[...] where infinite rewards are at stake, we need to expand upon our account of rationality. The natural way to do it is this: So if there's some number, n, such that if we set the value of the infinite reward at n, then the expected value of a particular option is greater than the expected value of all other options. And furthermore, if we set the value of the infinite reward at any finite number higher than n, then the expected value of that same option comes out as higher than the expected value of all other options. Then we rationally ought to take that first option.
[Prof Hare doesn't verbalise the following, which is only depicted in the video]:
Rational Behavior When An Outcome of Infinite Value is at Stake
It is rational for you to take an option when there is a finite number n, such that, if we assign any value n or higher to the outcome that is of infinite value, then that option has highest expected value.
It's a bit of a complicated idea, but it gives us the right results, which is that you ought to take the certain eternity of a heaven, over the 1/6 of a chance of eternity in heaven. And it gives us a response to these Many Gods, Weird Gods, Punitive Gods, Generous Gods, objections to Pascal's Wager. Because [...], just so long as you think it's very slightly more likely that you'll get eternity in heaven if you believe in a particular kind of god, (rather than doing anything else, believing in another kind of god or not believing in God,) then that is rationally what you ought to be doing. [...]
I don't understand the above. The bold requires you to assign some finite value to an outcome of infinite value, but how is this possible? Both (1 × ∞) and (1/6 × ∞) = ∞ .
2. How does assignment of value help? Instinctively, one would just assign the highest value to whatever one desires subjectivity. So this lack of objectivity is biased and self-defeating.