In this paper, I address two connected issues that arise when one considers a rational agent facing a decision problem. One is whether or not the agent may find that the dictates of rationality are such that they cannot all be followed. For example, one may ask whether or not the requirements on the agent's actions imposed by rationality can conflict in an irreconcilable way, making it impossible to satisfy all of them. Put differently, one may ask whether or not any apparent conflict of this type must in fact be capable of rational resolution. I shall say that an agent who is in a position in which the requirements of rationality cannot all be satisfied faces a feasibility dilemma, and I shall characterize certain conceptions of rationality that differ according to whether or not they admit such a possibility. A second issue concerns the number of options that may be deemed rational in a decision problem. Is rationality sufficiently determinate that it always dictates precisely one choice, or may there be more than one rationally permissible option? Is there anything about rationality itself that guarantees that any of the possible options could rationally be chosen? I shall call this issue – whether the concept of rationality itself places any limits on the number of options that may be deemed rational in a given problem – the numbers problem.

According to Wlodek Rabinowicz's (2008) fitting-attitude analysis of value relations, two items are on a par if and only if it is both permissible to strictly prefer one to the other and permissible to have the opposite strict preference. Rabinowicz's account is subject, however, to one important objection: if strict preferences involve betterness judgements, then his analysis contrasts with the intuitive understanding of parity. In this paper, I examine Rabinowicz's three responses to this objection and argue that they do not succeed. I then propose an alternative solution. I argue that the objection can be avoided if we ‘relativize’ Rabinowicz's account and define parity in terms of opposite strict preferences between two items that are only relatively permissible, rather than permissible simpliciter. I argue that this account of parity can be defended if we take seriously the distinction between sufficient and decisive reason for a preference relation. I also show that, on the basis of this distinction, we can arrive at a more extensive taxonomy of value relations than the one proposed by Rabinowicz.

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.

Kuhn and Moresi (1995) (henceforth, K&M) have proposed a useful taxonomy for classifying prisoners' dilemmas (henceforth, PDs). This comment is concerned with K&M's observation that legal penalties for defection can transform PDs into cooperative games, and their argument that the role of the law may vary depending on how the PD is classified by their taxonomy. The purpose of this note is to support K&M's analysis by demonstrating that the law of damages, as understood by economic analysis, already performs the function that K&M assign to legal penalties for defection.

While Bayesian methods are widely used in economics and finance, the foundations of this approach remain controversial. In the contemporary statistical literature Bayesian Ockham’s razor refers to the observation that the Bayesian approach to scientific inference will automatically assign greater likelihood to a simpler hypothesis if the data are compatible with both a simpler and a more complex hypothesis. In this paper I will discuss a problem that results when Bayesian Ockham’s razor is applied to nested economic models. I will argue that previous responses to the problem found in the philosophical literature are unsatisfactory and develop a novel reply to the problem.

Irrational people create problems not only for themselves and those around them, but also for those who study them. They cause trouble for social scientists because their actions are inexplicable, at least according to generally accepted models of explanation. Explanations in the social sciences normally assume the form of rationalizations: actions are explained by showing that, relative to what the subjects believe and desire, the actions were done for good reasons. Conversely, when good reasons cannot be found for why someone acted as they did, their behavior remains inscrutable. Irrational people, therefore, stymie social scientists because their actions do not reveal the rationality needed to produce adequate explanations.

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.

This paper responds to Gui and Nelson's separate comments on our paper ‘Fraternity’, which analysed sociality in markets as joint commitment to mutual assistance. We argue that our analysis is fundamentally different both from Nelson's analysis (a mixture of self-interested and intrinsic motivations) and from that provided by theories of warm glow or guilt aversion, as discussed by Gui. We agree with Gui that, in initiating and maintaining cooperative relationships, individuals sometimes incur personal costs to benefit others without any certainty of reciprocation, but we argue that the intentions underlying such actions are cooperative rather than self-sacrificing.

The effectiveness of heuristics has received contradicting interpretations in the behavioural sciences. We study the policy implications of two programmes that dispute the effectiveness of heuristics – the biases and heuristics and the fast and frugal heuristics programmes. While the first blames heuristics for most errors in judgement, the second posits heuristics as simple mental algorithms that work well in a range of environments. We argue that the fast and frugal programme is less paternalistic insofar as it models humans as effective decision-makers in a range of environments. However, in the rapidly changing environments of the 21st century, both are needed to inform evidence-based policies.

The Nash counterfactual considers the question: what would happen were I to change my behaviour assuming no one else does. By contrast, the Kantian counterfactual considers the question: what would happen were everyone to deviate from some behaviour. We present a model that endogenizes the decision to engage in this type of Kantian reasoning. Autonomous agents using this moral framework receive psychic payoffs equivalent to the cooperate-cooperate payoff in Prisoner’s Dilemma regardless of the other player’s action. Moreover, if both interacting agents play Prisoner’s Dilemma using this moral framework, their material outcomes are a Pareto improvement over the Nash equilibrium.