Put schematically:
- For any person S, and alternatives, α and β, available to S, if α carries a greater
expected utility than does β, S should choose α. And, - Given that the existence of God is as likely as not, the expected utility of believing in
God infinitely exceeds that of not believing. Therefore,
C. One should believe in God.
Hacking asserts that the assumption of equal chance is “monstrous.” Perhaps it is. The
beautiful thing about infinite utility, though, is that infinity multiplied by any finite value
is still infinite. The assumption that the existence of God is just as likely as not is
needlessly extravagant, for, as long as the existence of God is judged to be greater than
zero, believing will always carry an expected utility greater than that carried by
nonbelief. And this is true no matter the value or disvalue associated with the outcomes
F2, F3, and F4. This observation underlies the third version of the wager, which Hacking
titles the “argument from dominating expectation.” In this version, p represents an
indeterminate positive probability greater than zero and less than one-half: