Against the Gods: The Remarkable Story of Risk (15 page)

Pascal put together his thoughts about life and religion while he was
at Port-Royal and published them under the title Pensees.'8 In the course
of his work on that book, he filled two pieces of paper on both sides
with what Ian Hacking describes as "handwriting going in all directions
... full of erasures, corrections, and seeming afterthoughts." This fragment has come to be known as Pascal's Wager (le pari de Pascal), which
asks, "God is, or he is not. Which way should we incline? Reason cannot answer."

Here, drawing on his work in analyzing the probable outcomes of the
game of balla, Pascal frames the question in terms of a game of chance. He
postulates a game that ends at an infinite distance in time. At that moment,
a coin is tossed. Which way would you bet-heads (God is) or tails (God
is not)?

Hacking asserts that Pascal's line of analysis to answer this question
is the beginning of the theory of decision-making. "Decision theory,"
as Hacking describes it, "is the theory of deciding what to do when it
is uncertain what will happen."19 Making that decision is the essential
first step in any effort to manage risk.

Sometimes we make decisions on the basis of past experience, out of
experiments we or others have conducted in the course of our lifetime.
But we cannot conduct experiments that will prove either the existence
or the absence of God. Our only alternative is to explore the future consequences of believing in God or rejecting God. Nor can we avert the
issue, for by the mere act of living we are forced to play this game.

Pascal explained that belief in God is not a decision. You cannot
awaken one morning and declare, "Today I think I will decide to
believe in God." You believe or you do not believe. The decision,
therefore, is whether to choose to act in a manner that will lead to
believing in God, like living with pious people and following a life of
"holy water and sacraments." The person who follows these precepts is
wagering that God is. The person who cannot be bothered with that
kind of thing is wagering that God is not.

The only way to choose between a bet that God exists and a bet that
there is no God down that infinite distance of Pascal's coin-tossing game
is to decide whether an outcome in which God exists is preferablemore valuable in some sense-than an outcome in which God does not
exist, even though the probability may be only 50-50. This insight is
what conducts Pascal down the 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 though they did not turn it all the way, they inserted the key into
the lock. The significance of their pioneering work for business management, for risk management, and, in particular, for insurance was to
be seized upon by others-for whom the Port-Royal Logic was an
important first step. The idea of forecasting economic trends or of using probability to forecast economic losses was too remote for Pascal and
Fermat to have recognized what they were missing. It is only with
hindsight that we can see how close they came.

The inescapable uncertainty of the future will always prevent us from
completely banishing the fates from our hopes and fears, but after 1654
mumbo jumbo would no longer be the forecasting method of choice.

e all have to make decisions on the basis of limited data. One
sip, even a sniff, of wine determines whether the whole bottle is drinkable. Courtship with a future spouse is shorter
than the lifetime that lies ahead. A few drops of blood may evidence patterns of DNA that will either convict or acquit an accused murderer.
Public-opinion pollsters interview 2,000 people to ascertain the entire
nation's state of mind. The Dow Jones Industrial Average consists of just
thirty stocks, but we use it to measure changes in trillions of dollars of
wealth owned by millions of families and thousands of major financial
institutions. George Bush needed just a few bites of broccoli to decide
that that stuff was not for him.