Game Development Reference
In-Depth Information
Pascal's Strictly Dominant Strategy
Looking at those potential outcomes, the strictly dominating strategy is not very
coy. In fact, it kinda jumps right out at you. If we live well, the possibilities are +
∞
and -0. If we do not, our payouts are -
∞
and +0. Again, no matter what the prob-
ability of the fact that God exists—even if it is a 1% chance, we come out ahead by
living
as if
God exists. (1% of infinite happy stuff beats 1% of infinite nastiness.)
When you combine it with Pascal's premise that you gain and lose nothing if God
doesn't exist, the solution is obvious.
However, much of the controversy surrounding Pascal's Wager stems from
that last point. Pascal treated the two lifestyles in question as being equal. If they
were not, Pascal could not have made the claim that you gain nothing and lose
nothing if God does not exist. Apparently, Mr. P. found neither appeal in the ben-
efits of loose living, nor restriction in the relatively conservative nature of piety. For
all intents and purposes, the two rows of that decision matrix are no different in any
sense
other
than as it applies to the question of eternal life.
Much like the blanket assumptions that were made in the Prisoner's Dilemma
about how awful jail is, for Pascal's argument to be meaningful, we need to accept
his views on a number of counts. What do we gain or lose by living in a Godly fash-
ion? Exactly what does that mean for us? What are our “utility� values for lying,
cheating, drinking beer, swearing profusely, and kicking puppies? For that matter,
what are our views on the nature of Heaven and Hell? Do we have a way of quanti-
fying our preferences for the proffered trappings of those two afterlife extremes? If
we change those ideas based on our utility values, we also must change the payout
matrix. This can occur even to the point where what we may believe a priori about
whether God exists or not may come back into play much like we had to begin con-
sidering what our partner would do in the Prisoner's Dilemma.
What we must realize here is that the simple matrix is not so simple once we
begin questioning the inputs themselves. Again, while the basics of decision theory
can be expressed in such an uncomplicated manner, it also provides numerous
hooks upon which we can attach more interesting and expressive statements. And
when we do so, we inch ever closer on our quest for “interesting decisions.�
N
O
P
AIN
, N
O
G
AIN
Pascal cautioned us that we must know what is being wagered before we can make
a decision. However, while that is certainly valid and wise, that is really only part of
the issue. The other side to the equation when making a decision under risk is that
we have to have a good idea of
why
we are risking.
