This note provides an introduction to the accompanying article by Allan Gibbard that was originally written for the 1968–69 Harvard graduate seminar conducted by Kenneth Arrow, John Rawls and Amartya Sen.

Arrow’s impossibility result stems chiefly from a combination of two requirements: independence and fixity. Independence says that the social choice is independent of individual preferences involving unavailable alternatives. Fixity says that the social choice is fixed by a social preference relation that is independent of what is available. Arrow found that requiring, further, that this relation be transitive yields impossibility. Here it is shown that allowing intransitive social indifference still permits only a vastly unsatisfactory system, a liberum veto oligarchy. Arrow’s argument for independence, though, undermines any rationale for fixity.

We present a new class of models of players’ reasoning in non-cooperative games, inspired by David Lewis's account of common knowledge. We argue that the models in this class formalize common knowledge of rationality in a way that is distinctive, in virtue of modelling steps of reasoning; and attractive, in virtue of being able to represent coherently common knowledge of any consistent standard of individual decision-theoretic rationality. We contrast our approach with that of Robert Aumann (1987), arguing that the former avoids and diagnoses certain paradoxes to which the latter may give rise when extended in particular ways.

In this paper we explore game-theoretic reasoning in dynamic games within the framework of belief revision theory. More precisely, we focus on the forward induction concept of ‘common strong belief in rationality’ (Battigalli and Siniscalchi (2002) and the backward induction concept of ‘common belief in future rationality’ (Baltag et al. 2009; Perea 2014). For both concepts we investigate whether the entire collection of selected belief revision policies for a player can be characterized by a unique plausibility ordering. We find that this is indeed possible for ‘common strong belief in rationality’, whereas this may be impossible in some games for ‘common belief in future rationality’.

This article presents a community-based account of salience as an alternative and a complement to the ‘natural salience’ approach which is endorsed by almost all game theorists who use this concept. While in the naturalistic approach, salience is understood as an objective and natural property of some entities (events, strategies, outcomes), the community-based account claims that salience is a function of community membership. Building on David Lewis’s theory of common knowledge and on some of its recent refined accounts, I suggest that salience acts as a correlating device in a correlated equilibrium. What is constitutive of salience is common understanding, the fact that agents have common knowledge that they share the same modes of reasoning with respect to a well-identified set of events. I argue that the basis for common understanding is community membership. The relevance of this account stems from the fact that it answers the objection that salience is either unnecessary or unable to account for coordination between rational agents.

This paper examines a broad range of ethical perspectives and principles relevant to the analysis of issues raised by the science of climate change and explores their implications. A second and companion paper extends this analysis to the contribution of ethics, economics and politics in understanding policy towards climate change. These tasks must start with the science which tells us that this is a problem of risk management on an immense scale. Risks on this scale take us far outside the familiar policy questions and standard, largely marginal, techniques commonly used by economists; this is a subject that requires the full breadth and depth of what economics has to offer and a much more thoughtful view of ethics than economists usually bring to bear. Different philosophical approaches bring different perspectives on understanding and policy, yet they generally point to the case for strong action to manage climate change.

Both intertemporal and intratemporal equity are central to the examination of policy towards climate change. However, many discussions of intertemporal issues have been marred by serious analytical errors, particularly in applying standard approaches to discounting; the errors arise, in part, from paying insufficient attention to the magnitude of potential damages, and in part from overlooking problems with market information. Some of the philosophical concepts and principles of Paper 1 are applied to the analytics and ethics of pure-time discounting and infinite-horizon models, providing helpful insights into orderings of welfare streams and obligations towards future generations. Such principles give little support for the idea of discrimination by date of birth. Intratemporal issues are central to problematic and slow-moving international discussions and are the second focus of this paper. A way forward is to cast the policy issues and analyses in a way that keeps equity issues central and embeds them in the challenge of fostering the dynamic transition to the low-carbon economy in both developed and developing countries. This avoids the trap of seeing issues primarily in terms of burden-sharing and zero-sum games – that leads to inaction and the most inequitable outcome of all.

Martin Jones has criticized my account of the methodology of experimental economics on three points: the impossibility of testing external validity claims in the laboratory, my reconstruction of external validity inferences as analogical arguments, and the distinction between laboratory and non-laboratory sciences. I defend my account here and try to eliminate some misunderstandings that may have prompted Jones’s criticism.

This critical note concerns John Broome's book Rationality through Reasoning (2013). Broome claims that rationality amounts to satisfying rational requirements as opposed to responding correctly to reasons. My critique focuses on two issues. First, I try to show that Broome's account of rational requirements, in particular his answer to the so-called ‘symmetry-problem’, presupposes that responding correctly to reasons is part of rationality. Secondly, in discussing Broome's account of reasoning I criticize his claim that first-order reasoning involves no appeal to reasons and, hence, no normative thoughts on behalf of the reasoner.