Part intellectual autobiography and part exposition of complex yet contemporary economic ideas, this lively conversation with renowned scholar and public intellectual Kenneth J. Arrow focuses on economics and politics in light of history, current events, and philosophy as well. Reminding readers that economics is about redistribution and thus about how we treat each other, Arrow shows that the intersection of economics and ethics is of concern not just to economists but for the public more broadly. With a foreword by Amartya (...) Sen, this book highlights the belief that government can be a powerful force for good, and is particularly relevant in the current political climate and to the lay reader as well as the economist. (shrink)

The arrow of time is a familiar phenomenon we all know from our experience: we remember the past but not the future and control the future but not the past. However, it takes an effort to keep records of the past, and to affect the future. For example, it would take an immense effort to unmix coffee and milk, although we easily mix them. Such time directed phenomena are sub- sumed under the Second Law of Thermodynamics. This law characterizes our (...) experience of the arrow of time in terms of an increase of a theoretical magnitude called entropy. Statistical mechan- ics tries to explain the Second Law as an effect of the behavior of the microscopic particles that make up the universe. Since our senses are too coarse to see this microstructure, statistical mechanics describes our experience in terms of probability, or in terms of the partial information we have about the particles. In this paper we explain the workings of statistical mechanics; how it accounts for probability as an objective feature of the world based on the underlying dynamics; how it accounts for our memories of the past; how the statistical mechanical probability under- writes the Second Law; and how, at the same time, it leads to a violation of the Second Law by the so-called Maxwell’s Demon. (shrink)

From its first proposal, the Central Dogma had a graphical form, complete with arrows of different types, and this form quickly became its standard presentation. In different scientific contexts, arrows have different meanings and in this particular case the arrows indicated the flow of information among different macromolecules. A deeper analysis illustrates that the arrows also imply a causal statement, directly connected to the causal role of genetic information. The author suggests a distinction between two different kinds of causal links, (...) defined as 'physical causality' and 'biological determination', both implied in the production of biological specificity. (shrink)

Set theoretic formulation of Arrow's theorem, viewedin light of a taxonomy of transitive relations,serves to unmask the theorem's understatedgenerality. Under the impress of the independenceof irrelevant alternatives, the antipode of ceteris paribus reasoning, a purported compilerfunction either breaches some other rationalitypremise or produces the effet Condorcet. Types of cycles, each the seeming handiwork of avirtual voter disdaining transitivity, arerigorously defined. Arrow's theorem erects adilemma between cyclic indecision anddictatorship. Maneuvers responsive theretoare explicable in set theoretic terms. None ofthese gambits rival in (...) simplicity the unassistedescape of strict linear orderings, which, by virtueof the Arrow–Sen reflexivity premise, are notcaptured by the theorem. Yet these are therelations among whose n-tuples the effetCondorcet is most frequent. A generalization andstronger theorem encompasses these and all otherlinear orderings and total tierings. Revisions tothe Arrow–Sen definitions of `choice set' and`rationalization' similarly enable one to generalizeSen's demonstration that some rational choicefunction always exists. Similarly may onegeneralize Debreu's theorems establishing conditionsunder which a binary relation may be represented bya continuous real-valued order homomorphism. (shrink)

What is time? Does it pass? Is the future open? Why do we care? Philosophy of Time: The Basics doesn’t answer these questions. It does give you an opinionated introduction to thinking a bit more deeply about them. Written in a way that assumes no philosophical background from its readers, this book looks at central topics in philosophy of time and shows how they relate to other time-related topics – from theoretical physics (without the maths!) to your own mortality. Additional (...) questions include: -/- In what way is time different to space? How long is the present? Does the Theory of Relativity show time doesn’t pass? What makes time have a direction or ‘arrow’? Can you be harmed by your own death? -/- Allowing the reader to think more deeply about time, this book begins to untangle some of the most difficult knots in all of philosophy. It also provides practical advice to prospective time-travelers. (shrink)

This article investigates how different philosophical traditions and schools of thought have understood the practice and the discipline of archery. Whereas the scholarly literature on the history, the techniques and the uses of bows and arrows is diverse and extensive, my aim is to contribute to the less developed research on the relationship between philosophy and archery. Specifically, I will explore in what terms philosophers have employed the bow as a metaphor for both their standpoints and, more generally, significant aspects (...) of everyday life. (shrink)

Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels of abstraction. Indeed, it is (...) basically impracticable to maintain logic–and–metalogic without paying heed to cognitive theorizing. For it is cognitively irrelevant whether possible conclusions are deduced from some premises before the premises are determined to be true or whether the premises themselves are determined to be true first and, then, the conclusions are deduced from them. In this paper we consider the term metalogic as inherently embodied under the framework referred to as cognitive science and mathematics. We propose a metalogical interpretation of Arrow’s impossibility theorem and, to that end, choice theory is understood as a mental course of action dealing with logic and metalogic issues, in which a possible mathematical approach to model a mental course of action is adopted as a systematic operating method. Nevertheless, if we look closely at the core of Arrow’s impossibility theorem in terms of metalogic, a second fundamental contribution to this framework is represented by the Nash equilibrium. As a result of the foregoing, therefore, we prove the metalogical equivalence between Arrow’s impossibility theorem and the existence of the Nash equilibrium. More specifically, Arrow’s requirements correspond to the Nash equilibrium for finite mixed strategies with no symmetry conditions. To demonstrate this proof, we first verify that Arrow’s set and Nash’s set are isomorphic to each other, both sets being under stated conditions of non–symmetry. Then, the proof is completed by virtue of category theory. Indeed, the two sets are categories that correspond biuniquely to one another and, thus, it is possible to define a covariant functor that preserves their mutual structures. According to this, we show the proof–dedicated metalanguage as a precursor to a special equivalence theorem. (shrink)

Amartya Sen has recently urged that political philosophers pay attention to social choice theory in their deliberations about justice. However, despite its merits, social choice theory is not standardly part of undergraduate political philosophy. One difficulty is that it involves symbolic logic and difficult concepts. We can reduce this challenge by making the material no harder than it needs to be. I consider the standard proof of Arrow’s Theorem, a seminal result. Kenneth Arrow does not explicate the role of the (...) irrelevance of independent alternatives. Sen and Wulf Gaertner have offered clarifications, but I shall elucidate the full role. (shrink)

This essay offers a meta-level analysis in the sociology and history of physics in the context of the "Arrow of Time" or so-called "Two Times" problem. In effect, it argues that the two topics are intertwined, and it is only by coming to grips with the sociological aspects, involving adherence to certain metaphysical, epistemological and methodological beliefs and practices, that real progress can be made in the physics.

This paper is a critique of Kenneth Arrow's thesis concerning the logical impossibility of a constitution. I argue that one of the premises of Arrow's proof, that of the transitivity of indifference, is untenable. Several concepts of preference are introduced and counter-instances are offered to the transitivity of indifference defined along the standard lines in terms of these concepts. Alternate analyses of indifference in terms of preference are considered, and it is shown that these do not serve Arrow's purposes either. (...) Finally, it is argued that in the single special case in which indifference could plausibly be held to be transitive, Arrow's thesis is innocuous. (shrink)

Seeking the good life: Socrates' erotic revolution -- At home in the universe: the Stoics as Existentialists -- Senses of the self: Augustine and the ascent of the soul -- Overcoming alienation: Rousseau's search for authenticity -- Becoming who we are: Kierkegaard against his age (and ours) -- Single in the crowd: Thoreau's existential experiment at Walden Pond -- No short cut to Paradise: the lonely passion of William James -- Beyond Nihilism: Nietzsche and the ethics of utopia -- Between (...) solitude and solidarity: the two worlds of Albert Camus -- The desire to be God: Sartre and the winding roads of freedom -- Dramatist of a broken world: the soft theism of Gabriel Marcel -- Thinking without banisters: Hannah Arendt and the face of radical evil. (shrink)

'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

Every process studied in any science other than physics defines an arrow of time – to say nothing for the directedness of the processes of causation, inference, memory, control, and counterfactual dependence that occur in everyday life. The discussion in this chapter is confined to the arrow of time as it occurs in physics. The chapter briefly discusses those features of microscopic physics, which seem to conflict with time asymmetry. It explains just how this conflict plays out in the important (...) context of thermodynamics and statistical mechanics. The chapter then reviews the main strategies available for resolving the conflict between reversible microdynamics and irreversible macrodynamics, working within the context of the quantitative, time‐irreversible evolution laws that seem to apply to large‐scale phenomena. Finally, it offers a broad the discussion covering other arrows of time within physics. (shrink)

