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Bernheim, B. Douglas, and Antonio Rangel. 2007. “Toward Choice-Theoretic Foundations for Behavioral .” 97 (2): 464–70. https://doi.org/10.1257/aer.97.2.464. †

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Interest in has grown I. Preliminaries in recent years, stimulated largely by accu- mulating evidence that the standard model of A. Choice Situations and Choices consumer decision making provides an inad- equate, positive description of human behav- We use X to denote the set of all possible ior. Behavioral models are increasingly !nding choice objects. Elements of X could be stan- their way into policy evaluation, which inevi- dard objects such as state-contingent consump- tably involves welfare analysis. No consensus tion bundles or lotteries over such bundles, but concerning the appropriate standards and crite- these objects could also have nonstandard fea- ria for behavioral welfare analysis has emerged tures (e.g., as in Andrew Caplin and John Leahy yet. 2001). This paper summarizes our effort to develop A standard choice situation (SCS) consists a uni!ed framework for behavioral welfare eco- of a constraint set X # X, representing the set nomics (for a detailed discussion see Bernheim of objects from which the individual can choose and Rangel 2007)—one that can be viewed as according to the objective information at his a natural extension of standard welfare eco- disposal. We are concerned with making wel- nomics. Standard welfare analysis is based on fare judgments based on behavior for some par- choice, not on or preferences. In its sim- ticular domain of standard choice situations, X. plest form, it instructs the planner to respect the To accommodate choice inconsistencies, we choices an individual would make for himself. introduce the notion of a generalized choice The guiding normative principle is an exten- situation (GCS), G. This consists of a standard sion of the libertarian deference to freedom choice situation, X, and a set of ancillary con- of choice, which takes the view that it is bet- ditions, d. Thus, G 5 1X,d2. We will use G to ter to give a person the thing he would choose denote the set of generalized choice situations of for himself rather than something that someone potential . Examples of ancillary condi- else would choose for him. tions include the point in time at which the deci- We show that it is possible to extend the sion is made, the manner in which information standard choice-theoretic approach to welfare is presented, and the labelling of some options analysis to situations where individuals make as defaults. Behavior is represented by a choice inconsistent choices, which are prevalent in correspondence C : G S X; for any G [ G, any behavioral economics. x [ C1G2 is an action that the individual is willing to choose. As a general matter, it is dif!cult to draw a bright line between the characteristics of the objects in X and the ancillary conditions d † Discussant: , California Institute of Tech- (which, in principle, one could also view as a nology. characteristic of the objects in the choice set). * Bernheim: Department of Economics, Stanford Univer- Our analytic framework is applicable regardless sity, Stanford, CA 94305 (e-mail: [email protected]); Rangel: Division of Humanities and Social Science, Cali- of how one draws this distinction. fornia Institute of Technology, 228-77, Pasadena, CA 91125 Standard economics proceeds from the (e-mail: [email protected]). assumption that choice is invariant with respect

464 VOL. 97 NO. 2 TOWARD CHOICE-THEORETIC FOUNDATIONS FOR BEHAVIORAL 465 to ancillary conditions. Positive behavioral eco- over the elements of X, which summarizes what nomics challenges this basic premise since there is chosen from various SCSs. Under standard are many examples of choice reversals in which assumptions, R is an ordering. When we use

C1X, dr2 2 C1X, ds 2 for two ancillary condi- this ordering to conduct welfare analysis, we are tions dr and ds. simply asking what an individual or individu- als would choose. For example, the compensat- B. Positive versus Normative Analysis ing variation associated with some change in the economic environment equals the smallest Usually, choice data are not available for all payment that would induce the individual to elements of G, but rather for elements of some choose the change. Similarly, a social alterna- set H , G. The objective of positive economic tive x [ X is a Pareto optimum in X if there analysis is to extend the choice correspondence is no other alternative in X that all individuals C from observations on to the entire set G. In would choose over x. standard economics, this is accomplished by In behavioral economics, we often cannot de!ning preferences over X, estimating these summarize all choices with a consistent prefer- preferences with choice data for the opportunity ence ordering. Instead, choice evidence is some- sets in H, and using these estimated preferences times ambiguous. Fortunately, we can live with to infer