Thinking and Deciding

EXPECTED-UTILITY THEORY 239
Table 10.1: Decision table for Pascal’s wager
State of the world
Option God exists God does not exist
Live Christian life Saved (very good) Small inconvenience
Live otherwise Damned (very bad) Normal life
not exist, and if you live the Christian life, you lose at most a little worldly pleasure
compared to what you would get otherwise. The basic argument was that the expectation
of living the Christian life was higher than that of living otherwise, almost
without regard to the probability of God’s existence. Not to live the Christian life is
to take a risk of an eternity in hell, in exchange for a little extra worldly pleasure.
The expected utility of this choice is low.
We can express this situation in table form (Table 10.1). If we wanted to assign
numerical values to the various utilities expressed in the table, we could assign them
using an appropriate scale. For this table we could assume, for example, that the
utility of a “normal life” is 0; the utility of a small inconvenience is a small negative
number; the utility of being damned is a large negative number; and the utility of
being saved is a large positive number.
Zero utility can be assigned to any one of the outcomes (it does not matter which);
this then becomes our reference point. For example, in the table, we could assign a
utility of 0 to “normal life” and a small negative number to “small inconvenience,”
or we could assign 0 to “small inconvenience” and a positive number to “normal
life.” Likewise, the units of utility are arbitrary, but once we choose a unit, we
must stick with it. We could take the difference between “normal life” and “small
inconvenience” as our unit, or we could, just as reasonably, call that ten units.
In these respects, the measurement of utility resembles the measurement of longitude
on the earth’s surface. We take zero longitude to be the position of the observatory
at Greenwich, England, but we could just as well take it to be Greenwich,
Connecticut. Nothing in nature prefers one to the other. And we define the unit
of longitude as a degree, but we could also define it as a radian, or a mile on the
equator. We would still have a scale of longitude. The measurement of utility is unlike
the measurement of length or weight, where there is only one natural zero point
(although the units are still arbitrary). Of course, once we choose a zero point and
a unit, we must stick with them when we compare things. Utility is like longitude
in another way. Both are human inventions imposed on reality for our own convenience.
Neither existed before we invented them. We use longitude for navigation,
et cetera, and we use utility for evaluating choices.
The concepts and relationships displayed in tables of this sort lie at the heart of
most utility analyses of decisions that must be made under uncertainty. Given our
limited ability to predict the future, this includes most decisions. The outcome de-