Social choice theory is the study of collective decision processes and procedures. It is not a single theory, but a cluster of models and results concerning the aggregation of individual inputs (e.g., votes, preferences, judgments, welfare) into collective outputs (e.g., collective decisions, preferences, judgments, welfare). Central questions are: How can a group of individuals choose a winning outcome (e.g., policy, electoral candidate) from a given set of options? What are the properties of different voting systems? When (...) is a voting system democratic? How can a collective (e.g., electorate, legislature, collegial court, expert panel, or committee) arrive at coherent collective preferences or judgments on some issues, on the basis of its members' individual preferences or judgments? How can we rank different social alternatives in an order of social welfare? Social choice theorists study these questions not just by looking at examples, but by developing general models and proving theorems. (shrink)

The two most influential traditions of contemporary theorizing about democracy, social choice theory and deliberative democracy, are generally thought to be at loggerheads, in that the former demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the latter. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard-Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that (...) deliberation can promote these conditions, and hence that social choice theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect. (shrink)

This introductory text explores the theory of social choice. Written as a primer suitable for advanced undergraduates and graduates, this text will act as an important starting point for students grappling with the complexities of social choice theory. Rigorous yet accessible, this primer avoids the use of technical language and provides an up-to-date discussion of this rapidly developing field. This is the first in a series of texts published in association with the LSE.

This is a book about liberal democratic values and their implications for the design of political institutions. Its distinctive feature is the use of some simple mathematical techniques to clarify and defend a rather complex utilitarian conception of the liberal democratic 'way of life' based on John Stuart Mill's work. More specifically, the text focuses on three well-known 'social choice paradoxes' which are commonly held to destroy any possibility of an ideal harmony among liberal democratic values; and draws (...) upon suggestions implicit in Mill's writings to develop an ethically appealing liberal democratic social choice framework in which the aforementioned paradoxes no longer cause concern. The revised framework is a rather complex version of utilitarianism and should be of special interest to welfare economists, social choice theorists, democratic political theorists and philosophers concerned with utilitarian ethics. (shrink)

This book presents an exploration of the idea of the common or social good, extended so that alternatives with different populations can be ranked. The approach is, in the main, welfarist, basing rankings on the well-being, broadly conceived, of those who are alive. The axiomatic method is employed, and topics investigated include: the measurement of individual well-being, social attitudes toward inequality of well-being, the main classes of population principles, principles that provide incomplete rankings, principles that rank uncertain alternatives, (...) best choices from feasible sets, and applications. The chapters are divided, with mathematical arguments confined to the second part. The first part is intended to make the arguments accessible to a more general readership. Although the book can be read as a defense of the critical-level generalized-utilitarian class of principles, comprehensive examinations of other classes are included. (shrink)

Jonathan Aldred shares our desire to promote a reconciliation between social choice theory and deliberative democracy in the interests of a more comprehensive and compelling account of democracy.1 His comments on some details of our analysis – specifically, our use of Arrow’s conditions of universal domain and independence of irrelevant alternatives – give us an opportunity to clarify our position. His discussion of the independence condition in particular identifies some ambiguity in our exposition, and as such is (...) useful. We are less impressed by the way Aldred characterizes the overall terms of the reconciliation we propose. We believe that his argument on this matter should be resisted because it provides deliberative democrats with a bad excuse to dismiss social choice theory altogether, which is surely not what he intends. (shrink)

Wulf Gaertner provides a comprehensive account of an important and complex issue within social choice theory: how to establish a social welfare function while restricting the spectrum of individual preferences in a sensible way. Gaertner's starting point is K. J. Arrow's famous 'Impossibility Theorem', which showed that no welfare function could exist if an unrestricted domain of preferences is to be satisfied together with some other appealing conditions. A number of leading economists have tried to provide (...) avenues out of this 'impossibility' by restricting the variety of preferences: here, Gaertner provides a clear and detailed account, using standardized mathematical notation, of well over forty theorems associated with domain conditions. Domain Conditions in Social Choice Theory will be an essential addition to the library of social choice theory for scholars and their advanced graduate students. (shrink)

This introductory text explores the theory of social choice. This text is an important starting point for students grappling with the complexities of social choice theory. Rigorous yet accessible, with new chapter exercises, it avoids the use of technical language and provides an up-to-date discussion of this rapidly developing field.

