Plate iii in print

The Reversal

preference reversals; the same options ranked one way when chosen, the opposite way when priced.

Ask a person to choose, and she prefers the first; ask her what each is worth, and she prefers the second. The preference was not waiting to be found. It was made by the asking.

— the finding of this plate, after Sarah Lichtenstein & Paul Slovic, 1971

There is a fact about people that ought not to be possible, and it has outlasted every attempt to make it go away. Offer a person two gambles of about equal worth — one a high chance at a modest prize, the other a slim chance at a large one — and ask her to choose between them. She chooses the safe one; she likes the high probability of coming away a winner. Now ask her, of each gamble taken separately, the least she would sell it for. She prices the long shot higher. Set the two answers side by side and they contradict each other: by her choice she prefers the first, by her pricing she prefers the second. The same person, valuing the same two objects, has ranked them in opposite orders depending only on whether she was asked to pick or to price. This is the preference reversal, and it is no curiosity at the edge of the theory. It is a wound at its center.1

1. First reported by Sarah Lichtenstein and Paul Slovic (1971) and, independently, by Harold Lindman (1971). The two gambles are known as the P-bet (high probability, low prize) and the $-bet (low probability, high prize), constructed to carry nearly equal expected value so that neither plainly dominates.

To see why the contradiction cuts so deep, recall what the previous plate promised. A rational person has a single ranking of the options, and every way of consulting that ranking should agree, because there is only one ranking to consult. Choosing and pricing are two such consultations — two windows onto one underlying order — and the theory takes for granted, so quietly the assumption is seldom named, that they show the same view. The premise has a name: procedure invariance, the requirement that a preference not depend on the method used to elicit it. It is not an optional refinement. Without it the phrase her preference loses its referent, for there is no longer a single thing the various methods are methods of measuring. The reversal breaches procedure invariance directly and reproducibly. And in breaching it, it raises a possibility more unsettling than any mere inconsistency: that there was never one ranking behind the two windows — that the windows were making the view.

The finding came from psychologists, and economists' first instinct was to disbelieve it. Such reversals, they suspected, were artifacts of careless design — too little money at stake to fix the attention, confusion at an unfamiliar pricing task, some unmeant cue from the experimenter, the noise of subjects who did not care. In 1979 two economists, David Grether and Charles Plott, set out to document the artifact and dispose of it. They drew up the ways an economist would explain the reversals away, and built an experiment to close each one: real money, sharpened incentives, controls for order and for the experimenter's identity, a payment scheme that rewarded honest pricing. The reversals did not disappear. If anything they grew cleaner under the better controls. The paper is a landmark precisely for who wrote it and why — a hostile replication mounted by the discipline with the most to lose, which ended by confirming the thing it had meant to bury. After Grether and Plott the reversal could no longer be filed under the failings of psychological method. It had to be reckoned with as a fact about choice.2

2. David Grether and Charles Plott, Economic Theory of Choice and the Preference Reversal Phenomenon, in the American Economic Review (1979). They examined some thirteen candidate explanations — incentives, strategic misrepresentation, indifference, and the rest — and found the reversals robust to all of them. The honesty of the exercise, hunting its own preferred conclusion and failing to find it, is part of why it persuaded.
⁂

If the reversal is real, what produces it? The best account is also the most corrosive. When a person prices a gamble she answers in dollars, and the dimension of the gamble that is itself measured in dollars — the size of the prize — looms disproportionately large, because the response and the attribute speak one language. When she chooses, no dollar figure is demanded of her, and the probability of winning is freed to weigh more heavily. The response mode reaches into the considerations and magnifies whichever one matches it; the question selects its own answer. The preference is not retrieved from storage. It is assembled, on the spot, from materials the question makes salient, and a different question assembles a different preference from the same materials. This is the doctrine the reversals forced upon a part of the field: that preferences, at least over options of any complexity, are constructed in the act of elicitation rather than revealed by it — built to order, not read off a shelf.34

3. The mechanism is scale compatibility: an attribute is weighted more heavily when it shares its units with the required response. See Amos Tversky, Shmuel Sattath and Paul Slovic, Contingent Weighting in Judgment and Choice, in Psychological Review (1988).
4. The general thesis is stated in Paul Slovic, The Construction of Preference, in American Psychologist (1995): for all but the most familiar and rehearsed decisions, the preference does not precede the elicitation but is generated by it, and is therefore hostage to features of the elicitation that ought, by the theory, to be beside the point.

It is essential to see how this differs from the ordinary admission that people make mistakes, which the previous plate showed the theory can absorb. A mistake presupposes a truth departed from: to err is to take the worse option while a better one was, in some real sense, preferred. The companion notion of bias — the anchor that drags an estimate, the loss that looms larger than the equal gain — lives on exactly this presupposition, and is the matter of its own volume; a bias is a deviation, and a deviation requires a baseline.5 Constructed preference removes the baseline. If there is no single ranking prior to the question, then neither answer is the error and neither is the truth; they are two artifacts of two procedures, with nothing behind them against which either could be judged wrong. And this is what makes the reversal a problem not for psychology alone but for the foundations of welfare economics. The discipline's method for learning what is good for a person is to watch what she chooses and infer that she preferred it. That method assumes the preference was there to be revealed. If instead it was made in the act of choosing — and would have been made otherwise by an act of pricing, or by a differently worded choice — then the question which of her preferences is the one whose satisfaction counts as her good? has no answer the data can give. The instrument built to read welfare off behavior finds that the behavior has no single thing to say.

5. The systematic deviations — anchoring, loss aversion, the endowment effect, present bias — are gathered in the companion element № 24, The Bias. The endowment effect (Kahneman, Knetsch and Thaler, 1990), under which a person demands far more to give up a good than she would have paid to acquire it, is a near cousin of the reversal: valuation turns on the procedure — here, on whether one is selling or buying — rather than on the good alone.

The theory keeps its footing in one of two ways, and each costs it something. It can declare one elicitation authoritative — choice, most naturally, as the act the whole apparatus is finally about — and dismiss the others as distortions. But this is a stipulation, not a finding: it imports a standard of the correct way to measure preference into a theory that claimed to need no standard beyond behavior itself, and it must then explain why the authoritative procedure is authoritative without appealing to a true preference it has denied itself. Or the theory can save consistency by indexing preference to context — conceding that the person has one preference when choosing and another when pricing, that these are simply preferences over different things — so that no contradiction remains, the two rankings having never been rankings of the same objects. This rescue works, in the sense that a fine enough re-description absorbs any reversal whatever. But it works too well. A theory that can redescribe every inconsistency into consistency has stopped forbidding anything, and a theory that forbids nothing predicts nothing. Whether the indexing is an empty trick or a profound correction depends entirely on whether there is a principled reason for telling the contexts apart — a reason the next plate in print, following Sen, will try to supply, by arguing that context is not noise to be absorbed but information that was wrongly thrown away.6

6. The indexing move — preferences defined over pairs of option-and-context — is formally unimpeachable and substantively empty unless the relevant contexts can be specified in advance and on independent grounds. Lacking that, it is the re-description rescue of the next plate seen from the other side: rigor bought by saying nothing. Plate viii, The Menu, argues that context deserves admitting — but for a reason, because the menu carries meaning, not as a device for rescuing the axioms.