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satt comments on The greatest good for the greatest number - starting soonest, or ending last, or lasting longest? - Less Wrong
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I don't think there's anything baked into Millian utilitarianism that automatically says what to do here, but then (1) there are other kinds of utilitarianism and (2) bolting the notion of time discounting onto Millian utilitarianism ought to solve the question. Compute the time integral of time-discounted goodness for each of the three greatest goods over all time, and pick the greatest good that gives the most positive answer. [Dusts hands.]
How much time does it take to compute over all time?
Depends how gnarly the functions you're integrating are. The greatest goods in the top-level post sound time-independent (except for when they start & stop); if so one just integrates exp(-rt) over different t intervals, which is extremely fast & straightforward.