There is something about this book. My copy went missing twice in the last months, once at the London School of Economics and once at Erasmus University Rotterdam, due to people borrowing it, keeping it longer than promised and passing it on to others who were interested in it. It is easy to see why: for anyone with at least a passing familiarity with economics and philosophy it is already exciting to browse through the list of contributions by heavyweights that this handbook presents. For many of the topics in rational and social choice covered, the contributors are exactly the ones whose names come to mind first.

The handbook showcases an interdisciplinary field of research that has received increasing attention in recent years. Famously, rational and social choice theory consists of a collection of tools that analyse individual and collective decision-making. These tools, presented in the form of mathematical models, lend themselves to a wide range of applications in both economics and philosophy. In economics, rational and social choice constitutes an important building block of economic theory and as such, it serves as the basis for consumer theory, industrial economics and welfare economics, to name but a few fields. In philosophy, rational and social choice theory is on the one hand discussed as an important formal theory of instrumental rationality, and on the other hand it is employed in giving accounts of, for instance, cooperation, the evolution of morality, confirmation of scientific hypotheses, and social epistemology. Rational and social choice theory has seen a number of significant developments recently, including the growing acceptance of empirically informed decision theory in economics, the advancement of judgement aggregation as a generalization of social choice theory, a renewed attention to problems like belief change, choice over time, the informational basis of individual and collective choice, and the measurement of freedom. Indeed, rational and social choice theory is an increasingly interdisciplinary field of research, with contributors from economics and philosophy alike.

How does this handbook approach it? The volume is structured into two parts, one pertaining to individual choice, and the other one to collective choice. The editors Paul Anand, Prasanta K. Pattanaik and Clemens Puppe give a brief introduction, which is followed by 23 individual chapters. While the editors make an attempt to group the individual contributions into sub-themes in their introduction, the chapters are thereafter presented as follows: Part I comprises 12 chapters on individual choice, entitled ‘Utility Theory, Rationality, and Decision-Making’ and Part II contains 11 chapters on collective decision-making, entitled ‘Social Choice and Welfare’. Comparatively little is offered by way of structuring the material and giving it context. Here, more could have been made of the fact that several contributions relate to each other in an interesting way. Small introductions to sub-themes would have been of much help to the non-specialist and student alike to make use of the different contributions, even more so as the style, length and tone of the individual contributions is very diverse indeed: some are excellent introductions for the non-specialist while others are excellent overviews for the specialist; some chapters are written in a succinct encyclopedia-style and provide broad overviews of past developments while others present more recent advances in well-defined niches; some contributions are substantially longer than others; some are very formal and others are completely verbal. In the remainder of the review, I will attempt to present a guide through the material, to help potential readers and users of this handbook to reap the rich benefits of the contributions.

Part I of the handbook covers topics in individual rational choice. It opens with an impressive contribution by Grant and van Zandt who offer an attentive tour de force through fundamental elements of ‘Expected Utility Theory’. It includes a detailed exposition of revealed preference theory and discussion of several problems that are not often included in comparable expositions, such as different kinds of independence assumptions in the case of certainty and uncertainty, multi-attribute decision theories, a careful separation between preference and choice, detailed discussion of subjective and objective probabilities, as well as a presentation of important aspects of Savage's subjective expected utility theory, including the problem of ‘large worlds’ – the fact that the framework requires a detailed specification of states of the world. The presentation of this chapter is remarkably careful in the way the different building blocks of expected utility theory are introduced and discussed, it is ambitious, dense and rather fascinating for the specialist; it will not serve the non-specialist or graduate student with an introduction to expected utility theory.

A similarly comprehensive introduction to empirically informed decision theory is not available in this handbook. However, there are four contributions that jointly cover the relevant topics in this area. Abdellaoui introduces the framework of ‘Rank-Dependent Utility’, striking a balance between presenting the empirical findings it is supposed to capture and presenting the formal framework itself. Read reviews ‘Experimental Tests of Rationality’ and focuses on empirical findings of violations of expected utility theory, such as the Allais problem. In similar vein, the chapter entitled ‘Ambiguity’ by Eichberger and Kelsey discusses empirical findings related to how real-world agents handle situations of various types of uncertainty, such as in the Ellsberg paradox. Bleichrodt and Schmidt present ‘Applications of Non-Expected Utility Theory’, focusing on the health domain and auctions. Together, the contributions highlight the numerous advances that empirically informed decision theories have made in recent years by characterizing the way in which their formal frameworks differ from (subjective) expected utility theory, and discussing the famous examples and experiments that have played a crucial role in this literature. While the aforementioned chapters presume familiarity with technical details when they discuss the formal frameworks, most of the conceptual discussion and the presentation of the empirical content should still be accessible to the non-specialist.

Philosophical and conceptual problems associated with rational choice theory are addressed by three contributions in this handbook. Firstly, McClennen gives a succinct and accessible overview of ‘The Normative Status of the Independence Principle’ by way of presenting five attempted defences of it, including Savage's dominance reasoning, Broome's re-description proposal and Raiffa's money-pump argument. Secondly, Anand reviews the connections between rationality and the transitivity requirement in rational choice in his contribution ‘Rationality and Intransitive Preference: Foundations for the Modern View’, examining arguments for the permissibility of intransitive preference. Finally, Hájek offers an introduction to different types of so-called ‘Dutch Book Arguments’, which have been advanced to show that an agent's rational degrees of belief have to obey the probability calculus. These three chapters are much more accessible to the non-specialist than the chapters on expected utility theory and empirically informed non-expected utility theories, which is partly due to their conceptual focus. They will lend themselves to use in postgraduate and (with provisions) in third-year undergraduate teaching as well.