This study contends that existentialism is the perennial philosophy thus going against the assumption that it is a school of more recent provenance. Anthologies or introductory texts used begin with Kierkegaard and go on to emphasize Nietzsche, Sartre, and Heidegger. This book reflects a more catholic mapping, including three thinkers from the classical period , who are argued to be just as 'existential' as more modern thinkers and indeed influence the latter in important ways. Also included are three Americans who (...) are rarely considered existentialists. Furthermore, the book has a pedagogical emphasis, reflecting students' points-of-view: what they learn, how they react, questions they have, and how in general existentialism meets their education needs and expectations. It is, therefore, necessarily interdisciplinary in character, pointing out implications of existentialism for education, concerns like happiness, war and peace, democracy, sexuality, and terrorism. (shrink)

One of the questions that is addressed, from various perspectives, is the origin of time-asymmetry. Given the time-symmetry of the dynamical laws, all inferences about the future that are derivable from a dynamical theory are matched by inferences about the past. For Huw Price, who discusses the origins of cosmological time asymmetry, this is reason to treat all time-asymmetric cosmological theories with caution. He dismisses both the inflationary model and Stephen Hawking’s proposal to account for time-asymmetry with his famous “no (...) boundary condition.” Instead, on the basis of the fact that we have no a priori reasons to distinguish between initial and final conditions, he advocates Gold’s time-symmetric model for the universe, in which the thermodynamical arrow of time is tied to the expansion of the universe, so that in the contracting phase towards the big crunch, entropy decreases. (shrink)

Conceived by Johan van Benthem and Yde Venema, arrow logic started as an attempt to give a general account of the logic of transitions. The generality of the approach provided a wide application area ranging from philosophy to computer science. The book gives a comprehensive survey of logical research within and around arrow logic. Since the natural operations on transitions include composition, inverse and identity, their logic, arrow logic can be studied from two different perspectives, and by two (complementary) methodologies: (...) modal logic and the algebra of relations. Some of the results in this volume can be interpreted as price tags. They show what the prices of desirable properties, such as decidability, (finite) axiomatisability, Craig interpolation property, Beth definability etc. are in terms of semantic properties of the logic. The research program of arrow logic has considerably broadened in the last couple of years and recently also covers the enterprise to explore the border between decidable and undecidable versions of other applied logics. The content of this volume reflects this broadening. The editors included a number of papers which are in the spirit of this generalised research program. (shrink)

Review of Bryan W. Roberts: Reversing the Arrow of Time, Cambridge University Press, 2022.

The paradoxes and dilemmas of social choice theory can be taken as an argument against a certain view of democracy: For the identity theory democracy represents a collective actor standing for aggregated individual interests. According to a second model of society, democracy has its normative basis in structural traits of interaction and cooperation. Within the formal theory of politics both the Arrow-Theorem and the Liberal Paradox undermine the identity theory and give us reasons for the second, the normative theory which (...) takes democracy as being constituted by structural rules. (shrink)

Many philosophers and scientists have claimed that time has an arrow that points in a special direction. The Roman poet Ovid may have referred to this one-way property of time when he said, “Time itself glides on with constant motion, ever as a flowing river.” However, understanding this arrow is not … Continue reading The Arrow of Time →.

Based on the hypothesis that the (non-reversible) arrow of time is intrinsic in any system, no matter how small, the consequences are discussed. Within the framework of local quantum physics it is shown how such a semi-group action of time can consistently be extended to that of the group of spacetime translations in Minkowski space. In presence of massless excitations, however, there arise ambiguities in the theoretical extensions of the time translations to the past. The corresponding loss of quantum information (...) on states upon time is determined. Finally, it is explained how the description of operations in classical terms combined with constraints imposed by the arrow of time leads to a quantum theoretical framework. These results suggest that the arrow of time is fundamental in nature and not merely a consequence of statistical effects on which the Second Law is based. (shrink)

