We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

Is the overall value of a world just the sum of values contributed by each value-bearing entity in that world? Additively separable axiologies (like total utilitarianism, prioritarianism, and critical level views) say 'yes', but non-additive axiologies (like average utilitarianism, rank-discounted utilitarianism, and variable value views) say 'no'. This distinction is practically important: additive axiologies support 'arguments from astronomical scale' which suggest (among other things) that it is overwhelmingly important for humanity to avoid premature extinction and ensure the existence of a (...) large future population, while non-additive axiologies need not. We show, however, that when there is a large enough 'background population' unaffected by our choices, a wide range of non-additive axiologies converge in their implications with some additive axiology -- for instance, average utilitarianism converges to critical-level utilitarianism and various egalitarian theories converge to prioritiarianism. We further argue that real-world background populations may be large enough to make these limit results practically significant. This means that arguments from astronomical scale, and other arguments in practical ethics that seem to presuppose additive separability, may be truth-preserving in practice whether or not we accept additive separability as a basic axiological principle. (shrink)

Is the overall value of a world just the sum of values contributed by each value-bearing entity in that world? Additively separable axiologies (like total utilitarianism, prioritarianism, and critical level views) say 'yes', but non-additive axiologies (like average utilitarianism, rank-discounted utilitarianism, and variable value views) say 'no'. This distinction appears to be practically important: among other things, additive axiologies generally assign great importance to large changes in population size, and therefore tend to strongly prioritize the long-term survival of humanity over (...) the interests of the present generation. Non-additive axiologies, on the other hand, need not assign great importance to large changes in population size. We show, however, that when there is a large enough `background population' unaffected by our choices, a wide range of non-additive axiologies converge in their implications with additive axiologies—for instance, average utilitarianism converges with critical-level utilitarianism and various egalitarian theories converge with prioritarianism. We further argue that real-world background populations may be large enough to make these limit results practically significant. This means that arguments from the scale of potential future populations for the astronomical importance of avoiding existential catastrophe, and other arguments in practical ethics that seem to presuppose additive separability, may succeed in practice whether or not we accept additive separability as a basic axiological principle. (shrink)