choices for opportunity sets in G\H. this ambiguity. It is still possible to construct The objective of normative economic analysis binary relations based on unambiguous com- is to evaluate outcomes. Typically, we evaluate parisons that allow us to carry out meaningful outcomes at the level of the individual, and then welfare analyses. aggregate. For choice-based normative crite- ria, we allow the individual’s choices to govern A. Individual Welfare Orderings these evaluations. The fundamental problem of behavioral welfare economics is to identify In standard welfare economics, the statement appropriate criteria for evaluating alternatives xRy means that if x and y are available in X, and when, due to choice reversals and other behav- if y is in C1X2, then x is also in C1X2. Our pro- ioral anomalies, the individual’s choices fail to posal is to conduct behavioral welfare econom- provide clear guidance. ics by generalizing this binary relation. In effect, In conducting choice-based normative analy- xRy will mean that if x and y are available in G, sis, we take as given the individual’s choice cor- and if y is in C1G2, then x is in C1G2. We do not respondence, C, de!ned on G rather than H. pretend that this relation reveals . It is Preferences and utility functions, which are simply a summary of what is chosen. constructs used both in standard theory and in More speci!cally, for any x, y [ X, we will behavioral economics to extend C from H to G, say that xRy if, whenever x and y are avail- are therefore positive tools, not normative tools. able, x is sometimes chosen, and y is never In a behavioral setting, these constructs cannot chosen unless x is as well. Formally, (i) there meaningfully reconcile inconsistencies. They exists some (X, d) [ G with 5x, y6 # X such that can only reiterate the information contained in x [ C1X, d2, and (ii) there does not exist any the extended choice correspondence C. Thus, (X, d) [ G with 5x, y6 [ X such that y [ C1X, d2 one cannot resolve normative puzzles by iden- and x o C1X, d2. Note that xRx. tifying classes of preferences that rationalize As usual, we can de!ne xPy as xRy and ,yRx. apparently inconsistent choices, as in Faruk Gul This means that, whenever x and y are available, and Wolfgang Pesendorfer (2001). sometimes x is chosen but not y, and otherwise either both or neither is chosen. Likewise, we II. A Framework for Behavioral Welfare can de!ne xIy as xRy and yRx. This means that, Analysis whenever x is chosen, so is y, and vice versa. Finally, we will say that xP*y if, whenever x In the standard approach to normative analy- and y are available, sometimes x is chosen but sis, one evaluates individual welfare by apply- not y, and otherwise neither is chosen. Formally, ing a “revealed preference” relation, R, de!ned (i) for all (X, d) [ G with 5x, y6 # X, we have 466 AEA PAPERS AND PROCEEDINGS MAY 2007

y o C1X, d2, and (ii) for some (X, d) [ G with present, or there’s no GCS for which y is chosen 5x, y6 # X, we have x [ C1X, d2. and x is not with x present. In general, R, P, and P* need not be order- ings. For example, if C15x, y6, d92 5 5x6 and This result also has an immediate corollary: C15x, y6, d02 5 5y6, then we have neither xRy if x is the unique choice for some GSC involving nor yRx, so R is not complete. Moreover, R, X, then x is a strict individual welfare optimum P, and P* need not be transitive (though P* in X. A strict individual welfare optimum may is acyclic). For example, if choice does not not exist (see the example given at the end of depend on ancillary conditions, and if we have Section IA). C15x1, x262 5 x1, C15x2, x362 5 x2, C15x3, x162 C. Relationship to Multi-Self Pareto Optima 5 x3, and C15x1, x2, x362 5 5x1, x2, x36, then x1 Px2 Px3 Px1. Our notion of an individual welfare opti- mum is related to the idea of a multi-self Pareto B. Individual Welfare Optima optimum. Suppose, in particular, that the set of GCSs is the Cartesian product of the set of SCSs There are two natural criteria for determin- and a set of ancillary conditions (that is, G 5 X ing whether a choice is improvable. We will 3 D, where d [ D). Also imagine that, for each say that it is possible to strictly improve upon d [ D, choices follow standard axioms, and can a choice x [ X if there exists y [ X, such that be represented by a preference ranking Rd. If one yP*x. In other words, there is an alternative that imagines that each ancillary condition activates is unambiguously chosen over x. When a strict a different “self,” then one can conduct welfare improvement is impossible, we say that x is a analysis by examining multi-self Pareto optima. weak individual welfare optimum. It is possible Under the stated conditions, a weak multi-self to weakly improve upon a choice x [ X if there Pareto optimum corresponds to a weak individ- exists y [ X such that yPx. In other words, there ual welfare optimum (as we have de!ned it), and is an alternative y that is sometimes chosen over a strict multi-self Pareto optimum corresponds x, and that x is never chosen over y (except in