Responding to Hasok Chang’s vision of the history and philosophy of science as the continuation of science by other means, I illustrate the methods of HPS and their utility through a historico-critical examination of the problem of “time’s arrow‘, that is to say, the problem posed by the claim by Boltzmann and others that the temporal asymmetry of many physical processes and indeed the very possibility of identifying each of the two directions we distinguish in time must have a ground (...) in the laws of nature. I claim that this problem has proved intractable chiefly because the standard mathematical representation of time employed in the formulation of the laws of nature “forgets‘ one of the connotations of the word ”time’ as it is used in ordinary language and in experimental physics. (shrink)

This paper advances a framework to conceptualize societal care-giving arrangements abstractly. It is abstract in that it brackets the meaning of our particular relationships. This framework, which I call “the arrow of care map”, is a descriptive tracking model that is a necessary component of a theory of justice, but it is not a normative prescription in itself. The basic idea of the map is then multiply specifiable to track various ascriptive identity categories as well as different categories of care (...) labor. In this way, the idea of the arrow of care map serves as a conceptual frame within which to begin to understand every human society’s care-giving arrangement. I characterize it as a component of “ideal theory” insofar as it seeks to clarify our values, without the immediate aim of formulating principles to govern a just society. The resultant partial theory of justice is one that responds to non-ideal theory’s critiques of the ideological nature of liberal contractarianism’s idealizations and abstractions while moving towards new visions of a just society. (shrink)

There is a widespread assumption that the universe in general, and life in particular, is 'getting more complex with time'. This book brings together a wide range of experts in science, philosophy and theology and unveils their joint effort in exploring this idea. They confront essential problems behind the theory of complexity and the role of life within it: what is complexity? When does it increase, and why? Is the universe evolving towards states of ever greater complexity and diversity? If (...) so, what is the source of this universal enrichment? This book addresses those difficult questions, and offers a unique cross-disciplinary perspective on some of the most profound issues at the heart of science and philosophy. Readers will gain insights in complexity that reach deep into key areas of physics, biology, complexity science, philosophy and religion. (shrink)

In this paper, I draw on postphenomenology and material engagement theory to consider the material and emergent character of sociality in Homo faber. I approach this through the context of the bow and arrow, which is a technology that has received recent attention in cognitive archeology as a proxy for assessing criteria that made early human cognition distinct from that of other hominins. Through an ethnographic case study, I scrutinize the forms of knowledge that are required to use the technology (...) in the dynamic field of environmental practices that constitute the hunt. I demonstrate that the learning of the skill is a transformational process where beginners develop self and intentionality by attuning subjective capacities for sensory awareness and creative responsiveness. Through mutual participation, the bow and arrow aligns disposition and rapport among those whose life processes are shaped by the skill. As a mechanism of shared experience, the bow and arrow generates a community can together perceive and act creatively in an impermanent world. Through these observations, I argue that early human sociality was built not on a pre-evolved capacity for symbolic representation but on technical experience, and I consider important questions this raises about the nature of evolutionary processes at work in the development of communities through time. (shrink)

Why is the future so different from the past? Why does the past affect the future and not the other way round? The universe began with the Big Bang - will it end with a `Big Crunch'? Now in paperback, this book presents an innovative and controversial view of time and contemporary physics. Price urges physicists, philosophers, and anyone who has ever pondered the paradoxes of time to look at the world from a fresh perspective, and throws fascinating new light (...) on some of the great mysteries of the universe. (shrink)

Talk of mechanisms is ubiquitous in the natural sciences. Interdisciplinary fields such as biochemistry and pharmacy frequently discuss mechanisms with the assistance of diagrams. Such diagrams usually depict entities as structures or boxes and activities or interactions as arrows. While some of these arrows may indicate causal or componential relations, others may represent temporal or operational orders. Importantly, what kind of relation an arrow represents may not only vary with context but also be underdetermined by empirical data. In this manuscript, (...) we investigate how an analysis of pharmacological mechanisms in terms of producing and underlying mechanisms—as discussed in the contemporary philosophy of science—may shed light on these issues. Specifically, we shall argue that while pharmacokinetic mechanisms usually describe causal chains of production, pharmacodynamics tends to focus on mechanisms of action underlying the in vivo effects of a drug. Considering the action of thyroid gland hormones in the human body as a case study, we further demonstrate that pharmacodynamic schemes tend to incorporate entities and interactions on multiple levels. Yet, traditional pharmacodynamic schemes are sketched “flat”, i.e., non-hierarchically. We suggest that transforming flat pharmacodynamic schemes into mechanistic multi-level representations may assist in disentangling the different kinds of mechanisms and relations depicted by arrows in flat schemes. The resulting Baumkuchen model provides a powerful and practical alternative to traditional flat schemes, as it explicates the relevant mechanisms and relations more clearly. On a more general note, our discussion demonstrates how pharmacology and related disciplines may benefit from applying concepts from the new mechanist philosophy to guide the interpretation of scientific diagrams. (shrink)

