In this matrix there are two states of the world (possible ways that the world might be),
one in which God exists and one in which God does not exist; and two acts (choices
available to the agent), whether to bring about belief or not. Given that the outcomes
associated with the acts have the relations F1 >> F3, and F2 is at least as good as F4,
belief weakly dominates not believing.^5 Because nowhere in passage 680 does Pascal
suggest that nonbelief results in hell, or in an infinite disutility, if God exists, no great
disvalue has been assigned to F3. The argument from dominance proceeds as follows:
- For any person S, if one of the alternatives, α, available to S has an outcome better than
the outcomes of the other available alternatives, and never an outcome worse than the
others, S should choose α. And, - Believing in God is better than not believing if God exists, and is no worse if God does
not exist.^6
Therefore,
C. One should believe in God.
This first wager is an example of a decision under uncertainty. Whenever one deliberates
with knowledge of the outcomes but no knowledge of the probabilities associated with
those outcomes, one faces a decision under uncertainty. On the other hand, if one
deliberates armed with knowledge of both the outcomes and the probabilities associated
with those outcomes, one faces a decision under risk.
Typically, decisions under risk require an “objective evidential basis for estimating
probabilities, for example, relative frequencies, or actuarial tables, or the relative
strengths of the various propensities of things (states of affairs) that affect the outcome”
(Rawls 2001, 106). With decisions under uncertainty no such basis is available. Given
Pascal's claim that “if there is a god, he is infinitely incomprehensible to uswe are
incapable, therefore, of knowing either what He is or if
end p.173
He is” (1995, 153), it is not surprising that his first version of the wager is a decision
under uncertainty.