gained, or lost, by the decision. Both objective measurement and subjective degrees of belief are essential; neither is sufficient by itself.

Each author has his preferred approach. The Port-Royal author argues that only the pathologically risk-averse make choices based on the consequences without regard to the probability involved. The author of the New Theory argues that only the foolhardy make choices based on the probability of an outcome without regard to its consequences.

The author of the St. Petersburg paper was a Swiss mathematician named Daniel Bernoulli, who was then 38 years old.² Although Daniel Bernoulli’s name is familiar only to scientists, his paper is one of the most profound documents ever written, not just on the subject of risk but on human behavior as well. Bernoulli’s emphasis on the complex relationships between measurement and gut touches on almost every aspect of life.

Daniel Bernoulli was a member of a remarkable family. From the late 1600s to the late 1700s, eight Bernoullis had been recognized as celebrated mathematicians. Those men produced what the historian Eric Bell describes as “a swarm of descendants . . . and of this posterity the majority achieved distinction—sometimes amounting to eminence—in the law, scholarship, literature, the learned professions, administration and the arts. None were failures.”³

The founding father of this tribe was Nicolaus Bernoulli of Basel, a wealthy merchant whose Protestant forebears had fled from Catholic-dominated Antwerp around 1585. Nicolaus lived a long life, from 1623 to 1708, and had three sons, Jacob, Nicolaus (known as Nicolaus I), and Johann. We shall meet Jacob again shortly, as the discoverer of the Law of Large Numbers in his book Ars Conjectandi {The Art of Conjecture). Jacob was both a great teacher who attracted students from all over Europe and an acclaimed genius in mathematics, engineering, and astronomy. The Victorian statistician Francis Galton describes him as having “a bilious and melancholic temperament. . . sure but slow.”⁴ His relationship with his father was so poor that he took as his motto Invito patre sidera verso—”I am among the stars in spite of my father.”⁵

Galton did not limit his caustic observations to Jacob. Despite the evidence that the Bernoulli family provided in confirmation of Galton’s theories of eugenics, he depicts them in his book, Hereditary Genius as “mostly quarrelsome and jealous.”⁶

These traits seem to have run through the family. Jacob’s younger brother and fellow-mathematician Johann, the father of Daniel, is described by James Newman, an anthologist of science, as “violent, abusive . . . and, when necessary, dishonest.”^b7 When Daniel won a prize from the French Academy of Sciences for his work on planetary orbits, his father, who coveted the prize for himself, threw him out of the house. Newman reports that Johann lived to be 80 years old, “retaining his powers and meanness to the end.”

And then there was the son of the middle brother, Nicolaus I, who is known as Nicolaus II. When Nicolaus II’s uncle Jacob died in 1705 after a long illness, leaving The Art of Conjecture all but complete, Nicolaus II was asked to edit the work for publication even though he was only 18 at the time. He took eight years to finish the task! In his introduction he confesses to the long delay and to frequent prodding by the publishers, but he offers as an excuse of “my absence on travels” and the fact that “I was too young and inexperienced to know how to complete it.”⁸

Perhaps he deserves the benefit of the doubt: he spent those eight years seeking out the opinions of the leading mathematicians of his time, including Isaac Newton. In addition to conducting an active correspondence for the exchange of ideas, he traveled to London and Paris to consult with outstanding scholars in person. And he made a number of contributions to mathematics on his own, including an analysis of the use of conjecture and probability theory in applications of the law.

To complicate matters further, Daniel Bernoulli had a brother five years older than he, also named Nicolaus; by convention, this Nicolaus is known as Nicolaus III, his grandfather being numberless, his uncle being Nicolaus I, and his elder first cousin being Nicolaus II. It was Nicolaus III, a distinguished scholar himself, who started Daniel off in mathematics when Daniel was only eleven years old. As the oldest son, Nicolaus III had been encouraged by his father to become a mathematician. When he was only eight years old, he was able to speak four languages; he became Doctor of Philosophy at Basel at the age of nineteen; and he was appointed Professor of Mathematics at St. Petersburg in 1725 at the age of thirty. He died of some sort of fever just a year later.

Daniel Bernoulli received an appointment at St. Petersburg in the same year as Nicolaus III and remained there until 1733, when he returned to his hometown of Basel as Professor of Physics and Philosophy. He was among the first of many outstanding scholars whom Peter the Great would invite to Russia in the hope of establishing his new capital as a center of intellectual activity. According to Galton, Daniel was “physician, botanist, and anatomist, writer on hydrodynamics; very precocious.”⁹ He was also a powerful mathematician and statistician, with a special interest in probability.

Bernoulli was very much a man of his times. The eighteenth century came to embrace rationality in reaction to the passion of the endless religious wars of the past century. As the bloody conflict finally wound down, order and appreciation of classical forms replaced the fervor of the Counter-Reformation and the emotional character of the baroque style in art. A sense of balance and respect for reason were hallmarks of the Enlightenment. It was in this setting that Bernoulli transformed the mysticism of the Fort-Royal Logic into a logical argument addressed to rational decision-makers.

Daniel Bernoulli’s St. Petersburg paper begins with a paragraph that sets forth the thesis that he aims to attack:

Ever since mathematicians first began to study the measurement of risk, there has been general agreement on the following proposition: Expected values are computed by multiplying each possible gain by the number of ways in which it can occur, and then dividing the sum of these products by the total number of cases.^c,10

Bernoulli finds this hypothesis flawed as a description of how people in real life go about making decisions, because it focuses only on the facts; it ignores the consequences of a probable outcome for a person who has to make a decision when the future is uncertain. Price—and probability—are not enough in determining what something is worth. Although the facts are the same for everyone, “the utility . . . is dependent on the particular circumstances of the person making the estimate . . . . There is no reason to assume that . . . the risks anticipated by each [individual] must be deemed equal in value.” To each his own.

The concept of utility is experienced intuitively. It conveys the sense of usefulness, desirability, or satisfaction. The notion that arouses Bernoulli’s impatience with mathematicians—”expected value”—is more technical. As Bernoulli points out, expected value equals the sum of the values of each of a number of outcomes multiplied by the probability of each outcome relative to all the other possibilities. On occasion, mathematicians still use the term “mathematical expectation” for expected value.

A coin has two sides, heads and tails, with a 50% chance of landing with one side or the other showing—a coin cannot come up showing both heads and tails at the same time. What is the expected value of a coin toss? We multiply 50% by one for heads and do the same for tails, take the sum—100%—and divide by two. The expected...

Table of contents

• Cover
• Table of Contents
• Series
• Title
• Copyright
• Dedication
• Acknowledgments
• Introduction
• To 1200: Beginnings
• 1200–1700: A Thousand Outstanding Facts
• 1700–1900: Measurement Unlimited
• 1900–1960: Clouds of Vagueness and The Demand for Precision
• Degrees of Belief: Exploring Uncertainty
• Bibliography
• Name Index
• Subject Index
• End User License Agreement