The essays in this volume, first published in 1986, examine the philosophical foundations of social choice theory. This field, a modern and sophisticated outgrowth of welfare economics, is best known for a series of impossibility theorems, of which the first and most crucial was proved by Kenneth Arrow in 1950. That has often been taken to show the impossibility of democracy as a procedure for making collective decisions. However, this interpretation is challenged by several of the contributors (...) here. Other central issues discussed in the volume include the possibility of making interpersonal comparisons of utility, the question of whether all preferences are equally to be valued, and the normative individualism underlying the theoretical tradition. Criticisms of social choice theory are advanced and suggestions for alternative approaches are developed. (shrink)

The essays in this volume, first published in 1986, examine the philosophical foundations of social choice theory. This field, a modern and sophisticated outgrowth of welfare economics, is best known for a series of impossibility theorems, of which the first and most crucial was proved by Kenneth Arrow in 1950. That has often been taken to show the impossibility of democracy as a procedure for making collective decisions. However, this interpretation is challenged by several of the contributors (...) here. Other central issues discussed in the volume include the possibility of making interpersonal comparisons of utility, the question of whether all preferences are equally to be valued, and the normative individualism underlying the theoretical tradition. Criticisms of social choice theory are advanced and suggestions for alternative approaches are developed. (shrink)

This article explores public reason liberalism’s indeterminacy problem, a problem that obtains when we admit significant diversity into our justificatory model. The article argues first that Gerald Gaus’s solution to the indeterminacy problem is unsatisfactory and second that, contra Gaus’s concerns, social choice theory is able to solve public reason’s indeterminacy problem. Moreover, social choice theory can do so in a way that avoids the worries raised against Gaus’s solution to the indeterminacy problem as (...) well as the worries Gaus himself raises against the use of social choice mechanisms. Social choice theory thus rescues public reason liberalism by aggregating out of indeterminacy. (shrink)

Avalanche studies have undergone a transition in recent years. Early research focused mainly on environmental factors. More recently, attention has turned to human factors in decision making, such as behavioural and cognitive biases. This article adds a social component to this human turn in avalanche studies. It identifies lessons for decision making by groups of skiers from the perspective of social choice theory, a sub-field of economics, decision theory, philosophy and political science that investigates voting (...) methods and other forms of collective decision making. In the first part, we outline the phenomenon of wisdom of crowds, where groups make better decisions than their individual members. Drawing on the conceptual apparatus of social choice theory and using idealised scenarios, we identify conditions under which wisdom of crowds arises and also explain how and when deciding together can instead result in worse decisions than may be expected from individual group members. In the second part, we use this theoretical understanding to offer practical suggestions for decision making in avalanche terrain. Finally, we make several suggestions for risk management in other outdoor and adventure sports and for outdoor sports education. (shrink)

Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences—which is closely related to the latter’s foundational contribution to model theory. In this note we show in a model-theoretic framework how Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also (...) connects Arrow’s seminal result to key developments and concepts in the history of model theory, notably ultraproducts and preservation results. (shrink)

Axiomatic characterization results in social choice theory are usually compared either regarding the normative plausibility or regarding the logical strength of the axioms involved. Here, instead, we propose to compare axiomatizations according to the language used for expressing the axioms. In order to carry out such a comparison, we suggest a formalist approach to axiomatization results which uses a restricted formal logical language to express axioms. Axiomatic characterization results in social choice theory then turn (...) into definability results of formal logic. The advantages of this approach include the possibility of non-axiomatizability results, a distinction between absolute and relative axiomatizations, and the possibility to ask how rich a language needs to be to express certain axioms. We argue for formal minimalism, i.e., for favoring axiomatizations in the weakest language possible. (shrink)

