How should we define the feasible set? Even when individuals agree on facts and values, as traditionally construed, different views on feasibility may suffice to produce very different policy conclusions. Focusing on the difficulties in the feasibility concept may help us resolve some policy disagreements, or at least identify the sources of those disagreements. Feasibility is most plausibly a matter of degree rather than of kind. Normative economic reasoning therefore faces a fuzzy social budget constraint. Iterative reasoning about feasibility and desirability may help us overcome these problems.

It has become accepted that social choice is impossible in the absence of interpersonal comparisons of well-being. This view is challenged here. Arrow obtained an impossibility theorem only by making unreasonable demands on social choice functions. With reasonable requirements, one can get very attractive possibilities and derive social preferences on the basis of non-comparable individual preferences. This new approach makes it possible to design optimal second-best institutions inspired by principles of fairness, while traditionally the analysis of optimal second-best institutions was thought to require interpersonal comparisons of well-being. In particular, this approach turns out to be especially suitable for the application of recent philosophical theories of justice formulated in terms of fairness, such as equality of resources.

Roughly, according to conditional egalitarianism, equality is non-instrumentally valuable, but only if it benefits at least one individual. Some political theorists have argued that conditional egalitarianism has the important virtue that it allows egalitarians to avoid the so-called ‘levelling down’ objection. However, in the present article I argue that conditional egalitarianism does not offer the egalitarian a plausible escape route from this objection. First, I explain the levelling down objection and suggest some particular concerns from which it derives its force. Then I provide a more precise definition of conditional egalitarianism. Finally, I give two arguments against this principle. According to the first, it violates the transitivity of the betterness relation (or more specifically, ‘betterness with respect to equality’). According to the second, there is no plausible explanation of why equality must benefit at least one individual in order to be non-instrumentally valuable.

The incomparability of alternatives is thought to pose a problem for justified choice, particularly for proponents of comparativism – the view that comparative facts about alternatives determine what one rationally ought to choose. As a solution, it has been argued that alternatives judged incomparable by one of the three standard comparative relations, “better than,” “worse than,” and “equally good,” are comparable by some fourth relation, such as “roughly equal” or “on a par.” This solution, however, comes at what many would regard as too high a cost – namely, rejection of the transitivity of the relation “at least as good as.” In this paper, I argue that proponents of comparativism need not incur this cost. I defend the possibility of justified choice between incomparable alternatives on grounds that comparativists can accept. The possibility of incomparability has been met with resistance, in part because of the intuitive appeal of comparativism. By defending the possibility of justified choice between incomparable alternatives on grounds that comparativists can accept, this paper supports further inquiry into the subject of incomparability.

John Broome's ground-breaking Weighing Lives makes precise, and supplies arguments previously lacking for, several views which for centuries have been central to the utilitarian tradition. In gratitude for his enlightening arguments, I shall repay him in this paper by showing how he could make things easier for himself by denying neutrality and accepting hedonism.

In “Weighing Lives”, John Broome defends a very weak consequentialist account of the value of saving lives. This paper challenges the commitments of this kind of account and describes some reasons for saving lives that would appeal to a non-consequentialist.

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.

One response to Derek Parfit's ‘mere addition paradox’ invokes the relation of ‘parity’. Since parity is a form of ‘incommensurateness’ in John Broome's terms, three doubts which Broome raises about accounts involving incommensurateness in Weighing Lives pose a challenge for this response. I discuss two of these. They emerge from a discussion of various intuitions about ‘neutrality’. I argue that an account based on parity may be no less consistent with Broome's intuitions than is his own vagueness view.

I am extremely grateful to the five commentators for readingmy book and offering such interesting thoughts in reaction. Shortage of space may make my responses seem brusque. But of course they are not meant to be.