Since the nineteenth century, the problem of the arrow of time has been traditionally analyzed in terms of entropy by relating the direction past-to-future to the gradient of the entropy function of the universe. In this paper, we reject this traditional perspective and argue for a global and non-entropic approach to the problem, according to which the arrow of time can be defined in terms of the geometrical properties of spacetime. In particular, we show how the global non-entropic arrow can (...) be transferred to the local level, where it takes the form of a non-spacelike local energy flow that provides the criterion for breaking the symmetry resulting from time-reversal invariant local laws. (shrink)

There is a persisting tension that exists between the block universe conception of time in modern physics and philosophy and the conception of time that stems naturally from experience, and entropic asymmetries have been proposed to explain this tension. This article argues that as biochemical processes in the brain depend upon spontaneous entropy increases in the forward-time direction, this should provide an entropic basis for the unidirectionality of psychological processes. As this view does not depend on considerations of abstract information (...) processing or a past hypothesis, it provides advantages over previous entropy-based proposals attempting to explain asymmetries in temporal experience. (shrink)

It is claimed that the `problem of the arrow of time in classical dynamics' has been solved. Since all classical particles have a self-field (gravitational and in some cases also electromagnetic), their dynamics must include self-interaction. This fact and the observation that the domain of validity of classical physics is restricted to distances not less than of the order of a Compton wavelength (thus excluding point particles), leads to the conclusion that the fundamental classical equations of motion are not invariant (...) under time reversal: retarded self-interactions lead to different equations than advanced ones. Since causality (the time order of cause and effect) requires retarded rather than advanced self-interaction, it is causality which is ultimately responsible for the arrow of time. Classical motions described by equations with advanced self-interactions differ from retarded ones and do not occur in nature. (shrink)

While experience tells us that time flows from the past to the present and into the future, a number of philosophical and physical objections exist to this commonsense view of dynamic time. In an attempt to make sense of this conundrum, philosophers and physicists are forced to confront fascinating questions, such as: Can effects precede causes? Can one travel in time? Can the expansion of the Universe or the process of measurement in quantum mechanics define a direction in time? In (...) this book, researchers from both physics and philosophy attempt to answer these issues in an interesting, yet rigorous way. This fascinating book will be of interest to physicists and philosophers of science and educated general readers interested in the direction of time. (shrink)

We argue that the asymmetry between diverging and converging electromagnetic waves is just one of many asymmetries in observed phenomena that can be explained by a past hypothesis and statistical postulate (together assigning probabilities to different states of matter and field in the early universe). The arrow of electromagnetic radiation is thus absorbed into a broader account of temporal asymmetries in nature. We give an accessible introduction to the problem of explaining the arrow of radiation and compare our preferred strategy (...) for explaining the arrow to three alternatives: (i) modifying the laws of electromagnetism by adding a radiation condition requiring that electromagnetic fields always be attributable to past sources, (ii) removing electromagnetic fields and having particles interact directly with one another through retarded action-at-a-distance, (iii) adopting the Wheeler-Feynman approach and having particles interact directly through half-retarded half-advanced action-at-a-distance. In addition to the asymmetry between diverging and converging waves, we also consider the related asymmetry of radiation reaction. (shrink)

This paper critically engages Philip Mirowki's essay, "The scientific dimensions of social knowledge and their distant echoes in 20th-century American philosophy of science." It argues that although the cold war context of anti-democratic elitism best suited for making decisions about engaging in nuclear war may seem to be politically and ideologically motivated, in fact we need to carefully consider the arguments underlying the new rational choice based political philosophies of the post-WWII era typified by Arrow's impossibility theorem. A distrust of (...) democratic decision-making principles may be developed by social scientists whose leanings may be toward the left or right side of the spectrum of political practices. (shrink)

