It is notoriously difficult to find an intuitively satisfactory rule for evaluating populations based on the welfare of the people in them. Standard examples, like total utilitarianism, either entail the Repugnant Conclusion or in some other way contradict common intuitions about the relative value of populations. Several philosophers have presented formal arguments that seem to show that this happens of necessity: our core intuitions stand in contradiction. This paper assesses the state of play, focusing on the most powerful of these (...) ‘impossibility theorems’, as developed by Gustaf Arrhenius. I highlight two ways in which these theorems fall short of their goal: some appeal to a supposedly egalitarian condition which, however, does not properly reflect egalitarian intuitions; the others rely on a background assumption about the structure of welfare which cannot be taken for granted. Nonetheless, the theorems remain important: they give insight into the difficulty, if not perhaps the impossibility, of constructing a satisfactory population axiology. We should aim for reflective equilibrium between intuitions and more theoretical considerations. I conclude by highlighting one possible ingredient in this equilibrium, which, I argue, leaves open a still wider range of acceptable theories: the possibility of vague or otherwise indeterminate value relations. (shrink)

Suppose one sets up a sequence of less and less valuable objects such that each object in the sequence is only marginally worse than its immediate predecessor. Could one in this way arrive at something that is dramatically inferior to the point of departure? It has been claimed that if there is a radical value difference between the objects at each end of the sequence, then at some point there must be a corresponding radical difference between the adjacent elements. The (...) underlying picture seems to be that a radical gap cannot be scaled by a series of steps, if none of the steps itself is radical. We show that this picture is incorrect on a stronger interpretation of value superiority, but correct on a weaker one. Thus, the conclusion we reach is that, in some sense at least, abrupt breaks in such decreasing sequences cannot be avoided, but that such unavoidable breaks are less drastic than has been suggested. In an appendix written by John Broome and Wlodek Rabinowicz, the distinction between two kinds of value superiority is extended from objects to their attributes. (shrink)

Suppose that A and B are two kinds of goods such that more of each is better than less. A is strongly superior to B if any amount of A is better than any amount of B. It is weakly superior to B if some amount of A is better than any amount of B. There are many examples of these relations in the literature, sometimes under the labels “higher goods” and “discontinuity.” The chapter gives a precise and generalized statement (...) of Strong and Weak Superiority and discusses different ways in which these relations can be relevant to the aggregation of welfare. It also proves a number of general results. One of the results gives rise to a dilemma: It can be used as an argument against the existence of value superiority or, alternatively, as an argument against the view that superiority entails a radical difference in value. (shrink)

According to the Repugnant Conclusion: Compared with the existence of many people who would all have some very high quality of life, there is some much larger number of people whose existence would be better, even though these people would all have lives that were barely worth living. I suggest some ways in which we might be able to avoid this conclusion. I try to defend a strong form of lexical superiority.

Act Utilitarianisms divide into Total and Average versions. Total versions seem to imply Parfit’s “Repugnant Conclusion”. Average versions are proposed in part to avoid the Repugnant Conclusion, but these are subject to “Mere Addition” arguments as detailed by Hudson in “The Diminishing Marginal Value of Happy People”. Thus, various intermediate versions of utilitarianism, such as the one investigated by Hurka in “Value and Population Size”, take on interest. But Hudson argues that such compromise theories are subject to the mere addition (...) arguments, and are therefore no improvement over Average Utilitarianism. I disagree: some such compromise solutions escape Hudson’s Mere Addition arguments. (shrink)

Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations “is better than” and “is as good as”. This field has been riddled with “paradoxes” which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. Already in Derek Parfit’s seminal contribution to the topic, an informal paradox — the Mere Addition Paradox — was presented and later contributions have (...) proved similar results.1 All of these contributions, however, have one thing in common: They all involve an adequacy condition that rules out Parfit’s Repugnant Conclusion: The Repugnant Conclusion: For any perfectly equal population with very high positive welfare, there is a population with very low positive welfare which is better, other things being equal.2 A number of theorists, however, have argued that we should accept the Repugnant Conclusion and hence that avoidance of this conclusion is not a convincing adequacy condition for a population axiology. Torbjörn Tännsjö, for example, argues that the Repugnant Conclusion is not at all repugnant but rather “an unsought, but acceptable, consequence of hedonistic utilitarianism”:3.. (shrink)

