In 1970 Amartya Sen exposed an apparent antinomy that has come to be known as the Paradox of the Paretian Libertarian (Sen, 1970b, pp. 152–57). Sen introduced his paradox by establishing a simple but startling theorem. Roughly put, what he proved was that if a mechanism for selecting social choice functions satisfies two standard adequacy conditions, there are possible situations in which it will violate either the very weak libertarian precept that every individual has at least some rights or the seemingly innocuous Paretian principle that an option should be judged unacceptable if there is an available alternative that everyone prefers to it. Many economists and philosophers have proposed solutions to Sen's problem, but there is no general consensus on what solution (if any) is correct. In the present paper I argue that Sen's original theorem fails to establish the existence of any conflict between libertarianism and Paretianism. Furthermore, I contend that Sen has misinterpreted certain other theorems which he has used to defend the existence of a paradoxical conflict between these two doctrines. In general, I try to show that whenever Sen posits a Paretian-libertarian conflict to explain an apparently troubling result in social choice theory, the difficulty can be better dealt with either by claiming that the theorem in question imposes overly strong background constraints on the form of social choice functions or by claiming that it relies on an unacceptable construal of individual rights.

Ethical theories grounded in utilitarianism suggest that social welfare is improved when agents seek to maximize others' welfare in addition to their own (i.e., are altruistic). However, I use a simple game-theoretic model to demonstrate two shortcomings of this argument. First, altruistic preferences can generate coordination problems where none exist for selfish agents. Second, when agents care somewhat about others' utility but weight their own more highly, total social welfare may be lower than with selfish agents even in the absence of coordination problems.

It is widely agreed that the concept of general equilibrium and, in particular, general equilibrium existence proofs play a central role within the neoclassical approach to economic theory. There is much less agreement, however, on the concepts of general equilibrium and of neoclassical economic theory themselves.

Backwards induction is an intriguing form of argument. It is used in a number of different contexts. One of these is the surprise exam paradox. Another is game theory. But its use is problematic, at least sometimes. The purpose of this paper is to determine what, exactly, backwards induction is, and hence to evaluate it. Let us start by rehearsing informally some of its problematic applications.

I carved a massive cake of beeswax into bits and rolled them in my hands until they softened … Going forward I carried wax along the line, and laid it thick on their ears. They tied me up, then, plumb amidships, back to the mast, lashed to the mast, and took themselves again to rowing. Soon, as we came smartly within hailing distance, the two Sirens, noting our fast ship off their point, made ready, and they sang … The lovely voices in ardor appealing over the water made me crave to listen, and I tried to say ‘Untie me!’ to the crew, jerking my brows; but they bent steady to the oars. (Homer, c. –900, pp. 227–28)

This paper is about the measurement of specific freedoms – the freedom of an agent to undertake some particular action. In a recent paper, Dowding and van Hees discuss the need for, and general form of, a “freedom function” that assigns a value between 0 and 1 to a freedom or right and that describes the expectation that a person may have about being in a position to exercise (“being free to perform”) that freedom or right. An examination of the literature shows that there is as yet no agreed framework for defining such a function. Based on the framework of a game form, I develop a very simple and natural measure of specific freedom as the “conditional probability of success.” It is also shown that in an important way “negative freedom is membership of powerful coalitions.”

According to some accounts of exploitation, most notably Ruth Sample’s (2003) degradation-based account and Robert Goodin’s (1987) vulnerability-based account, exploitation occurs when an advantaged party fails to constrain their advantage in light of another’s disadvantage, regardless of the cause of this disadvantage. Because the duty of constraint in these accounts does not depend on the cause of the disadvantage, the advantaged’s duty of constraint is what I call a ‘come-what-may’ duty. I show that come-what-may duties create moral hazards that can themselves be exploited by the disadvantaged parties. In such cases these accounts of exploitation are either self-frustrating or over-demanding.

The “Adam Smith problem” has traditionally been concerned with the issue of authorial integrity: the issue of how a single author, Adam Smith, could have written two such apparently dissimilar, even contradictory, works as The Theory of Moral Sentiments (TMS) and The Wealth of Nations (WN). As the problem to be resolved was the single authorial origin of two such works, the perceived incompatibilities between them were explained in terms of Smith's intellectual biography – for example, Smith's travels to France, Smith's meetings with the physiocrats, or the mental incapacities of an aging man. The current consensus is that the Adam Smith problem is a “pseudo problem” and that Smith's works represent a unified project, but the same reference to authorial origins now provides thr opposite claim that “the same man” wrote both books (Raphael and Macfie, 1976, p. 20). Here the postulate of authorial integrity, “of stable integrated character, not subject to deep intellectual doubts or fissures” provides an assurance that such a man is unlikely to have written two entirely different books (Macfie, 1967, p. 76), an assurance underwritten by a coherent authorial intentionality that guarantees the consistency of the two works.

