Social choice theory is characterized by ornate mathematical results. This, some have suggested, gives it a baroque façade. Just like the baroque style, works in social choice can look wholly unconcerned with the world around us.
But if this is true, then a curious puzzle emerges: What is Amartya Sen—the author of some of the most influential ideas in contemporary social thought—doing in a theoretical world that appears unconcerned with the “real” world? To address this puzzle we need to recognize the baroque façade of social choice as just that—a façade! What appears as mathematical wizardry can illuminate some of the most fundamental issues that a society faces.
There is no better evidence for this claim than Collective Choice And Social Welfare. This book has been recognized as a classic since it first appeared in 1970. In it, Amartya Sen weaves together logic, economics and philosophy to establish some propositions. These propositions are the foundations from which Sen has proceeded to articulate the influential ideas we associate with him. Further, these propositions transformed the disciplines of welfare economics, development economics, political philosophy, and ethics. Now, almost 50 years since it first appeared, this classic has been reissued in a new edition. This new edition has preserved the original text. But it supplements the 1970 edition with a new introduction and 11 new chapters.
The first thing a reader will observe is the unusual structure of the book. Each chapter is partitioned into starred and unstarred parts. In the unstarred part, a discussion proceeds in ordinary language. But in the starred part, the ordinary language discussion transforms beautifully, if I may indulge, in an aesthetic remark, into a line of reasoning using precise definitions, axioms and proofs. This stylistic experiment anticipates a feature that characterizes Amartya Sen’s work: the beautiful and accessible exposition of essentially abstract ideas.
But, what is the problem these chapters are addressing?
The problem of social choice is owed to a work of genius that came in the form of a devastating exercise in logic—the misleadingly named “General Possibility Theorem” due to Kenneth Arrow. In Arrow’s formulation, the problem of social choice is this: How do we move from many different rankings of a set of options into a single ranking of that set of options? This move is called an aggregation, and is at the heart of social choice theory.
An aggregation has the appearance of a quixotic mathematical exercise, but once you recognize it, they are ubiquitous activities in a society. To illustrate their ubiquity: The outcome of an election requires aggregating the votes of different individuals, a judgement of the Supreme Court requires aggregating the verdict of individual judges that constitute a bench, the measurement of poverty or inequality in a society requires aggregating the different welfare levels of individuals in that society, among others. Arrow’s theorem is devastating because it established that an aggregation is “impossible” to get. Impossible, anyway, without violating some very weak conditions of rationality. Another way to formulate this is to say: A rational aggregation is impossible.
The 1970 edition of this book took Arrow’s problem as its point of departure and extended it in various directions. Two of these are, for me, the most luminous. First, Sen deepened Arrow’s aggregation problem. Second, he discussed possible ways out of this problem.
How does one deepen a problem that has been described as devastating? Arrow established the impossibility of a “rational” aggregation. By rational we mean some normative demands of consistency. Sen established The Impossibility Of A Paretian Liberal. While this was published as an independent paper in 1970, it appears here in chapter six (“The Liberal Paradox”). This result argues: It is impossible to get an aggregation, say an allocation of resources, that is both “efficient” (in a weak utilitarian way) and respects individual liberty (in a very minimal form). Discussing this result more fully is beyond the scope of this review. I note, however, what this result achieved. While Arrow’s aggregation was concerned with satisfying normative demands that are in the domain of rationality, the normative demands that Sen wanted an aggregation to satisfy are in the domain of ethics. While the line that divides the two domains is not as distinct as some economists make it out to be, it is useful to highlight the distinction. In particular, it is useful to see a feature that characterizes Amartya Sen’s work—the importance of ethics, non-utilitarian ethics in particular, to the concerns of economics. Even those unfamiliar with social choice will associate this as being characteristically Sen.
Is there a way out of Arrow’s devastating exercise in logic? The most luminous chapters of the 1970 edition are addressing this question. In Arrow’s system, the information contained in the different rankings to be aggregated is unjustifiably restrictive. Two assumptions about the ranking contribute to what Sen calls the “informational penury”. First, the ranking is ordinal, or cannot be represented numerically. Second, the different rankings are not comparable, or there is no interpersonal comparability. To illustrate this, assume I rank caviar above fries, and a vegan ranks an apple above an orange. Then, by these two assumptions we cannot say that I prefer caviar more than a vegan prefers an apple. Neither can we say that changing from fries to caviar increases my welfare more than the change from an orange to an apple increases a vegan’s welfare. Sen relaxed both assumptions in a series of logical steps. This allowed more information to be part of the aggregation exercise. I will not go into the details of these steps, but will leave you with the upshot. If we allow numerical representation without interpersonal comparability, then the impossibility does not go away. However, if we allow interpersonal comparability, then there is a way out of impossibility, and we can proceed in this way with or without numerical representation. A remarkable feature about this exercise was that Sen did not treat the concept of interpersonal comparability in a binary way—either we have comparability or we have incomparability. Instead Sen established a series of results that allow a continuum of comparisons between these two ends. Sen called this continuum “partial comparability”.
Now, all this, I concede, even without the mathematical detail does have a baroque appearance. But to see how this sheds light on the world around us, consider the following: A rational aggregation rule which is “possible” if we allow interpersonal comparability is a version of John Rawls’ Difference Principle. In the jargon of social choice, this rule is called the maximin; an extension of this is the leximin, which Rawls himself endorsed. Another example is that unsophisticated measure of poverty which is unfortunately popular in Indian policy circles—the headcount measure. Sen’s well-known critique of both Rawls and the headcount measure might be familiar to people. That both critiques use the insight of partial comparability might not be as familiar.
As this shows, social choice techniques form the basis of such diverse and important activities as the measurement of poverty, and the specification of principles of distributive justice. However, there is more to the luminosity of social choice, especially when applied by a master like Sen. Let me illustrate with a final example. At an abstract level, exploring what aggregation we can get by allowing interpersonal comparability is a mathematical exercise—how can we characterize meaningful comparisons? But if we change the terrain of this question from epistemology to ethics, then the question becomes, “Comparisons of what information is justified?” The answer to this is the most famous of Sen’s formulations—capabilities! Sen would go on to develop this more fully in Commodities And Capabilities, which remains the best book on the subject.
Indeed, the ideas that we associate with the more classical Amartya Sen—the value of freedom and agency, the profound critique of John Rawls, a humane vision of development and progress, the advance of human rights, the importance of public reasoning, and most famously the capability approach, among others—are grounded by an insight from this book. This, alas, is not very well understood. It is this misunderstanding that the new edition is trying to fix. While the new chapters in the expanded edition are responding to critiques, presenting shorter proofs, generalizing some older results, and providing a systematic overview of how the literature has developed since Arrow’s devastating exercise. It is mainly concerned with showing how the supposedly baroque world of social choice has informed the ideas we associate with the more classical Sen.
However, the relevance of this book to the concerns of the world does not mean that it can be read on the beach. The arguments presented here are abstract even when judged by the conventional standards of an academic work. Further, in advancing these arguments, Sen responds to interlocutors from various academic disciplines, and draws from sources all over the world. All this can make engaging with this book an intimidating prospect. Nevertheless, it is these intimidating features of the book that make reading it one of the most intellectually rewarding experiences you will encounter. It is like attending a masterclass, where one of the great thinkers of our age orchestrates the instruments of logic, normative reasoning, economic analysis and history, to answer some of the deepest questions that living together in groups or societies throws up. For this reason, I hope this book gets banned, so that everyone reads it.
Akshath Jitendranath is a PhD candidate and junior lecturer at the John Stuart Mill College and the philosophy department, VU Amsterdam.
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