Plate iv in print

The Revelation

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.

Posit no pleasure and no preference behind the deed; watch only what a person takes when other things were within her reach, and let that be called her preference — so that want is no longer a hidden cause inferred from choosing but the choosing itself, set down as a rule and asked of nothing except that it not contradict itself.

— the proposal of this plate, after Paul Samuelson, 1938

The ordinalists had thrown away the magnitude of want and kept its order, but they had kept something still — a preference, a ranking that lived in the person and that her choices were taken to express. The next move went further, and it was the most radical retreat the concept ever made. Why keep even the ranking as a thing behind the choosing, a mental fact the choice reports on? Why not begin from the choosing alone — the one event the economist actually observes — and let it be primitive, owing nothing to any preference supposed to lie beneath it? This is the proposal of revealed preference, set down by Paul Samuelson in 1938 and pursued for two decades after: not to infer want from choice, but to define it as choice, emptied of feeling and of mind alike, and to ask whether the entire theory of the consumer could be rebuilt on that bare behavioral footing. The plate's question is the one the proposal forces: can a want be defined, without remainder, by the choices it leaves behind — and if it can, is the thing so defined the want at all, or only its cast-off shadow given the want's name?

Samuelson's construction begins by refusing to start where everyone before him had started. The classical theory began with a utility function or a preference ranking and deduced what a person would buy; revealed preference reverses the arrow. It begins with what a person is seen to buy — at this set of prices, on this income, she took bundle A — and extracts from that observation a relation defined entirely by it. If A was chosen when bundle B was also affordable, then A is said to be revealed preferred to B, and the whole of the relation means just this and no more: that when both lay within reach, A is what she took. There is no claim that A was chosen because it stood higher on some inner scale; the inner scale has been dismissed from the account. The preference is not a cause of the choice but a name for it, a tally of what was taken over what was foregone, built up across many occasions of purchase into a structure that, Samuelson proposed, could carry the full weight the old utility function had carried.1

1. Revealed preference reverses the arrow. The classical theory began with a utility function and deduced what a person buys; Samuelson begins with what she is seen to buy — at these prices, on this income, she took A — and extracts a relation defined entirely by it. If A was chosen when B was affordable, A is revealed preferred to B, meaning just this: when both lay within reach, A is what she took. No claim that A stood higher on an inner scale; the scale is dismissed. The preference is not a cause of the choice but a name for it, a tally of taken over foregone.

What makes this more than a redescription is that a single condition of consistency, imposed on the tally, turns out to yield the working content of the older theory. The condition is the weak axiom of revealed preference: if A is ever revealed preferred to B, then B must never, on any other occasion, be revealed preferred to A — a person who took A when she could have had B must not, when both are again affordable, be found taking B. From this modest demand of non-contradiction the central proposition of demand theory follows: that the substitution effect of a price change is always negative, that compensated demand curves slope down, that the behavior the cardinalists had derived from diminishing utility and the ordinalists from bowed indifference curves can be derived a third time, from nothing but the requirement that choice not turn back on itself. Hendrik Houthakker later showed that a strengthened version of the axiom, closing it under chains of comparison, guarantees that the choices can be rationalized by some utility function after all — so that the behavioral relation, if it is consistent enough, is mathematically indistinguishable from a person maximizing a ranking. The want had been emptied out, and the empty form still worked.2

2. A single consistency condition yields the older theory's content. The weak axiom: if A is ever revealed preferred to B, then B must never be revealed preferred to A. From this non-contradiction the central proposition follows — the substitution effect is negative, compensated demand slopes down — derived a third time, from nothing but choice not turning back on itself. Houthakker showed a strengthened axiom, closed under chains, guarantees the choices can be rationalized by some utility function: the behavioral relation, if consistent enough, is indistinguishable from maximizing a ranking.
⁂

