David Lewis is widely credited with the first formulation of common knowledge and the first rigorous analysis of convention. However, common knowledge and convention entered mainstream game theory only when they were formulated, later and independently, by other theorists. As a result, some of the most distinctive and valuable features of Lewis' game theory have been overlooked. We re-examine this theory by reconstructing key parts in a more formal way, extending it, and showing how it differs from more recent game theory. In contrast to current theories of common knowledge, Lewis' theory is based on an explicit analysis of the modes of reasoning that are accessible to rational individuals and so can be used to analyse the genesis of common knowledge. Lewis' analysis of convention emphasises the role of inductive reasoning and of salience in the maintenance of conventions over time.

Over the years, egalitarian philosophers have made some challenging claims about the nature of egalitarianism. They have argued that egalitarian reasoning should make us reject the Pareto principle; that the Rawlsian leximin principle is not an egalitarian idea; that the Pigou–Dalton principle needs modification; that the intersection approach faces deep problems; that the numbers should not count within an egalitarian framework, and that egalitarianism should make us reject the property of transitivity in normative reasoning. In this paper, taking the recent philosophical debate on equality versus priority as the starting point, I review these claims from the point of view of an economist.

The paper considers some differences in the ways that economics and philosophy study equality and egalitarianism in general. First, economics tends to understand a value simply as an ordering over outcomes while philosophy attempts to find a deeper explanation of the ordering in terms of intuitive ideas about the value. Sometimes the supposedly deeper explanation turns out to be insightful, but, in other cases, it is misleading or fails to be explanatory. Second, economists often propose impossibility results intended to show that apparently innocuous ideas about a value can have surprising consequences when they are combined. However, the significance of the results can be difficult to interpret and, sometimes, they do not establish as much as they initially seem to. Third, economists often criticize philosophical work about equality for making misguided assumptions about the possibility of measuring utility or well-being. The paper does not attempt to answer this criticism, but it points out some specific ways in which the scepticism about measurement might be exaggerated.

The article considers a surprisingly resilient argument, going back to Adam Smith, for the fairness of proportionate taxation: that proportionate taxation represents the fair way to divide the surplus value produced by social cooperation among all of society's members. The article considers two recent variants on that argument, one by Richard Epstein in Takings and one by David Gauthier in Morals by Agreement. It concludes that the normative and empirical assumptions that underlie these, and all other variants, of the argument are so implausible as to suggest the argument cannot be taken seriously as a defense of proportionate taxation. The article concludes by considering other possible explanations for the enduring attraction of proportionate taxation for political philosophers, particularly those with libertarian and quasi-libertarian leanings.

This paper aims to illuminate some issues in the equality, priority, or what debate. I characterize egalitarianism and prioritarianism, respond to the view that we should care about sufficiency or compassion rather than equality or priority, discuss the levelling down objection, and illustrate the significance of the distinction between prioritarianism and egalitarianism, establishing that the former is no substitute for the latter. In addition, I respond to Bertil Tungodden's views regarding the Slogan, the levelling down objection, the Pareto Principle, leximin, the principle of personal good, strict moderate egalitarianism, the Hammond Equity Condition, the intersection approach, and non-aggregative reasoning.

This paper examines how people assess inequality of income distribution and how inequality could be measured. We start from the philosophical analysis of Temkin, who distinguishes nine plausible aspects of inequality. His approach is based on the concept of ‘complaints’ or distances between incomes. We examine the Temkin approach by means of the questionnaire-experimental method pioneered by Amiel and Cowell to find out whether the aspects of equality have any plausibility for student respondents and, if so, whether there are aspects which are more appealing than others. Both the numerical and verbal responses show that a considerable majority of the respondents might be influenced by the intuitions included in the combination of the Weighted Additive Principle and the Average view of complaints. The questionnaire results also shed some empirical light on the acceptance of the Transfer Principle and the attitudes towards the Sequence.

It is common to define egalitarianism in terms of an inequality ordering, which is supposed to have some weight in overall evaluations of outcomes. Egalitarianism, thus defined, implies that levelling down makes the outcome better in respect of reducing inequality; however, the levelling down objection claims there can be nothing good about levelling down. The priority view, on the other hand, does not have this implication. This paper challenges the common view. The standard definition of egalitarianism implicitly assumes a context. Once this context is made clear, it is easily seen that egalitarianism could be defined alternatively in terms of valuing a benefit to a person inversely to how well off he is relative to others. The levelling down objection does not follow from this definition. Moreover, the common definition does not separate egalitarian orderings from prioritarian ones. It is useful to do this by requiring that on egalitarianism, additively separable orderings should be excluded. But this requirement is stated as a condition on the alternative definition of egalitarianism, from which the levelling down objection does not follow.

Should democracts value the freedom to choose? Do people value facing distinct choices when they make collective decisions? ‘Autonomy’ – the ability to participate in the making of collective decisions – is a paltry notion of freedom. True, democrats must be prepared that their preferences may not be realized as the outcome of the collective choice. Yet democracy is impoverished when many people cannot even vote for what they most want.