the to a strict individual welfare optimum. For these sense that both could be chosen). When a weak narrow settings, our approach is equivalent to improvement is impossible, we say that x is a the multi-self Pareto criterion. Our approach strict individual welfare optimum. is also more general, however, in that it does When is x [ X an individual welfare opti- not require the assumptions stated at the outset mum? The following simple results (which we of this paragraph. Moreover, it can justify the state without proof) assume that G includes all multi-self Pareto criterion without reference to pairwise comparisons (that is, for all a, b [ X, questionable psychological assumptions. there is some dab such that ({a, b, dab) [ G). D. Equivalent and Compensating Variation FACT 1: x is a weak individual welfare optimum in X if and only if for each y [ X (other than x), The concepts of equivalent and compensating there is some GCS for which x is chosen with y variation are central to applied welfare econom- present (y may be chosen as well). ics. Fortunately, they have natural counterparts within our framework. Here, we will focus on This result has an immediate corollary. If x compensating variation. Our treatment of equiv- is chosen for some GSC involving X, then x is a alent variation is analogous. weak individual welfare optimum in X. Notice We will write the individual’s SCS as X1a, m2, that this corollary guarantees the existence of where a is a vector of parameters, and m is the weak individual welfare optima. level of compensation. Let a0 be the initial param- eter vector, d0 the initial ancillary conditions, and FACT 2: x is a strict individual welfare opti- 1X1a0, 02, d0 2 the initial GCS. We will consider mum in X if for each y [ X (other than x) either a change in parameters to a1, coupled with some x is chosen and y is not for some GCS with y level of compensation, as well as (potentially) VOL. 97 NO. 2 TOWARD CHOICE-THEORETIC FOUNDATIONS FOR BEHAVIORAL WELFARE ECONOMICS 467 a change in ancillary conditions that could, in arbitrariness” documented by , George principle, depend on the compensation level. We Loewenstein, and Drazen Prelec (2003). write the new GCS as 1X1a1, m2, d1m2 2. One Let M denote the consumer’s initial income. natural possibility, but certainly not the only Consider a change in the of y from p0 to p1, one, is to take d1m2 5 dr for some !xed dr. This along with a change in ancillary conditions from allows us, for example, to evaluate compensating d0 to d1. Let y0 denote the amount of y purchased variations for !xed changes in , ancillary at price p0, and let y1 denote the amount pur- conditions, or both. chased at price p1. Assume that y0 . y1. Since Here, we will de!ne the compensating variation there are no income effects, y1 will not change relative to particular selections from the choice as the individual is compensated (holding the correspondence (see Bernheim and Rangel 2007 ancillary condition !xed). for some alternatives). Accordingly, we assume Now let us calculate CV-A. We wish to !nd the individual selects x0 [ C1X1a0, 02, d0 2, and the smallest m such that (y1, M 2 p1y1 1 m) x1m2 [ C1X1a1, m2, d1m2 2. P*(y0, M 2 p0 y0 ). It is straightforward to show In de!ning the compensating variation, we that the solution is encounter an ambiguity concerning the standard of compensation. Do we consider compensation y0 CV2A suf!cient when x1m2 is always weakly chosen m 5 [p1 2 p0 ]y1 1 3 [dHv9(y) 2 p0 ] dy. y over x0, or when x0 is not always weakly cho- 1 sen over x1m2? This ambiguity is an essential feature of welfare evaluations with inconsistent Through similar reasoning, one can show that choice. Accordingly, we de!ne two notions of compensating variation: y0 CV2B m 5 [p1 2 p0 ]y1 1 3 [dLv9(y) 2 p0 ] dy. CV2A y m 5 inf x1m2P*x0, 1 m CV2B CV2A m 5 sup x0 P*x1m2. Figures 1(A) and 1(B) illustrate m (the m CV2B shaded area above p0) and m (the shaded We illustrate the application of these concepts area above p0 minus the shaded area below p0), by discussing the measurement of consumer respectively, for the case where d0 5 d1 5 d. surplus. Notice that these values bracket standard con- sumer surplus. Moreover, as the range of possi- E. Consumer Surplus ble ancillary conditions narrows, they converge to standard consumer surplus. This underscores For simplicity, we will examine a case where the fact that the standard framework is a spe- the individual consumes two : x and y. cial case of the framework considered here. Suppose that positive analysis delivers the fol- Moreover, it also implies that, when inconsis- lowing utility representation (which involves tencies are minor (that is, dH 2 dL is small), the no income effects, so that Marshallian con- ambiguity in welfare, as measured by the differ- sumer surplus would be valid in the standard ence between mCV2A and mCV2B, is small. framework): F. Generalized Pareto Optima

