scal's mugging is a thought-experiment demonstrating a problem in expected utility maximization. A rational agent should choose actions whose outcomes, when weighed by their probability, have higher utility. But some very unlikely outcomes may have very great utilities, and these utilities can grow faster than the probability diminishes. Hence the agent should focus more on vastly improbable cases with implausibly high rewards; this leads first to counter-intuitive choices, and then to incoherence as the utility of every choice becomes unbounded.

the Repugnant Conclusion is stated as follows: “For any possible population of at least ten billion people, all with a very high quality of life, there must be some much larger imaginable population whose existence, if other things are equal, would be better even though its members have lives that are barely worth living” (Parfit 1984).

The Repugnant Conclusion highlights a problem in an area of ethics which has become known as population ethics.

Parfit finds the Repugnant Conclusion unacceptable and many philosophers agree. However, it has been surprisingly difficult to find a theory that avoids the Repugnant Conclusion without implying other equally counterintuitive conclusions.

straightforward way of capturing the No-Difference View is total utilitarianism according to which the best outcome is the one in which there would be the greatest quantity of whatever makes life worth living (Parfit 1984 p. 387). However, this view implies that any loss in the quality of lives in a population can be compensated for by a sufficient gain in the quantity of a population; that is, it leads to the Repugnant Conclusion.

2.1.1 The average principle One proposal that easily comes to mind when faced with the Repugnant Conclusion is to reject total utilitarianism in favor of a principle prescribing that the average welfare per life in a population is maximized.

2.1.2 Variable value principles An attempt to produce a compromise between a total principle and an average principle is provided by a variable value principle. The idea behind this view is that the value of adding worthwhile lives to a population varies with the number of already existing lives in such a way that it has more value when the number of these lives is small than when it is large (Hurka 1983, Ng 1989; Sider 1991).

More exactly, Ng’s theory implies the “Sadistic Conclusion” (Arrhenius 2000a): For any number of lives with any negative welfare (e.g. tormented lives), there are situations in which it would be better to add these lives rather than some number of lives with positive welfare.

Roughly, the arguments share the following structure: in comparison between three population scenarios the second scenario is considered better than the first and the third better than the second, leading to the conclusion that the third scenario is better than the first. By iterated application of this line of reasoning one ends up with the Repugnant Conclusion (that Z is better than A). One of the more radical approaches to such arguments has been to reject the transitivity of the relation “better than” (or “equally as good as”). According to transitivity, if p is better than q, and q is better than r, then p is better than r. However, if transitivity of “better than” is denied then the reasoning leading the Repugnant Conclusion is blocked (Temkin 1987, 2012; Persson 2004; Rachels 2004).

Fred Feldman has proposed a desert-adjusted version of utilitarianism, ‘justicism’ which he claims avoids the Repugnant Conclusion (Feldman 1997). In justicism, the value of an episode of pleasure is determined not only by the hedonic level but also by the recipient’s desert level. Feldman’s proposal is that there is some level of happiness that people deserve merely in virtue of being people. He assumes that this level corresponds to 100 units of pleasure and that people with very low welfare enjoy only one unit of pleasure. He suggests that the life of a person who deserves 100 units of pleasure and receives exactly that amount of pleasure has an intrinsic value of 200, whereas the life of a person deserving 100 units but who only receives one unit of pleasure has an intrinsic value of −49. It follows that any population consisting of people with very low welfare and desert level 100 has negative value, whereas any population with very high welfare has positive value.

It has been held that it can be proven that there is no population ethics that satisfies a set of apparently plausible adequacy conditions on such a theory. In fact, several such proofs have been suggested (Arrhenius 2000b, 2011). What such a theorem would show about ethics is not quite clear. Arrhenius has suggested that an impossibility theorem leaves us with three options: (1) to abandon some of the conditions on which the theorem is based; (2) to become moral sceptics; or (3) to try to explain away the significance of the proofs—alternatives which do not invite an easy choice (cf. Temkin 2012).

When confronted with the Repugnant Conclusion, many share the view that the conclusion is highly counterintuitive. However, it has been suggested that it is premature to conclude from this that the conclusion is morally unacceptable.