A search is under way for a theory that can accommodate our intuitions in population axiology. The object of this search has proved elusive. This is not surprising since, as we shall see, any welfarist axiology that satisfies three reasonable conditions implies at least one of three counter-intuitive conclusions. I shall start by pointing out the failures in three recent attempts to construct an acceptable population axiology. I shall then present an impossibility theorem and conclude with a short discussion of (...) how it might be extended to pluralist axiologies, that is, axiologies that take more values than welfare into account. (shrink)

John Broome's Weighing Lives provides a much-needed framework for the intriguing problems of population ethics. It is also an impressive attempt to find a workable solution to these problems. I am not sure that Broome has found the right solution, but I think he has done the ethics profession a tremendous service in tidying up the discussion. The framework he presents will make it possible for the participants in this debate to formulate their positions in a clear and precise manner. (...) Even people who disagree with him will be helped by this framework, since they will now be able to show exactly where their views differ. (shrink)

This paper argues for the existence of a fourth positive generic value relation that can hold between two items beyond ‘better than’, ‘worse than’, and ‘equally good’: namely ‘on a par’.

This paper begins with a response to Josh Gert’s challenge that ‘on a par with’ is not a sui generis fourth value relation beyond ‘better than’, ‘worse than’, and ‘equally good’. It then explores two further questions: can parity be modeled by an interval representation of value? And what should one rationally do when faced with items on a par? I argue that an interval representation of value is incompatible with the possibility that items are on a par (a mathematical (...) proof is given in the appendix). I also suggest that there are three senses of ‘rationally permissible’ which, once distinguished, show that parity does distinctive practical work that cannot be done by the usual trichotomy of relations or by incomparability. In this way, we have an additional argument for parity from the workings of practical reason. (shrink)

Advances in technology have made it possible for us to take actions that affect the numbers and identities of humans and other animals that will live in the future. Effective and inexpensive birth control, child allowances, genetic screening, safe abortion, in vitro fertilization, the education of young women, sterilization programs, environmental degradation and war all have these effects. Although it is true that a good deal of effort has been devoted to the practical side of population policy, moral theory has (...) not dealt adequately with the new possibilities. The dilemma faced by moral theory is that traditional theories cannot answer moral questions involving the creation of people. Two related problems arise. The first concerns numbers: how many people should there be? The second asks what sort of people should live and what their levels of well-being should be. Conventional social-contract theories, including the work of Rawls (1971), are restricted to situations with a fixed number of individuals. Sumner (1978) attempts to extend a Rawlsian veil-of-ignorance approach to possible people but is aware of the difficulties involved. The main problem is that possible people must be thought to benefit when they move from non-existence to existence, a view that we reject (see Section 1, Heyd, 1992, Chapter 1; McMahan, 1996a; Parfit, 1984, Appendix G). Rights-based and duty-based theories suffer from a similar problem; there must be a person who has the right or a person to whom the duty is owed (see McMahan, 1981). (shrink)

Parfit's requirements for an ideal Theory X cannot be fully met since the Mere Addition Principle and Non-Antiegalitarianism imply the Repugnant Conclusion: Theory X does not exist. However, since the Repugnant Conclusion is really compelling, the Impersonal Total Principle should be adopted for impartial comparisons concerning future generations. Nevertheless, where our own interests are affected, we may yet choose to be partial, trading off our concern for future goodness with our self-interests. Theory X' meets all Parfit's requirements except the Mere (...) Addition Principle in less compelling cases. (shrink)

Thomas Hurka has recently proposed a utilitarian theory which would effect a compromise between Average and Total utilitarianism, the better to deal with issues in population ethics. This Compromise theory would incorporate the principle that the value which an extra happy person contributes to a possible world is a decreasing function of the total population of that world: that happy people are of diminishing marginal value. In spite of its initial plausibility I argue against this principle. I show that the (...) Compromise theory is actually no improvement over the two original versions of utilitarianism; in particular, it is subject to almost all the objections which are fatal to Average utilitarianism, and more besides. And I attempt to dispell the appearance that intuition supports the Compromise theory as against Total utilitarianism, by arguing that the latter's Repugnant Conclusion, when properly understood, is not intuitively unacceptable. Total utilitarianism remains a plausible ethical theory, while both the Average and the Compromise theories should be definitely rejected. (shrink)

Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations \is better than" and \is as good as". This eld has been riddled with para- doxes and impossibility results which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. All of these results have one thing in common, however. They all involve an adequacy condition that rules out Derek (...) Par t's Repugnant Conclusion. Moreover, some theorists have argued that we should accept the Repugnant Conclusion and hence that avoidance of this conclusion is not a convincing adequacy condition for a population axiology. As I shall show in this chapter, however, one can replace avoid- ance of the Repugnant Conclusion with a logically weaker and intuitively more convincing condition. The resulting theorem involves, to the best of my knowledge, logically weaker and intuitively more compelling con- ditions than the other theorems presented in the literature. As such, it challenges the very existence of a satisfactory population ethics. (shrink)

Suppose one sets up a sequence of less and less valuable objects such that each object in the sequence is only marginally worse than its immediate predecessor. Could one in this way arrive at something that is dramatically inferior to the point of departure? It has been claimed that if there is a radical value difference between the objects at each end of the sequence, then at some point there must be a corresponding radical difference between the adjacent elements. The (...) underlying picture seems to be that a radical gap cannot be scaled by a series of steps, if none of the steps itself is radical. We show that this picture is incorrect on a stronger interpretation of value superiority, but correct on a weaker one. Thus, the conclusion we reach is that, in some sense at least, abrupt breaks in such decreasing sequences cannot be avoided, but that such unavoidable breaks are less drastic than has been suggested. In an appendix written by John Broome and Wlodek Rabinowicz, the distinction between two kinds of value superiority is extended from objects to their attributes. (shrink)

For the last thirty years or so, there has been a search underway for a theory that can accommodate our intuitions in regard to moral duties to future generations. The object of this search has proved surprisingly elusive. The classical moral theories in the literature all have perplexing implications in this area. Classical Utilitarianism, for instance, implies that it could be better to expand a population even if everyone in the resulting population would be much worse off than in the (...) original. The main problem has been to find an adequate population theory, that is, a theory about the moral value of states of affairs where the number of people, the quality of their lives, and their identities may vary. Since, arguably, any reasonable moral theory has to take these aspects of possible states of affairs into account when determining the normative status of actions, the study of population theory is of general import for moral theory. A number of theories have been proposed in the literature that purport to avoid counterintuitive implications such as the one mentioned above. The suggestions are diverse: introducing novel ways of aggregating welfare into a measure of value, revising the notion of a life worth living, questioning the way we can compare and measure welfare, counting people’s welfare differently depending on the temporal location or the modal features of their lives, and challenging the logic of axiological and normative concepts. We investigate the concepts and assumptions involved in these theories as well as their implications for population theory. In our discussion, we propose a number of intuitively appealing and logically weak adequacy conditions for an acceptable population theory. Finally, we consider whether it is possible to find a theory that satisfies all of these conditions. We prove that no such theory exists. (shrink)

Book reviewed:David A. Jopling, Self‐knowledge and the Self.

Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations “is better than” and “is as good as”. This field has been riddled with impossibility results which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies.1 All of these results have one thing in common, however. They all involve an adequacy condition that rules out Derek Parfit’s Repugnant Conclusion: (...) The Repugnant Conclusion: For any perfectly equal population with very high positive welfare, there is a population with very low positive welfare which is better, other things being equal.2 1 The informal Mere Addition Paradox in Parfit (1984), pp. 419ff is the locus classicus. For an informal proof of a similar result with stronger assumptions, see Ng (1989), p. 240. A formal proof with slightly stronger assumptions than Ng’s can be found in Blackorby and Donaldson (1991). For theorems with much weaker assumptions, see my (1999), (2000b), and especially (2000a), (2001), and (2009). 2 See Parfit (1984), p. 388. My formulation is more general than Parfit’s apart from that he doesn’t demand that the people with very high welfare are equally well off. Expressions such as “a population with very high positive welfare”, “a population with very low positive welfare”, etc., are elliptical for the more cumbersome phrases “a population consisting only of lives with.. (shrink)

A principal aim of the branch of ethics called ‘population theory’ or ‘population ethics’ is to find a plausible welfarist axiology, capable of comparing total outcomes with respect to value. This has proved an exceedingly difficult task. In this paper I shall state and discuss two ‘trilemmas’, or choices between three unappealing alternatives, which the population ethicist must face. The first trilemma is not new. It originates with Derek Parfit's well-known ‘Mere Addition Paradox’, and was first explicitly stated by Yew-Kwang (...) Ng. I shall argue that one horn of this trilemma is less unattractive than Parfit and others have claimed. The second trilemma, which is a kind of mirror image of the first, appears hitherto to have gone unnoticed. Apart from attempting to resolve the two trilemmas, I shall suggest certain features which I believe a plausible welfarist axiology should possess. The details of this projected axiology will, however, be left open. (shrink)