U1x, y 0 d2 5 x 1 dv1y2, Next, we turn to environments with many indi- with v strictly increasing, differentiable, and viduals, and formulate a generalization of strictly concave. Thus, for any given d, the Pareto ef!ciency. Suppose there are N individu- inverse for y is given by p 5 als indexed i 5 1, … , N. Let X denote the set of dv91y2, where p is the price of y. Notice that all conceivable social choice objects, and let X the ancillary condition, d [ [dL, dH ], simply denote the set of feasible objects. Let Ci be the shifts the weight attached to v1y2. This might, choice function for individual i, de!ned over Gi for example, represent the type of “coherent (where the subscript re0ects the possibility that 468 AEA PAPERS AND PROCEEDINGS MAY 2007

F,$#)( 1 the set of ancillary conditions may differ from vector of ancillary conditions, dˆ 5 (dˆ1, … , dˆN), individual to individual). These choice func- which clear all markets. Though behavioral * tions induce the relations Ri and Pi over X. competitive equilibria may not exist, those that We will say that x is a weak generalized Pareto do exist are necessarily ef!cient. * optimum in X if there exists no y [ X with yPi x for all i. We will say that x is a strict generalized THEOREM 1: The allocation in any behavioral Pareto optimum in X if there exists no y [ X is a strict generalized * with yRix for all i, and yPi x for some i. Pareto optimum. Since strict individual welfare optima do not always exist, we cannot guarantee the existence It is worth emphasizing that a perfectly com- of strict generalized Pareto optima with a high petitive equilibrium may be inef!cient when degree of generality. We can guarantee the exis- judged by a re!ned welfare relation, after of!- tence of a weak generalized Pareto optimum, ciating choice con0icts, as described in the next however. section. This observation alerts us to the fact that, in behavioral economics, choice reversals lead to a new class of potential failures. G. The Ef!ciency of Competitive Equilibria III. Re!nements To illustrate the usefulness of these concepts, we have provided a generalization of the !rst welfare A. The Logic of Re!nements theorem. Speci!cally, we consider a production economy consisting of N consumers, F !rms, and In any particular context, the relation R and K goods. The economy is standard in all respects, P* that we have de!ned may not be very discern- except that consumer i’s behavior is governed by ing, which means that many choice alternatives a general choice correspondence mapping budget might be individual welfare optima. In this sec- sets and ancillary conditions into sets of consump- tion, we consider the possibility that one might tion vectors. We make one simple assumption re!ne the relations R and P* by altering the data (akin to nonsatiation) with respect to consumer used to construct them. Most obviously, one can behavior: if xn . wn (where . indicates a strict add choice data (by creating new GCSs, expand- inequality for every good), then consumer n never ing the domain G), or delete data (by ignoring chooses wn when xn is available. certain GCSs, reducing the domain G). There is A behavioral competitive equilibrium involves also the possibility of reinterpreting choice data, a price vector, pˆ 5 (pˆ 1, … , pˆ K), along with a which we mention brie0y below. VOL. 97 NO. 2 TOWARD CHOICE-THEORETIC FOUNDATIONS FOR BEHAVIORAL WELFARE ECONOMICS 469

We say that Rr is coarser than R if xRry implies choice when making a selection from X? Not in xRy. When Rr is coarser than R, we say that R our view. is !ner than Rr. Subject to a technical quali!ca- Why would the individual believe himself tion, the addition of data (that is, the expansion to be choosing from some set, Y, when in fact, of G) makes R weakly coarser, while the elimi- according to the available objective informa- nation of data (that is, the reduction of G) makes tion, he is choosing from the set X? His atten- R weakly !ner. Thus, to usefully re!ne the wel- tion may focus on some small subset of X. His fare relations, one must either eliminate or rein- memory may fail to call up facts that relate terpret data. Accordingly, if there is one GCS in choices to consequences. He may forecast the which x is chosen over y, and another in which consequences of his choices incorrectly. He may y is chosen over x, we look for objective criteria have learned from his past experiences more that might allow us to of!ciate between these slowly than the objective information would GCSs, with the object of discarding or reinter- permit. Thus, the operations of these cognitive preting one of them. We can then construct a processes pertain to the question of whether, at new welfare relation, Rr, based on the revised the moment of choice, he appreciates that he is choice correspondence, which may be !ner than choosing from X. R and contain fewer welfare optima. The same In principle, if we understand the individual’s comments apply for P*. cognitive processes suf!ciently well, we may be How might we of!ciate between con0ict- able to identify his perceived choice set Y, and ing GCSs? One seemingly natural possibility, to reinterpret the choice as pertaining to the set which