Firstly, excellent post! A cool idea, well-written, and very thought-provoking. Some thoughts on the robustness of the result:
Suppose that every individual were able to produce at least 1 unit of resources throughout their life. Then total utility is monotonically increasing in the number of people, and you have the repugnant conclusion again. How likely is this supposition? Assuming we have arbitrarily advanced technology, including AI, humans will be pretty irrelevant to the production of resources like food or compute (if we’re in simulation). But plausibly humans could still produce “goods” which are valuable to other humans, like friendship. Let’s plug this into your model above and see what happens. I’ll assume that humans need at least 1/K physical resources to survive, but otherwise their utility is logarithmic in the amount of physical resources + friendship that they get. Also, assume that every person receives as much friendship as they produce. So
U=∑log(R/N+F)=Nlog(R/N+F)
, with an upper bound of N = KR. When F >= 1, then the optimal value of N is in fact KR, and so utility per person is
log(1/K+F)
, which can be arbitrarily close to 0 (depending on K). When 0 ⇐ F < 1, then I think you get something like your original result again, but I’m not sure. Empirically, I expect that the best friends can produce F >> 1, i.e. if you had nothing except just enough food/water to keep yourself alive, but also you were the sole focus of their friendship, then you’d consider your life well worth living. Idk about average production, but hopefully that’ll improve in the future too. In summary, friendship may make things repugnant :P
Here’s another version of the repugnant conclusion and your argument. Suppose that the amount of resources used by each person is roughly fixed per unit time (because, say, we’re living in simulation), but that there’s a period of infancy and early childhood which uses up resources and isn’t morally valuable. Then the resources used up by one person are I + L, where I is the length of their infancy and L is the length of the rest of their life, but the utility gained from their life is a function of L alone. What function of L? Perhaps you think that it’s linear in L—for example, If you’re a hedonic utilitarian, it’s plausible that people will be just as happy later in their life as earlier. (In fact, right now, old people tend to be happiest). If so, you must endorse the anti-repugnant conclusion, where you’d prefer a population with very few very long-lived people, to minimise the fixed cost of infancy. If you’re a preference utilitarian, maybe you think that there’s diminishing marginal utility to having your preferences satisfied. It then follows that there’s an optimal point at which to kill people, which isn’t too soon (otherwise you’re incurring high fixed costs) and isn’t too late (otherwise people’s marginal utility diminishes too much) - a conclusion which is analogous to your result.
Firstly, excellent post! A cool idea, well-written, and very thought-provoking. Some thoughts on the robustness of the result:
Suppose that every individual were able to produce at least 1 unit of resources throughout their life. Then total utility is monotonically increasing in the number of people, and you have the repugnant conclusion again. How likely is this supposition? Assuming we have arbitrarily advanced technology, including AI, humans will be pretty irrelevant to the production of resources like food or compute (if we’re in simulation). But plausibly humans could still produce “goods” which are valuable to other humans, like friendship. Let’s plug this into your model above and see what happens. I’ll assume that humans need at least 1/K physical resources to survive, but otherwise their utility is logarithmic in the amount of physical resources + friendship that they get. Also, assume that every person receives as much friendship as they produce. So
, with an upper bound of N = KR. When F >= 1, then the optimal value of N is in fact KR, and so utility per person is
, which can be arbitrarily close to 0 (depending on K). When 0 ⇐ F < 1, then I think you get something like your original result again, but I’m not sure. Empirically, I expect that the best friends can produce F >> 1, i.e. if you had nothing except just enough food/water to keep yourself alive, but also you were the sole focus of their friendship, then you’d consider your life well worth living. Idk about average production, but hopefully that’ll improve in the future too. In summary, friendship may make things repugnant :P
Here’s another version of the repugnant conclusion and your argument. Suppose that the amount of resources used by each person is roughly fixed per unit time (because, say, we’re living in simulation), but that there’s a period of infancy and early childhood which uses up resources and isn’t morally valuable. Then the resources used up by one person are I + L, where I is the length of their infancy and L is the length of the rest of their life, but the utility gained from their life is a function of L alone. What function of L? Perhaps you think that it’s linear in L—for example, If you’re a hedonic utilitarian, it’s plausible that people will be just as happy later in their life as earlier. (In fact, right now, old people tend to be happiest). If so, you must endorse the anti-repugnant conclusion, where you’d prefer a population with very few very long-lived people, to minimise the fixed cost of infancy. If you’re a preference utilitarian, maybe you think that there’s diminishing marginal utility to having your preferences satisfied. It then follows that there’s an optimal point at which to kill people, which isn’t too soon (otherwise you’re incurring high fixed costs) and isn’t too late (otherwise people’s marginal utility diminishes too much) - a conclusion which is analogous to your result.