Against the Gods: The Remarkable Story of Risk by Peter L. Bernstein Page A
Authors: Peter L. Bernstein
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path to a decision-a choice in which the value of the outcome and the likelihood that it may occur will differ because the consequences of the two outcomes are different.*
If God is not, whether you lead your life piously or sinfully is immaterial. But suppose that God is. Then if you bet against the existence of God by refusing to live a life of piety and sacraments you run the risk of eternal damnation; the winner of the bet that God exists has the possibility of salvation. As salvation is clearly preferable to eternal damnation, the correct decision is to act on the basis that God is. "Which way should we incline?" The answer was obvious to Pascal.
Pascal produced an interesting by-product when he decided to turn over the profits from his bus line to help support the Port-Royal monastery.20 In 1662, a group of his associates at the monastery published a work of great importance, La logique, ou fart de penser (Logic, or the Art of Thinking), a book that ran to five editions between 1662 and 1668.t Although its authorship was not revealed, the primary-but not the sole-author is believed to have been Antoine Arnauld, a man characterized by Hacking as "perhaps the most brilliant theologian of his time."21 The book was immediately translated into other languages throughout Europe and was still in use as a textbook in the nineteenth century.
The last part of the book contains four chapters on probability that cover the process of developing a hypothesis from a limited set of facts; today, this process is called statistical inference. Among other matters, these chapters contain a "rule for the proper use of reason in determining when to accept human authority," rules for interpreting miracles, a basis of interpreting historical events, and the application of numerical measures to probability.22
The final chapter describes a game in which each of ten players risks one coin in the hope of winning the nine coins of his fellow players. The author then points out that there are "nine degrees of probability of losing a coin for only one of gaining nine."23 Though the observation is innocuous, the sentence has earned immortality. According to
Hacking, this is the first occasion in print "where probability, so called,
is measured.""
The passage deserves immortality for more reasons than that. The
author admits that the games he has described are trivial in character,
but he draws an analogy to natural events. For example, the probability of being struck by lightning is tiny but "many people ... are excessively terrified when they hear thunder. "25 Then he makes a critically
important statement: "Fear of harm ought to be proportional not
merely to the gravity of the harm, but also to the probability of the
event."26 Here is another major innovation: the idea that both gravity
and probability should influence a decision. We could turn this assertion around and state that a decision should involve the strength of our
desire for a particular outcome as well as the degree of our belief about
the probability of that outcome.
The strength of our desire for something, which came to be known
as utility, would soon become more than just the handmaiden of probability. Utility was about to take its place at the center of all theories of
decision-making and risk-taking. It will reappear repeatedly in the
chapters ahead.
Historians are fond of referring to near-misses-occasions when
something of enormous importance almost happened but, for one reason or another, failed to happen. The story of Pascal's Triangle is a
striking example of a near-miss. We have seen how to predict the probable number of boys or girls in a multi-child family. We have gone
beyond that to predict the probable outcome of a World Series (for
evenly matched teams) after part of the Series has been played.
In short, we have been forecasting! Pascal and Fermat held the key
to a systematic method for calculating the probabilities of future events.
Even
If God is not, whether you lead your life piously or sinfully is immaterial. But suppose that God is. Then if you bet against the existence of God by refusing to live a life of piety and sacraments you run the risk of eternal damnation; the winner of the bet that God exists has the possibility of salvation. As salvation is clearly preferable to eternal damnation, the correct decision is to act on the basis that God is. "Which way should we incline?" The answer was obvious to Pascal.
Pascal produced an interesting by-product when he decided to turn over the profits from his bus line to help support the Port-Royal monastery.20 In 1662, a group of his associates at the monastery published a work of great importance, La logique, ou fart de penser (Logic, or the Art of Thinking), a book that ran to five editions between 1662 and 1668.t Although its authorship was not revealed, the primary-but not the sole-author is believed to have been Antoine Arnauld, a man characterized by Hacking as "perhaps the most brilliant theologian of his time."21 The book was immediately translated into other languages throughout Europe and was still in use as a textbook in the nineteenth century.
The last part of the book contains four chapters on probability that cover the process of developing a hypothesis from a limited set of facts; today, this process is called statistical inference. Among other matters, these chapters contain a "rule for the proper use of reason in determining when to accept human authority," rules for interpreting miracles, a basis of interpreting historical events, and the application of numerical measures to probability.22
The final chapter describes a game in which each of ten players risks one coin in the hope of winning the nine coins of his fellow players. The author then points out that there are "nine degrees of probability of losing a coin for only one of gaining nine."23 Though the observation is innocuous, the sentence has earned immortality. According to
Hacking, this is the first occasion in print "where probability, so called,
is measured.""
The passage deserves immortality for more reasons than that. The
author admits that the games he has described are trivial in character,
but he draws an analogy to natural events. For example, the probability of being struck by lightning is tiny but "many people ... are excessively terrified when they hear thunder. "25 Then he makes a critically
important statement: "Fear of harm ought to be proportional not
merely to the gravity of the harm, but also to the probability of the
event."26 Here is another major innovation: the idea that both gravity
and probability should influence a decision. We could turn this assertion around and state that a decision should involve the strength of our
desire for a particular outcome as well as the degree of our belief about
the probability of that outcome.
The strength of our desire for something, which came to be known
as utility, would soon become more than just the handmaiden of probability. Utility was about to take its place at the center of all theories of
decision-making and risk-taking. It will reappear repeatedly in the
chapters ahead.
Historians are fond of referring to near-misses-occasions when
something of enormous importance almost happened but, for one reason or another, failed to happen. The story of Pascal's Triangle is a
striking example of a near-miss. We have seen how to predict the probable number of boys or girls in a multi-child family. We have gone
beyond that to predict the probable outcome of a World Series (for
evenly matched teams) after part of the Series has been played.
In short, we have been forecasting! Pascal and Fermat held the key
to a systematic method for calculating the probabilities of future events.
Even
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