Sports tournaments provide a procedure for producing a champion and ranking the contestants based on game results. As such, tournaments mirror aggregation methods in social choice theory, where diverse individual preferences are put together to form an overall social preference. This connection allows us a novel way of conceptualizing sports tournaments, their results, and significance. I argue that there are genuine intransitive dominance relationships in sports, that social choice theory provides a framework for (...) understanding rankings in such situations and that these considerations provide a new reason to endorse championship pluralism. (shrink)

In models of multi-level selection, the property of Darwinian fitness is attributed to entities at more than one level of the biological hierarchy, e.g. individuals and groups. However, the relation between individual and group fitness is a controversial matter. Theorists disagree about whether group fitness should always, or ever, be defined as total (or average) individual fitness. This paper tries to shed light on the issue by drawing on work in social choice theory, and pursuing an analogy (...) between fitness and utility. Social choice theorists have long been interested in the relation between individual and social utility, and have identified conditions under which social utility equals total (or average) individual utility. These ideas are used to shed light on the biological problem. (shrink)

A platitude that took hold with Kuhn is that there can be several equally good ways of balancing theoretical virtues for theory choice. Okasha recently modelled theory choice using technical apparatus from the domain of social choice: famously, Arrow showed that no method of social choice can jointly satisfy four desiderata, and each of the desiderata in social choice has an analogue in theory choice. Okasha suggested that one (...) can avoid the Arrow analogue for theory choice by employing a strategy used by Sen in social choice, namely, to enhance the information made available to the choice algorithms. I argue here that, despite Okasha’s claims to the contrary, the information-enhancing strategy is not compelling in the domain of theory choice. (shrink)

The usual procedure in the theory of social choice consists in postulating some desirable properties which an aggregation procedure should verify and derive from them the features of a corresponding social choice function and the outcomes that arise at each possible profile of preferences. In this paper we invert this line of reasoning and try to infer, up from what we call social situations the criteria verified in the implicit aggregation procedure. This inference process, (...) which extracts intensional from extensional information can be seen as an exercise in “qualitative statistics”. (shrink)

Kuhn’s famous thesis that there is ‘no unique algorithm’ for choosing between rival scientific theories is analysed using the machinery of social choice theory. It is shown that the problem of theory choice as posed by Kuhn is formally identical to a standard social choice problem. This suggests that analogues of well-known results from the social choice literature, such as Arrow’s impossibility theorem, may apply to theory choice. If an (...) analogue of Arrow’s theorem does hold for theory choice this would refute Kuhn’s thesis, but it would also pose a threat to the rationality of science, a threat that is if anything more worrying than that posed by Kuhn. Various possible ‘escape routes’ from Arrow’s impossibility result are examined, in particular Amartya Sen’s idea of ‘enriching the informational basis’. It is shown that Sen’s idea can be applied to the problem of theory choice in science. This in turn sheds light on two well-known approaches to inductive inference in philosophy of science: Bayesianism and statistical model selection. (shrink)

Distributed cognition refers to processes which are (i) cognitive and (ii) distributed across multiple agents or devices rather than performed by a single agent. Distributed cognition has attracted interest in several fields ranging from sociology and law to computer science and the philosophy of science. In this paper, I discuss distributed cognition from a social-choice-theoretic perspective. Drawing on models of judgment aggregation, I address two questions. First, how can we model a group of individuals as a distributed cognitive (...) system? Second, can a group acting as a distributed cognitive system be ‘rational’ and ‘track the truth’ in the outputs it produces? I argue that a group’s performance as a distributed cognitive system depends on its ‘aggregation procedure’ – its mechanism for aggregating the group members’ inputs into collective outputs – and I investigate the properties of an aggregation procedure that matter. (shrink)

