Numéraire
Volume the Eighth · of the table of twenty-six
The Quantities · Group II · № 08 · Ut

The Utility

the want price claims to track

Every price is a claim about how much a thing is wanted. But the want itself — the satisfaction the price is built to register — has never once been seen. It is inferred from the choosing, and the choosing is all we ever observe. This is the volume of the ghost in the machine: the quantity the whole apparatus is constructed to track, and which no instrument has read. Its twelve plates follow the concept across two centuries — from the morning it was declared a measurable substance to the day economics learned, twice over, to do without it, and on to the stranger morning when the dreamed-of instrument began, at last, to give a reading.

in print · № VIII · 12 of 12 plates
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The argument of the volume

Economics is a science of prices, and a price is only ever a number attached to a want. Yet of the two things, only one can be observed. We see the dollar change hands; we never see the wanting that is supposed to justify it. The entire edifice is therefore built upon a quantity that lies permanently out of view — present everywhere in the theory, nowhere in the evidence — and the history of the concept is the long, unfinished attempt to come to terms with that fact.

It is a history shaped like a pendulum. Utility began as a substance: a real magnitude of pleasure that Bentham believed could in principle be counted, and that the marginalists made, for the first time, explain a price. Then the discipline lost its nerve about the substance, and rebuilt the whole theory twice without it — once by keeping only the ranking and discarding the magnitude, once by keeping only the choosing and discarding the mind behind it. Risk briefly handed the number back; the paradoxes, and then the framing of the question itself, took it away again.

Beneath all of these moves lies the deepest difficulty, and it is not a gap in technique but a fact about what the quantity is. Even granting each of us a private utility, there is no operation that lays mine alongside yours. The sum that welfare economics cannot do without may be, read strictly, a sentence with no meaning — and Arrow made the impossibility into a theorem. And yet the oldest dream returns at the end: Edgeworth's imagined instrument that would read pleasure off a person directly, now pursued in the chemistry of the brain. The volume closes by asking whether reading the dial would answer the question at all — and by turning, in its final plates, to the proposal that want was never the right thing to measure, and to the bare assumption of choice on which the entire table quietly rests.

The argument remains open. What follows is an attempt to fix its exact edges.

The twelve plates of this volume

  1. i The Substancein print Bentham's calculus; want as a real, countable quantity of pleasure, named before it could be measured. Read the plate →
  2. ii The Marginin print the marginalists; diminishing marginal utility, and want made at last to govern a price. Read the plate →
  3. iii The Orderin print the ordinalist revolution; cardinal magnitude declared meaningless and only the ranking left standing, and what was lost when the size of a want was thrown away. Read the plate →
  4. iv The Revelationin print revealed preference; want emptied of feeling and rebuilt from consistent choice alone, and whether the preference so recovered is any less a ghost than the want it replaced. Read the plate →
  5. v The Wagerin print expected utility; cardinality returns, but only as a shadow cast by choice among risks. Read the plate →
  6. vi The Paradoxin print Allais and Ellsberg; the self-evident axioms failing exactly where they seemed surest. Read the plate →
  7. vii The Framein print prospect theory; the same outcome worth more, or less, by the way it is described. Read the plate →
  8. viii The Comparisonin print the interpersonal problem; why the sum of two people's utility may be a sentence with no meaning. Read the plate →
  9. ix The Impossibilityin print Arrow's theorem; the refusal to compare, with a few innocent conditions, making the common good incoherent. Read the plate →
  10. x The Hedonimeterin print Edgeworth's dreamed-of instrument, and the modern attempt to read pleasure off the brain itself. Read the plate →
  11. xi The Capabilityin print Sen's exit; advantage measured not by satisfaction but by what a person is able to do and to be. Read the plate →
  12. xii The Choicein print the tie-back; want as the silent assumption beneath every plate of the table. Read the plate →

In closing

This volume began with a want conceived as a substance — a real, homogeneous magnitude, present in a person as mass is present in a stone, in principle weighable and, Bentham hoped, addable across an afternoon and across a crowd. The weighing was proposed and the scale was never delivered; the unit was christened, two centuries late, in something close to embarrassment. Everything after follows from that first unpaid promise. Each plate is a further step back from the hope that the want is a quantity of the kind the physical world affords — a homogeneous stuff, held in common, of which each of us owns more or less.

Six of those steps are set down here in full, and the first five are doors that close. The substance of the first plate was posited and never found. The ranking of the third kept the order of a person's wants and let the magnitude go, buying a hard-won rigor at the price of no longer being able to say how much more one thing is wanted than another, or to lay one person's wants beside another's at all. The revelation of the fourth went further, emptying want of feeling and of mind alike and rebuilding it from consistent choice — only for the preference so recovered to prove as unobservable, and as circular, as the want it had replaced, the choosing relabeled as the wanting. The comparison of the eighth — one person's want set against another's — was shown impossible not for any want of finer measurement but as a matter of what the quantities are, a barrier in the nature of the thing that no instrument removes. And the instrument of the tenth, the dreamed hedonimeter that would read the want plainly off the matter of the brain, proved on inspection to be, even granted in full, a witness against the theory it was built to save rather than its rescue. The want was never found; it was pared to an order and then to a pattern of choice; it cannot be summed across persons; and the machine that would at last reveal it would not, in revealing it, hand economics back the quantity it had lost. The sixth step set down here turns from the want altogether. Where every plate before it had asked how the want might yet be measured — as substance, as order, as choice, across persons, off the brain — the eleventh asks whether the want was ever the thing worth measuring, and answers, with Sen, that it was not: that what is worth weighing is not the satisfaction a person feels but the range of what a person is able to do and to be, the doors a life has open rather than the pleasure it registers. It is the volume's one step that closes no door but leaves the building.

What the discipline kept, in the end, was not the quantity but a use for its name. Utility survived as the word for the consistency of a choice — the ghost's outline, traced from the outside by watching what a person does, never once by reading what a person feels. The hidden cause became a visible summary; the thing presumed to lie behind the choosing turned out to be the choosing itself, seen from the side that faces in. And once that inversion is complete, the standing question is no longer about the want at all. It is about the act. The inquiry opened here, as a question about a magnitude no one can see, is taken up again at № 23, The Choice, as a question about the one thing in the whole apparatus that can be seen plainly: that a person chooses. Whether the choosing tracks what is best for them — whether it ever did — is where the next volume begins.

When a price claims to measure how much a person wants a thing, is it weighing something within them — or only reading back the choice they have already made?