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we can write the utilities from both outcomes as an inequality. the sophomoric utilitarian might simply write this as utils from current world on the left side, and utils from current world + utils from erasing unhappiness - utils of perpetual suffering.
however, this model neglects something very important. advanced utilitarians may realize we are lacking the probability of masochism. indeed, some people may actually enjoy this eternal suffering. current studies estimate that 1-5% of the population are masochists. we will take the average as 3% of the population being masochists. assume that torture for the median human is more painful than it is pleasurable for the masochists.

following conventions, we assign median human -1000 util/time and the masochist +100 util/time. we can then rewrite the right side of the inequality as follows

utils from current world + utils from eliminating unhappiness - ( 1000 utils/time)(0.97)(infinity (time) ) + (100 utils /time) (0.03)(infinity (time)).

we can then reduce the infinity terms to simply infinity as infinity times any number is equal to infinity. the infinities cancel, and we are left with

utils from current world + utils from eliminating unhappiness

which is necessarily bigger than the left side utils from current world.

therefore, we push the button.

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