we call “self-of!ciation,” is to of!ciate Y rather than to the set X. We refer to this pro- based on choices. If the individual makes con- cess as “deconstructing choices.” While it may 0icting choices for two GCSs, G1 5 1X, d1 2 be possible to accomplish this in some instances and G2 5 1X, d2 2, simply allow him to choose (see, e.g., Botond Ko˝szegi and between these GCSs. This, however, creates 2007), we suspect that, in most cases, this is another GCS, call it G3 5 1X, d3 2. Since the beyond the current capabilities of science. We expansion of G to include G3 does not re!ne nevertheless submit that there are circumstances usefully either the welfare relation or the sets in which nonchoice evidence can reliably estab- of welfare optima, we have an “irresolvability lish the existence of a signi!cant discrepancy principle”—new choices cannot resolve norma- between the actual choice set, X, and the per- tive ambiguities associated with existing choice ceived choice set, Y. This occurs, for example, in con0icts. To of!ciate, we must therefore rely on circumstances where it is known that attention nonchoice data. wanders, memory fails, forecasting is naive, and/or learning is slow. In these instances, we B. Re!nements Based on Information say that the GCS is suspect. Processing We propose using nonchoice evidence to of!ciate between con0icting choice data by When we say that an individual’s standard deleting suspect GCSs. Thus, for example, if choice situation is X, we mean that, based on all someone chooses x from X under condition dr, of the objective information that is available to where he is likely to be distracted, and chooses him, he is actually choosing among elements of y from X under condition ds, where he is likely X. In standard economics, we use this objective to be focused, we would delete the data asso- information to reconstruct X, and then infer that ciated with (X, d9) before constructing the wel- he prefers his chosen element to all the uncho- fare relations. In effect, we take the position sen elements of X. But what if he fails to use that (X, d0) is a better guide for the planner than all of the information available to him, or uses (X, d9). Even with the deletion of choice data, it incorrectly? What if the objective informa- the welfare relations may remain ambiguous in tion available to him implies that he is actually many cases due to other unresolved choice con- choosing from the set X, while in fact he believes 0icts, but they nevertheless become (weakly) he is choosing from some other set, Y? In that !ner, and the sets of welfare optima grow case, should a planner nevertheless mimic his (weakly) smaller. 470 AEA PAPERS AND PROCEEDINGS MAY 2007

What types of nonchoice evidence might one this may provide a compelling basis for declar- use to determine the circumstances in which ing the choice suspect. Other considerations, internal information processing systems work such as the complexity of a GCS, could also well, and the circumstances in which they work come into play. poorly? Evidence from neuroscience concerning the functioning of various cognitive processes REFERENCES can potentially shed light on the operation of processes governing attention, memory, fore- Ariely, Dan, , and Drazen casting, and learning. This evidence can provide Prelec. 2003. “Coherent Arbitrariness”: Stable an objective basis for determining whether a par- Demand Curves without Stable Preferen- ticular choice situation is suspect. For example, ces.” Quarterly Journal of Economics, 118(1): if memory is shown to function poorly under 73–105. certain environmental conditions, GSCs that Bernheim, B. Douglas, and Antonio Rangel. are associated with those conditions, and that 2004. “Addiction and Cue-Triggered Decis- require factual recall, are suspect. Our work on ion Processes.” American Economic Review, addiction (Bernheim and Rangel 2004) provides 94(5): 1558–90. a more elaborate illustration. Citing evidence Bernheim, B. Douglas, and Antonio Rangel. from neuroscience, we argue that the habitual 2007. “Beyond Revealed Preference: Choice- use of addictive substances causes speci!c infor- Theoretic Foundations for Behavioral Welfare mation processing systems to malfunction under Economics.” Unpublished. identi!able circumstances. The choices made in Caplin, Andrew, and John Leahy. 2001. “Psy- these circumstances are therefore suspect, and chological Expected Utility Theory and welfare evaluations should be guided by choices Anticipatory Feelings.” Quarterly Journal of made in other circumstances. More generally, Economics, 116(1): 55–79. these observations de!ne a normative agenda Gul, Faruk, and Wolfgang Pesendorfer. 2001. for the emerging !eld of . “Temptation and Self-Control.” Econometrica, In many situations, simpler forms of evidence 69(6): 1403–35. may suf!ce. If, for example, an individual char- Ko˝szegi, Botond, and Matthew Rabin. 2007. “Re- acterizes a choice as a mistake on the grounds vealed Mistakes and Revealed Preferences.” that he neglected or misunderstood information, Unpublished.