Linda Zagzebski has recently argued that there is a conflict between a common view of the asymmetry of time and various other metaphysical hypotheses. She identifies conflicts in the case of the modal arrow of time and in the case of the causal arrow of time. In the case of the modal arrow I argue that on one view there is no conflict and that on another the principle should be abandoned that there are entailments between propositions about the past (...) and the future. In the case of the causal arrow I argue that the conflict can be avoided by the adoption of a suitable closure principle. (shrink)

This essay is a philosophical evaluation of some of the findings of Wald and Penrose in which they claim to have supported an arrow (or the irreversibility) of time in quantum gravity. First, the notion of lawlike irreversibility (or anisotropy) of time is spelled out, then the general situation in quantum mechanics is briefly discussed. Finally, the findings in quantum gravity are evaluated against such a background. My conclusion is that the arrow of time found in quantum gravity is at (...) best de facto (nonlawlike). (shrink)

I criticize two accounts of the temporal asymmetry of electromagnetic radiation - that of Huw Price, whose account centrally involves a reinterpretation of Wheeler and Feynman's infinite absorber theory, and that of Dieter Zeh. I then offer some reasons for thinking that the purported puzzle of the arrow of radiation does not present a genuine puzzle in need of a solution.

In this paper, I investigate the relationship between preference and judgment aggregation, using the notion of ranking judgment introduced in List and Pettit. Ranking judgments were introduced in order to state the logical connections between the impossibility theorem of aggregating sets of judgments and Arrow’s theorem. I present a proof of the theorem concerning ranking judgments as a corollary of Arrow’s theorem, extending the translation between preferences and judgments defined in List and Pettit to the conditions on the aggregation procedure.

The problem of time's arrow has sparked two distinct metaphysical approaches, each stemming from opposing Humean and non-Humean perspectives on laws of nature. This paper contends that these approaches, despite their differences and inherent challenges, ultimately converge on a common goal: to explain time's arrow, we must comprehend the structure of spacetime during the universe's early stages. The problem of time's arrow has sparked two distinct metaphysical approaches, each stemming from opposing Humean and non-Humean perspectives on laws of nature. This (...) paper contends that these approaches, despite their differences and inherent challenges, ultimately converge on a common goal: to explain time's arrow, we must comprehend the structure of spacetime during the universe's early stages. (shrink)

The recent surge of interest in the origin of the temporal asymmetry of thermodynamical systems (including the accessible part of the universe itself) has put forward two possible explanatory approaches to this age-old problem. Hereby we show that there is a third possible alternative, based on the generalization of the classical (“Boltzmann–Schuetz”) anthropic fluctuation picture of the origin of the perceived entropy gradient. This alternative (which we dub the Acausal-Anthropic approach) is based on accepting Boltzmann's statistical measure at its face (...) value, and accomodating it within the quantum cosmological concept of the multiverse. We argue that conventional objections raised against the Boltzmann–Schuetz view are less forceful and serious than it is usually assumed. A fortiori, they are incapable of rendering the generalized theory untenable. On the contrary, this analysis highlights some of the other advantages of the multiverse approach to the thermodynamical arrow of time. (shrink)

Kenneth Arrow’s “impossibility” theorem—or “general possibility” theorem, as he called it—answers a very basic question in the theory of collective decision-making. Say there are some alternatives to choose among. They could be policies, public projects, candidates in an election, distributions of income and labour requirements among the members of a society, or just about anything else. There are some people whose preferences will inform this choice, and the question is: which procedures are there for deriving, from what is known or (...) can be found out about their preferences, a collective or “social” ordering of the alternatives from better to worse? The answer is startling. Arrow’s theorem says there are no such procedures whatsoever—none, anyway, that satisfy certain apparently quite reasonable assumptions concerning the autonomy of the people and the rationality of their preferences. The technical framework in which Arrow gave the question of social orderings a precise sense and its rigorous answer is now widely used for studying problems in welfare economics. The impossibility theorem itself set much of the agenda for contemporary social choice theory. Arrow accomplished this while still a graduate student. In 1972, he received the Nobel Prize in economics for his contributions. (shrink)