Here was a vindication that looked, for a while, like the end of the whole inquiry. The unobservable want that had haunted the discipline since Bentham could be set aside entirely; one need never speak of pleasure, or of preference as an inner state, but only of choices and a law they obey. Economics could at last present itself as a pure science of behavior, its primitives all on the surface, its single assumption — consistency — checkable in principle against any record of what people actually buy. The pleasure-meter the next plate will chase had been rendered, it seemed, beside the point: you do not need to read the dial of want if want is nothing over and above the choosing, and the choosing is in plain sight. The ghost had not been measured; it had been declared a non-entity, its work taken over by a pattern in observable behavior, and the pattern asked only to hang together. For a theory that had spent a hundred and fifty years apologizing for a quantity it could not produce, this was emancipation.3

3. For a while this looked like the end of the inquiry. The unobservable want could be set aside; one need never speak of pleasure, only of choices and a law they obey. Economics could present itself as a pure science of behavior, its primitives on the surface, its one assumption — consistency — checkable against any record of buying. The pleasure-meter of the next plate was rendered beside the point: you need not read the dial of want if want is nothing over and above the choosing, and the choosing is in plain sight. The ghost was not measured but declared a non-entity.

The emancipation, however, was partly an illusion of bookkeeping, and the plate's question exposes where. Grant that a want can be defined entirely by the choices it leaves behind — revealed preference is precisely that definition, and it is coherent. But notice what the defined object is. It is the pattern of the choosing, summarized and named; and to call that pattern the person's preference is not to have discovered the want behind her choices but to have agreed to stop talking about anything behind them. The relation does not explain why she chose A over B; it merely records, in the grammar of preference, that she did. Ask why, and the answer revealed preference can give — she preferred it — is true by construction and empty by the same stroke, for the preference was nothing but the choice rewritten. The cause has not been found and measured; it has been retired, and its name reassigned to the effect. So the want is, in the only sense the theory now allows, fully captured by the choices — and exactly as unseen as it ever was, because what the choices capture is themselves. This is the inversion on which the whole volume will be seen to turn: the hidden interior that price was meant to be measuring turns out, when one looks, to be the visible exterior viewed from the inside, the choosing relabeled as the wanting.4

4. Grant that a want can be defined by the choices it leaves behind — revealed preference is that definition, and it is coherent. But the defined object is the pattern of choosing, summarized and named. To call it preference is not to have found the want behind the choices but to have agreed to stop talking about anything behind them. Ask why she chose A — the answer, she preferred it, is true by construction and empty by the same stroke, the preference being the choice rewritten. The cause is not found but retired, its name reassigned to the effect. The want is captured by the choices, and as unseen as ever, because what they capture is themselves.

There is, besides, a flaw nearer the surface, and it will reopen in the volume on choice. The whole construction leans on that one axiom of consistency, and consistency is an empirical claim, not a guarantee.5 It supposes that a person confronted with the same options will take the same one, that her choosing answers to a stable order which different occasions merely sample. But people do not always oblige. The same options ranked one way when chosen are ranked the other way when priced; a want recast by the wording of its offer comes out larger or smaller; the axiom that A taken over B forbids B taken over A is, in the laboratory, broken and broken again. When the consistency fails, the reconstruction fails with it — there is no single coherent preference for the choices to reveal, because the choices do not cohere — and the behavioral foundation, which had seemed firmer than the mentalist one for asking so little, turns out to have asked for the one thing real choosers least reliably supply. So revealed preference answers the plate's question with a yes that curdles in the saying. A want can be defined by the choices it leaves behind; but the definition holds only where the choices are consistent, captures only their pattern and never their felt force, and in the end does not reveal the want so much as do without it — handing the inquiry on to its successor, where the bare fact that a person chooses, having absorbed everything else, must finally be examined on its own.

5. The construction leans on one axiom of consistency, and consistency is an empirical claim, not a guarantee. It supposes a person confronted with the same options takes the same one, her choosing answering to a stable order different occasions merely sample. But people do not oblige: the same options ranked one way when chosen are ranked the other when priced; a want recast by the wording of its offer comes out larger or smaller. When consistency fails the reconstruction fails with it — no single preference for the choices to reveal — and the behavioral foundation asked for the one thing real choosers least reliably supply.