The Substance — The Utility, Plate i

Utility did not enter economics as a metaphor. It entered as a substance — a real, homogeneous magnitude of pleasure and pain that a man named Bentham believed could, in principle, be counted as a chemist counts grains. The ambition was openly that of physics. If morality and legislation were to become a science rather than a confusion of sentiment, they needed a quantity to be a science of; and the quantity Bentham proposed was felicity itself, the net balance of pleasure over pain, summed across the acts of a life and, he hoped, across the lives of a community. Conduct was to be judged by a single arithmetic: the act that produced the greatest quantity of happiness was the right one, and the legislator's task was to arrange the incentives of a society so that its arithmetic came out well.¹

1. Bentham set this out in the Introduction to the Principles of Morals and Legislation (1789). The procedure is variously called the felicific, the hedonic, or the moral calculus. Its governing rule — the greatest happiness of the greatest number — Bentham took from earlier hands, but the apparatus of measurement was his own.

To call something a quantity is to promise a way of measuring it, and Bentham, to his credit, tried to keep the promise. He laid down the dimensions along which a pleasure was to be reckoned: its intensity and its duration, the two that anyone would think of first; then its certainty, and its nearness in time, since a pleasure likely and soon is worth more than one remote and doubtful; then two subtler properties, its fecundity, the chance that it would be followed by more of its kind, and its purity, the chance that it would not be followed by its opposite. These six fixed the value of a pleasure to a single person. A seventh, its extent, counted the number of persons it reached.² Set the dimensions out, assign each its figure, and the rightness of an action would fall out of the sum the way a weight falls out of a balance.

2. Intensity, duration, certainty, propinquity, fecundity, purity, extent. The first four measure a single pleasure; fecundity and purity measure its sequel; extent alone leaves the individual and counts heads.

The trouble is that the balance was never built, and Bentham half-knew it would not be. The calculus has no unit. There is no agreed quantum of pleasure, no natural zero from which to measure, no scale on which a figure could be entered without arbitrariness — and a quantity without a unit is not yet a quantity but an aspiration dressed in the costume of one. Later economists, needing a word for the thing they could not measure, coined the util; but they coined it half in embarrassment, and it never acquired an operational meaning, never named an amount that any procedure could read off the world.³ The felicific calculus, in two centuries, was not once performed. It remains the most influential computation in the history of the moral sciences that nobody has ever carried out.

3. The util is a creature of the textbook, not the laboratory. No experiment fixes how many utils a glass of water yields, and the more candid expositions concede that the unit is a notation for reasoning, never a reading taken from a person.

There is a second difficulty, quieter than the first and far deeper, and it is hidden in the seventh dimension. To reckon the extent of a pleasure — to add the satisfaction it gives one person to the satisfaction it gives another, and so arrive at a happiness of the community — is to assume that the two satisfactions are quantities of the same kind, laid on the same scale, with a common zero and a common unit. It is to assume, in short, exactly the thing that can never be shown: that my pleasure and yours can be added. Bentham built interpersonal comparison into the foundations of the calculus as though it were the most natural step in the world, a matter of counting heads. It is in fact the single assumption that the next century of economics would spend its rigor trying to expel, and that this volume will find, in its eighth plate, to be not a small technical gap but the central scandal of the whole subject.⁴

4. See Plate viii, The Comparison. What Bentham treats as addition, Robbins will treat as a smuggled ethical judgment, and Arrow will treat as formally impossible. The crack is present at the creation.

⁂

And yet it would be a mistake to read the substance theory as a simple error, corrected and discarded. It did work that has never been undone. By insisting that welfare was a magnitude — something with a more and a less, something one could in principle have twice as much of — Bentham gave economics its most durable habit of mind. The habit is this: that the good is a quantity to be maximized, and that a policy, an institution, even a life can be assessed by how much of it they produce. Every later apparatus inherits the habit even as it abandons the metaphysics. The marginalists who follow in the next plate do not measure pleasure, but they reason about its increments as though the increments were real. The welfare economist who refuses, on principle, to compare one person's utility with another's still arranges his entire theory around the idea of a sum he is forbidden to take. The substance is denied at the front door and admitted at the back.

One crack opened early, from within the camp. Bentham had insisted that pleasure was homogeneous — that, quantity aside, pushpin was as good as poetry, a child's game as good as the highest art. His most gifted heir would not accept it. Pleasures, Mill argued, differ in kind and not only in amount; some are higher and some are lower, and the verdict on which is which belongs to those who have known both.⁵ The concession seems humane, and it is. But notice what it costs. The moment pleasures differ in quality, the single scale is gone, and with it the arithmetic; for one cannot add quantities that are not of one kind, and a calculus that must first rank its pleasures by a judgment of quality has smuggled back in, before the counting begins, exactly the evaluation the counting was meant to replace. The substance, pressed for honesty, begins to dissolve into the very thing it was built to avoid: a matter of judgment rather than measurement.

5. J. S. Mill, Utilitarianism (1863). The doctrine of higher and lower pleasures rescues utilitarianism from the charge of being a philosophy fit for swine, but at the price of its arithmetic: qualitative difference and a single additive scale cannot both stand.

What the substance theory bequeaths to the rest of this volume, then, is not a measurement but a predicament, stated at full strength because stated first. Here is a quantity that the entire science needs — for a price is a claim about how much something is wanted, and wanting, if it is anything, is a more or a less. And here, in the same breath, is the discovery that the quantity has no unit, no zero, no instrument, and that the one operation the science most needs to perform on it, the adding of one person's share to another's, is the one operation it cannot justify. Everything that follows is a response to this predicament. One response is to build the missing instrument and read the substance off the world directly; that is the dream of the tenth plate, and it is older and more nearly realized than one would think. The opposite response is to give up the substance altogether — to keep the ranking and throw away the magnitude, or to keep the choosing and throw away the mind — and to ask whether a science of want can be conducted with no want left in it at all. It is to that second, stranger response that the volume turns first.