‘The point is not to be free, but to act freely.’ Rosa Luxemburg

Economic theory has generally acknowledged the role that institutions have in shaping economic space. The distinction, however, between physical and institutional descriptions of economic activity has not received adequate attention within the mainstream paradigm. In this paper I show how a proper distinction between the physical and institutional space in economic models will help clarify the concept of externality and provide a better interpretation of the relationship between externality and nonconvexity. I argue that within the Arrow-Debreu framework externality should be viewed as incongruence between the physical and institutional descriptions of the economic space. I also argue that, contrary to conventional wisdom, detrimental externality has no special association with nonconvexity. Starrett's (1972) fundamental nonconvexity has to do with the specific institutional structure of Arrow markets rather than the detrimental nature of externality. Indeed, Arrow markets may not eliminate externalities. In a similar vein, it is not detrimental externality, however intense, that causes the production possibility set to become nonconvex, as argued by Baumol and Bradford (1972), but the particular interpretation of intensity that would make even conventional production possibility sets nonconvex. These points become apparent when one distinguishes between the convexity of the physical and institutional production sets.

The so-called “Levelling Down Objection” is commonly believed to occupy a central role in the debate between egalitarians and prioritarians. Egalitarians think that equality is good in itself, and so they are committed to finding value even in such equality as may only be achieved by “levelling down”–i.e., by merely reducing the better off to the level of the worse off. Although egalitarians might deny that levelling down could ever make for an all-things-considered improvement, they cannot deny that it may make things better in at least one respect. Prioritarians, on the other hand, do deny this; according to them, levelling down cannot make things better in any respect. In this paper I argue that the Levelling Down Objection leans far too heavily on a heretofore unanalysed notion: namely, the notion of “being better in this or that respect.” I propose what I take to be a plausible analysis of that notion, and show that, given the proposed analysis, the prioritarian is no less vulnerable to the Levelling Down Objection than is the egalitarian. I conclude that proponents of the Levelling Down Objection need either to suggest a better analysis or abandon the Levelling Down Objection altogether.

Jean Hampton has argued that an important case of the free-rider problem has the structure of a battle-of-the-sexes game, rather than the Prisoner's Dilemma, as is often assumed. This case occurs when the collective good to be produced is a ‘step’ or ‘lumpy’ good, one that is produced in a single production step. Battle of the Sexes is a coordination game, with stronger equilibria than games such as the Prisoner's Dilemma or Chicken. Hampton argues that, because of this difference, there is good reason to think that players facing a battle-of-the-sexes game can more easily reach mutually desirable outcomes than players facing these other games. An examination of Hampton's argument, however, shows that she has failed to specify a condition that would clearly distinguish her examples of battle-of-the-sexes games from chicken games. Consequently, Hampton's claim that free riding in the provision of step goods is less tempting than other analyses have suggested because of the presence of coordination equilibria is incorrect as it stands.

Natural Goodness, PHILIPPA FOOT. Clarendon Press, 2002, 125 pages.

Philippa Foot begins her short but intriguingly rewarding book on Natural Goodness by recounting a story about Wittgenstein.

Wittgenstein interrupted a speaker who had realized that he was about to say something that, although it seemed compelling, was clearly ridiculous, and was trying (as we all do in such circumstances) to say something sensible instead. “No,” said Wittgenstein. “Say what you want to say. Be crude and then we shall get on.” (p. 1)

So it is no surprise that Natural Goodness itself is full of bold sayings which, although elegantly cast, will shock many readers' philosophical sensibilities. In this discussion of Foot's book I will complete compliance with Wittgenstein's advice by way of a crude attempt to interpret Foot's bold sayings.

This is a wonderful book; indeed, it is easily one of the most important and creative books I have ever read on the subject of causation and causal inference. Causality is impressive on many levels and should be of great interest to many different audiences. Philosophers will find of particular interest Pearl's defense of what might be described as a broadly manipulationist or interventionist treatment of causation: Causal claims have to do with what would happen under ideal, suitably surgical experimental manipulations (‘interventions’). But Pearl moves far beyond philosophical generalities on this theme: He makes the case for the approach that he favors by developing a formal apparatus (‘a calculus of interventions’, as he calls it) for talking about interventions and how they relate to causation and information about probabilities that is at once both intuitively compelling and genuinely useful for purposes of calculation and estimation. He also actively engages the philosophical literature on causation at many points – for example, there are illuminating discussions of evidential decision theory, of probabilistic theories of causation of the sort favored by Eells and Cartwright, of Lewisian counterfactual theories of causation, and of the relationship between so-called type and token causal claims, as well as a quite novel treatment of the latter.

I thank Dr. Woodward for his illuminating review of my book Causality, for explicating so clearly the basic contributions of the book, and for giving me the opportunity to further clarify some aspects of the do-calculus, specifically those that pertain to the notion of intervention.