The paper addresses the ‘rational choice only’ reconstruction, characterization, and interpretation of classical and neoclassical economics. It argues that such a reconstruction is inaccurate failing to do justice to the dual theoretical character of classical/neoclassical economics. The paper instead proposes and shows that the latter involves not only elements of ‘rational choice theory’ but also those of an alternative conception. It identifies various and important ideas, observations, and implications of irrational choice and action within classical/neoclassical economics. (...) One class of such ingredients involves forms, expressions, and cases—i.e. specification and classification—of irrational choices in the economy. Another class comprises the social and other factors—i.e. economic sociology or social economics—of irrational choices in the economy. The paper’s intended contribution is to help identify and clarify the extant sources and alternatives of rational choice theory in conventional economics.... (shrink)

In a recent article, Okasha challenges Kuhn’s claim that there is no ‘neutral’ algorithm for theory choice. He argues using Arrow’s ‘impossibility’ theorem that — except under certain favourable conditions concerning the measurability and comparability of theoretical values — there are no theory choice algorithms at all, neutral or otherwise. But Okasha’s argument does not apply to important theory choice problems, among them the case of Copernican and Ptolemaic astronomy that much occupied Kuhn. The (...) reason is that Kuhn’s choice criteria can rank rival theories in only a few ways, which makes the analogue of Arrow’s domain assumption inappropriate. It is hard to see any consequences for Kuhn’s claim, or threat to the rationality of science. (shrink)

In this paper we explore the relation between three areas: judgment aggregation, belief merging and social choice theory. Judgment aggregation studies how to aggregate individual judgments on logically interconnected propositions into a collective decision on the same propositions. When majority voting is applied to some propositions it may however give a different outcome than majority voting applied to another set of propositions. Starting from this so-called doctrinal paradox, the paper surveys the literature on judgment aggregation, and shows (...) that the application of a well known belief merging operator can dissolve the paradox. Finally, the use of distances is shown to establish a link between belief merging and preference aggregation in social choice theory. (shrink)

This article makes two arguments: first, it argues that theories connecting ethnic group mobilization with democratic bargaining are based, often unwittingly, on primordialist assumptions that bias them toward overestimating the intractability of ethnic group demands. Second, it proposes a synthesis of constructivist approaches to ethnic identity and social choice theory to show how we who study ethnic mobilization might build theories that rely on the more realistic and more powerful assumption of instability in ethnic group boundaries and (...) preferences. It illustrates the promise of this approach through a study of the language bargain struck in India's constituent assembly between 1947 and 1949. (shrink)

In democracies citizens are supposed to have some control over the general direction of policy. According to a pretheoretical interpretation of this idea, the people have control if elections and other democratic institutions compel officials to do what the people want, or what the majority want. This interpretation of popular control fits uncomfortably with insights from social choice theory; some commentators—Riker, most famously—have argued that these insights should make us abandon the idea of popular rule as traditionally (...) understood. This article presents a formal theory of popular control that responds to the challenge from social choice theory. It makes precise a sense in which majorities may be said to have control even if the majority preference relation has an empty core. And it presents a simple game-theoretic model to illustrate how majorities can exercise control in this specified sense, even when incumbents are engaged in purely re-distributive policymaking and the majority rule core is empty. (shrink)

Donald Green and Ian Shapiro discover a curious gulf between the prestige of rational choice approaches and the dearth of solid empirical findings. But we can understand neither the prestige of rational choice theory nor its pathologies unless we see it as a variant of the equilibrium analysis found in physics, economics, and biology. Only such a global perspective on rational choice theory will reveal its core assumptions and the likely shape of its future in (...) political science. In this light, the growing dominance of rational choice theory in political science is all but inevitable and its pathologies are all but inescapable. (shrink)

An analogue of Arrow’s theorem has been thought to limit the possibilities for multi-criterial theory choice. Here, an example drawn from Toy Science, a model of theories and choice criteria, suggests that it does not. Arrow’s assumption that domains are unrestricted is inappropriate in connection with theory choice in Toy Science. There are, however, variants of Arrow’s theorem that do not require an unrestricted domain. They require instead that domains are, in a technical sense, ‘rich’. (...) Since there are rich domains in Toy Science, such theorems do constrain theory choice to some extent—certainly in the model and perhaps also in real science. (shrink)