Faustian bargain is paying a finite amount of pleasure with an infinite amount of pain. Contrary to the Pascal bargain (wager) where he is purchasing the infinite amount of pleasure with a finite amount of pain.
In fact, Pascal tries to switch between the infinite amount of pain and the infinite amount of pleasure with some finite effort. What is the essence of the Christianity.
In fact, Pascal tries to switch between the infinite amount of pain and the infinite amount of pleasure with some finite effort. What is the essence of the Christianity.
A Christian would reply that it's explained by God doing a token gesture of respect for Man's free will, carrying out almost all of the (unfathomable) work of absolving a soul's sins, but stopping His hand just in time to require the sinner to acknowledge their salvation.
I was reading TV Tropes on Hell, and it occurred to me: If your discounting was sufficiently hyperbolic, or indeed plain exponential with a low enough time preference, it would in some sense be rational to take a literal Faustian bargain. The integral to infinite time of some constant amount of torture per unit time, discounted exponentially or hyperbolically, is finite; enough worldly power and pleasure would outweight it.
But this clashes rather strongly with my intuition. Notice that the argument doesn't depend on hyperbolic discounting; no preference pumping is involved. It works just fine with exponentials and a high decay constant. Or, if the worldly pleasures were strong enough, a low decay constant, that is, a high time preference, such as (I assume) most LWers have. For example, would you take eternal torture for a guarantee of living until the heat-death of the universe, 10^130 years from now, with all the refinements of Fun Theory along the way? Intuition says no, infinity being infinity, but then again intuition is notoriously bad at dealing with very large and very small numbers. If I calculate the thing in time-discounted utilons, it seems to me that my decay constant has to be very tiny indeed for me to care about what happens at the end of *10^130* years.
So should I discard my intuition, and take such a bargain if Mephistopheles should suddenly turn up? (Noting that in 10^130 years, I might learn a thing or two about getting out of such difficulties...) Or alternatively, should I stop discounting future utilons?