Four contributions that offer and discuss extensions to rational choice theory round off the first part of the handbook. Karni introduces ‘State-Dependent Utility’, which formalizes the idea that the utility of outcomes can vary with regards to the circumstance in which they occur. After the presentation of the framework that includes a careful distinction between state independence of preferences and utilities, Karni uses subjective expected utility with state-dependent utilities to discuss moral hazard, risk aversion and the application of disability insurance. Manzini and Mariotti review different approaches to time discounting in their chapter on ‘Choice over Time’. A concise rehearsal of representation frameworks for time discounting is followed by a discussion of recent contributions that are empirically informed, which makes this chapter an excellent starting point for further exploring problems of time and decision, both theoretically and empirically. Alós-Ferrer and Schlag present accounts of ‘Imitation and Learning’ in a framework of population dynamics which can be classified as one that views agents as boundedly rational, in the sense that their behaviour is modelled by rules. Nehring and Puppe discuss measures of ‘Diversity’, which includes an account of dissimilarity metrics that can be an important tool for the rational choice theorist. Overall, the aforementioned contributions present extensions to or variants of rational choice theory, and carry them further to analyse a wider range of phenomena. As such, they are again more demanding on the reader, and will be of great interest especially for those working in rational choice theory or employing it as a tool – though the contributions could also be used as secondary readings in some postgraduate teaching settings.

Part II of the handbook covers topics in social choice theory. While there is no comprehensive overview of key topics in standard social choice theory, as was offered by Grant and van Zandt for expected utility theory, there are three contributions that provide reviews of parts of the building blocks of social choice theory. Firstly, Pattanaik discusses the ‘Limits of Utilitarianism as the Ethical Basis of Public Action’, raising conceptual issues such as how far the notion of utility can be broadened, and what kinds of assumptions underlie aggregation procedures. Secondly, Suzumura and Xu present ‘Consequentialism and Non-Consequentialism: The Axiomatic Approach’, in which they provide a unifying framework for welfarist and non-welfarist analysis of social states. Thirdly, List and Puppe provide an introduction to the comparatively new field of ‘Judgement Aggregation’, briefly motivating the framework with the discursive dilemma, and then reviewing different sets of aggregation conditions and stating the most important impossibility theorems. The accessibility of the three chapters differs, and corresponds to the level of formal analysis they include. While a review of the traditional Arrovian social choice framework is not included in the handbook, together the three chapters offer insights into key elements of modern social choice theory.

Four papers are included in Part II that discuss topics that arise in the context of social choice theory, such as freedom, responsibility, equality and justice. Dowding and van Hees review ‘Freedom of Choice’, beginning with the cardinality-based approach that characterizes freedom of choice by the number of available options. Two families of responses are reviewed: firstly, the diversity (or non-preference-based) response, that criticizes the absence of information about the differences between alternatives in the cardinality-based approach, and secondly, the opportunity (or preference-based) approach that criticizes the cardinality-based approach for not taking into account the preferences of individuals over the various options. The chapter ends by considering open questions and avenues for future research in this field. Fleurbaey discusses issues related to ‘Responsibility’, focusing on the question of how redistribution can be responsibility-sensitive. He presents four approaches that are derived from a distinction between a liberal versus a utilitarian approach on the one hand, and a compensation-oriented versus a reward-oriented approach on the other hand. Tungodden reviews problems related to ‘Equality and Priority’ providing an analysis of different types of egalitarianism, and the kinds of assumptions implied in their responses to the levelling-down objection, as well as highlighting the problem of uncertainty. Peter presents ‘Rawlsian Justice’ in two steps: firstly, a succinct overview of the main elements of Rawls’ theory is given, and secondly, its problems with regards to normative economics are discussed, including the maximin principle, the use of expected utility theory behind the veil of ignorance, and the problem of interpersonal comparisons. All four contributions mentioned here will be very valuable guides to their respective areas for researchers in social choice, especially since they succeed in bringing together different strands of literatures in philosophy and economics. At the same time, the manner of their presentation makes the material accessible to non-specialists and postgraduate students alike.

Papers that discuss the informational basis and applied problems of social choice round off Part II of the handbook. Blackorby, Bossert and Donaldson give a concise introduction to ‘Population Ethics’ by presenting aggregation results based on principles that apply to variable populations. Schokkaert's introduction to ‘The Capabilities Approach’ reviews the basic elements of Sen's framework and asks how such a multidimensional account of wellbeing can be combined with other tools in social choice theory. Gaertner's contribution ‘Distributive Justice: An Overview of Experimental Evidence’ presents data on how individuals apply different principles of justice when making decisions about the distribution of goods, suggesting, for instance, that the equity axiom in Rawls’ second principle is widely supported by the participants in the experiments. Tsuchiya and Miyamoto write on ‘Social Choice in Health and Health Care’, employing tools from social choice theory to the health domain, focusing on questions concerning equal access to health. All four of these contributions will be of interest to researchers within social choice, as well as valuable for postgraduate teaching.

In conclusion, the handbook offers a rich resource of material in individual and collective choice. For all the strengths of the individual contributors and contributions of this handbook, there are nevertheless a few missed opportunities to lament, such as the fact that the contributions seem to serve very different purposes and that more could have been done to offer context for them. One missed opportunity that has not been mentioned yet consists in the distinct lack of diversity of contributors. Most strikingly, only two out of 35 contributors are female. For edited handbooks of this significance and volume, the editors just have to do better. Overall, the reader of this handbook feels like she or he is looking at an impressive collection of snapshots of various workshops in which ‘a fertile dialogue between economic theory and philosophy that has continued to flourish in recent years’ is in the making, as the editors aptly put it in their introduction. As such, the handbook will be useful for and of interest to anyone working in economics and philosophy, specialists and non-specialists in rational and social choice alike. I will want to keep a very keen eye on this handbook – and so do you.