The Distribution View provides a model that integrates four distributional concerns in the evaluation of risky prospects. Starting from these concerns, we can generate an ordering over a set of risky prospects, or, starting from an ordering, we can extract a characterization of the underlying distributional concerns. Separability of States and/or Persons for multiple-person risky prospects, for single-person risky prospects and for multiple-person certain prospects are discussed within the model. The Distribution View sheds light on public health policies and provides a framework for the discussion of Parfit's Priority View for risky prospects.

Richard Thaler and Cass Sunstein (T/S) have defended ‘nudges’ aimed at smoking, overeating, etc. as a ‘means’ paternalism that leaves its targets ‘better off as judged by themselves’. Their libertarian critics have charged that these behaviours are often perfectly rational and that the nudges would ‘impose’ on their targets ‘ends’ that they reject. This paper argues that whether or not the behaviours are rational is difficult to say, but the critics are right in claiming that T/S fail to take seriously their targets’ true preferences. This is evident, in particular, in Sunstein's recent reply to an ‘autonomy objection’ to nudging. The upshot is that the nudging paternalism T/S support cannot be defended as a means paternalism that is deferential to its targets’ own ends or values. The only way to defend it is via a ‘prudential’ paternalism that, given the preferences of many of its targets, will often be ‘ends’ paternalism.

In his widely-discussed book, Real Freedom for All, Philippe Van Parijs argues that justice requires the provision of a universal, unconditional basic income. Some critics reject that conclusion on the grounds that it violates requirements of reciprocity or prohibitions on exploitation, free-riding and parasitism. This paper explores a less familiar critique, which operates within the same resource egalitarian parameters as Van Parijs's argument, and leaves unchallenged his conviction that justice requires a basic income. Instead the paper suggests two reasons to doubt his ambitious claims about its magnitude. First, the paper argues that if envy elimination is the fundamental egalitarian aim then Van Parijs's argument for boosting basic income by including jobs within the class of external assets to be equalized is unsuccessful. Second, it argues that Van Parijs fails to show that the provision of basic income should not be constrained by a more restrictive principle for correcting inequalities in personal resources than his favored compensatory norm. Before defending these criticisms, two preliminary sections describe Van Parijs's distributive principles and his central argument for basic income.

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.

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash equilibrium concept are predominantly available.

In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi (1973a), see also Rubinstein (1991), and Aumann and Brandenburger (1991), a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others.

Consider a transitive value ordering of outcomes and lotteries on outcomes, which satisfies substitutivity of equivalents and obeys “continuity for easy cases,” i.e., allows compensating risks of small losses by chances of small improvements. Temkin (2001) has argued that such an ordering must also – rather counter-intuitively – allow chances of small improvements to compensate risks of huge losses. In this paper, we show that Temkin's argument is flawed but that a better proof is possible. However, it is more difficult to determine what conclusions should be drawn from this result. Contrary to what Temkin suggests, substitutivity of equivalents is a notoriously controversial principle. But even in the absence of substitutivity, the counter-intuitive conclusion is derivable from a strengthened version of continuity for easy cases. The best move, therefore, might be to question the latter principle, even in its original simple version: as we argue, continuity for easy cases gives rise to a sorites.

When does self-interest counsel cooperation? This question pertains both to the labile behaviors produced by rational deliberation and to the more instinctive and fixed behaviors produced by natural selection. In both cases, a standard starting point for the investigation is the one-shot prisoners' dilemma. In this game, each player has the option of producing one or the other of two behaviors (labeled “cooperate” and “defect”). The pay-offs to the row player are as follows:

In general, capitalists deserve profits and losses for their contribution to the general welfare. Market imperfections and the range of permissible prices (at least within the boundaries of exploitation) prevent the alignment from being a direct one, but the connection generally holds. In the context of the market, this thesis preserves the central place of moral responsibility in moral desert. It also satisfies the fittingness and proportionality conditions of moral desert and provides a backward-looking and pre-institutional ground of it. In addition, the focus on contribution unifies several different types of act-based desert, specifically deserved profits and losses, deserved punishment, and deserved wages. Hence, to the extent that desert-satisfaction is relevant in the selection of an economic system, this result strengthens the case for capitalism.