Irrational Increments for the Self-Torturer

Recall that the Self-Torturer (ST) gets $10 000 for each turn of a dial that permanently increases the pain he feels for the rest of his life by a negligible amount.  Each individual increment
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Recall that the Self-Torturer (ST) gets $10 000 for each turn of a dial that permanently increases the pain he feels for the rest of his life by a negligible amount.  Each individual increment seems worth making, the thought goes, but 1000 increments would leave ST in intense agony, which no amount of money can compensate for.It seems intuitively clear to me that ST would soon reach a point at which additional increments -- even considered in isolation -- are not worth it.For example, if one hundred equal increments yielding 100x pain for $100y are collectively not worth it, then the badness of 100x pain outweighs the value of $100y.  On average, then, the harm of x outweighs the benefit of y, over the 100 increments. If the increments are all of equal net value, then each increment is of negative net value, and hence irrational to choose.  If instead we allow that the first few increments were worth the money (due perhaps to the diminishing marginal utility of. . .

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