John Broome

Intuition suggests there is no value in adding people to the population if it brings no benefits to people already living: creating people is morally neutral in itself. This paper examines the difficulties of incorporating this intuition into a coherent theory of the value of population. It takes three existing theories within welfare economics - average utilitarianism, relativist utilitarianism, and critical-level utilitarianism - and considers whether they can satisfactorily accommodate the intuition that creating people is neutral.

This chapter sets out an intertemporal addition theorem, the exact analog, across the dimension of time, of the interpersonal addition theorem. A premise of the new theorem is the 'principle of temporal good', the exact analog of the principle of personal good. It turns out that the principle of temporal good would, if true, give crucial support to the utilitarian principle. The chapter explains that the principle of temporal good is dubious, and describes how this principle might nevertheless be defended. The defence is metaphysical. It is founded on a disuniting metaphysics of personhood. A complete argument was made out by deducing the principle of temporal good from a disuniting metaphysics. The chapter shows that the principle of temporal good, if true, lends very strong support to the utilitarian principle of distribution. So a chain of argument would have been completed, linking the disuniting metaphysics to the utilitarian principle.

This chapter concerns with rational preferences in the face of uncertainty. The goodness of uncertain prospects is best understood in terms of rational preferences. The chapter discusses some necessary spadework. Its particular purpose is to defend some parts of expected utility theory as an account of rational preferences. It explains the general idea of expected utility theory, and particularly how it is founded on axioms. The principal axiom is also explained. It is often called the 'sure‐thing principle', and it amounts to an assumption of strong separability. The chapter further aims to develop an argument about individuation in the context of a simpler axiom, namely transitivity. It extends the argument to the sure‐thing principle and then discusses a threat to another of the axioms of expected utility theory, which is raised by author's defence of the sure‐thing principle.

This chapter sets out the theorems, and presents some examples that show in a rough way how the theorems work. It explains separability precisely, and states the theorems. The chapter starts the work of interpreting the theorems, and also explains the significance of their conclusions from a formal, mathematical point of view. It then discusses a significant assumption that is used in the proofs of the theorems. The published proofs of both the separability theorems depend on an assumption that may be objectionable in some contexts. These theorems are about an ordering defined on a field of alternatives. If an ordering can be represented by an additively separable utility function, the theorem shows it can be represented by a whole family of additively separable functions. Each member of the family is an increasing linear transform of the others, and the family includes every increasing linear transform of each of its members.

The coherence of general good turns out to conflict with the widely accepted Pareto principle. This chapter explains the conflict and resolves it in favour of coherence. It also presents an example of a head‐on collision between coherence and the Pareto principle. The example relies on an auxiliary assumption, but one that is very plausible. The principle of personal good is immune to the difficulty raised by the probability agreement theorem. The theorem presents welfare economics with a dilemma: it must abandon either the coherence of social preferences or else the traditional Pareto principle. Either way, it will have to repudiate Harsanyi's theorem. The ex‐ante school of welfare economists abandons coherence. This is the best established school. The ex‐ante school cleaves to the traditional Pareto principle. Consequently, it has to accept incoherent social preferences.

This chapter explains that the principle of personal good is a principle of separability in the dimension of people. Together with the coherence of good, it provides a basis for applying the separability theorem across the two dimensions of people and states of nature. This chapter starts by qualifying the principle of personal good in some ways, and explains the defence of the principle. One possible line of defence is metaphysical. It is to argue that suprapersonal entities such as nations are simply aggregates of people, and therefore cannot possess a good of their own apart from the good of the people who make them up. The principle is intended to apply to probability‐relative goodness to the goodness of uncertain prospects. The chapter defends it as applied to outcomes, and then extends the argument to probability‐relative goodness. An argument is certainly needed to justify the principle of personal good for probability‐relative goodness.

One part of ethics is concerned with good. This chapter talks generally about the idea of the structure of good. According to some ethical theories, the concern for good amounts to the whole of ethics, not just a part. Most nonteleological theories give some role to good. Since side‐constraint theory is an important example of nonteleological ethics, the popular belief that it is necessarily agent relative helps to sustain the popular association between nonteleological ethics and agent‐relative ethics. But what makes side‐constraint theory nonteleological is not agent relativity. It is the way it takes ethical considerations to work: side constraints determine what ought or ought not to be done directly, and not by determining goodness. The chapter describes some ways of making the distinction between teleological and nonteleological ethics, and explains why they are unsatisfactory. It then discusses what type of priority the concept of good has in ethics.

The weighing up of goods is one aspect of the structure of good. This chapter describes the general problem of weighing goods, and illustrates it with examples. The states of nature are locations of good. Separability says that the value of what happens in one location is independent of what happens in other locations. When the locations are states of nature, the leading theory about how good should be aggregated across them is expected utility theory, and separability is the key assumption of this theory. The chapter gives the examples that show how locations of good are spread across three dimensions: states of nature, people and times. In the most general case, goods are strung out on a three‐dimensional grid of locations. Each location is a person, at a time, in a state of nature.

The chapter describes Derek Parfit's argument that aims to cast light on distributive justice by comparing it with the distribution of good across time. It also describes John Harsanyi's argument by comparing it with the distribution of good across states of nature. More particularly, both arguments are intended to offer some support to the utilitarian principle of distribution. The utilitarian principle is about the distribution of good across the dimension of people. Parfit's defence compares this distribution with the distribution of good across the dimension of time, within the life of a single person. Harsanyi's argument exploits the similarity between the dimensions of people and states of nature. A weighing of the goods across the dimension of states of nature is being identified with a weighing of different people's goods across the dimension of people. That is the strategy of the Harsanyi's argument.

This chapter explains the interpersonal addition theorem. The theorem leads to two remarkable points. Firstly, it links the aggregation of good across the dimension of people with its aggregation across the dimension of states of nature. The result is that, in favourable circumstances, it links the value of equality in the distribution of good with the value of avoiding risk to good. The chapter also explains this link. The second point is even more remarkable. The theorem shows that general utility is the sum of individual utilities. Since these utilities represent the general and individual betterness relations, this may seem, at first glance, to say that general good is the total of individual good. Joined with the addition theorem Bernoulli's hypothesis implies the utilitarian principle of distribution, which implies in turn that there is no value in avoiding inequality in the distribution of good between people. The chapter discusses the assessment of Bernoulli's hypothesis.

The main difficulty for the principle of personal good arises from egalitarianism. Egalitarianism is the view that equality between people is good. Equality is a relation between people. So it seems as though it will have to be a nonpersonal or interpersonal or suprapersonal good. This chapter outlines a utilitarian argument for equality. This argument is the point of departure for other egalitarian theories. It also describes two broad divisions of egalitarian thinking: the communal and the individualistic. The chapter shows that individualistic egalitarianism is consistent with the principle of personal good, and that communal egalitarianism is generally not. It further takes up the question of grounds: it asks why equality is good. Its answer is to ground egalitarianism in a theory of fairness. This theory supports individualistic egalitarianism against communal egalitarianism. So it supports the principle of personal good.

This chapter discusses one of the main subjects: the structure of good. It aims to establish one point about all of the general relation and the individual relations: they all conform to the axioms of expected utility theory. The theory proves that, if a relation satisfies the axioms, it can be represented by an expectational utility function. The details of the representation and its significance are spelt out. The chapter also aims to show that individual and general betterness relations satisfy the axioms of expected utility theory: they are coherent. It extends the defence to betterness relations. The most straightforward way of showing the coherence of betterness would be to show first the coherence of rational preference relations, and then identify each betterness relation with some rational preference relation. The chapter explores that route, and explains that it cannot be completely successful.