Choice Bracketing PDF (1999)

# Choice Bracketing ## Journal of Risk and Uncertainty, 19: 1-3; 171-197 (1999) ### Daniel Read Leeds University Business School, Leeds, UK LS2 9JT ### George Loewenstein Department of Social and Decision Sciences, Carnegie Mellon University ### Matthew Rabin Department of Economics, University of...

# Choice Bracketing ## Journal of Risk and Uncertainty, 19: 1-3; 171-197 (1999) ### Daniel Read Leeds University Business School, Leeds, UK LS2 9JT ### George Loewenstein Department of Social and Decision Sciences, Carnegie Mellon University ### Matthew Rabin Department of Economics, University of California-Berkeley ## Abstract When making many choices, a person can broadly bracket them by assessing the consequences of all of them taken together, or narrowly bracket them by making each choice in isolation. We integrate research conducted in a wide range of decision contexts which shows that choice bracketing is an important determinant of behavior. Because broad bracketing allows people to take into account all the consequences of their actions, it generally leads to choices that yield higher utility. The evidence that we review, however, shows that people often fail to bracket broadly when it would be feasible for them to do so. In addition to documenting the diverse effects of bracketing, we also discuss factors that determine whether people bracket narrowly or broadly. We conclude with a discussion of normative aspects of bracketing and argue that there are some situations in which narrower bracketing results in superior decision making. ## Key Words: Decision framing, simultaneous and sequential choice addiction, procrastination, risk attitude ## 1. Introduction The consequences of choices can rarely be fully appreciated in isolation. Even seemingly trivial decisions, such as whether or not to indulge in desert, save small amounts of money, or purchase lottery tickets, can have profound cumulative effects on our physical and material well-being. When we make choices without considering these effects, we can do to ourselves what the bad general can do to his army-make a series of local choices that each appear to be advantageous but which collectively lead to a bad global outcome. In this paper we introduce the concept of **choice bracketing**, a term which designates the grouping of individual choices together into sets. A set of choices are bracketed together when they are made by taking into account the effect of each choice on all other choices in the set, but not on choices outside of the set. When the sets are small, containing one or very few choices, we say that bracketing is narrow, while when the sets are large, we say that it is broad. **Broad bracketing** allows people to consider all the hedonic consequences of their actions, and hence promotes utility maximization. **Narrow bracketing**, on the other hand, is like fighting a war one battle at a time with no overall guiding strategy, and it can have similar consequences. To illustrate the effects of choice bracketing, consider the decision to smoke or abstain. If choices are made one cigarette at a time, the expected pleasure from each cigarette can easily seem to outweigh its trivial health consequences, so lighting up may appear to be the best choice. But if 7,300 single-cigarette choices (one year's worth, for a pack-a-day smoker) are combined, the health consequences may appear less trivial, and might well outweigh the pleasure. The individual who makes 7,300 individually inconsequential decisions to smoke, therefore, makes an aggregate choice that might have been rejected had all the decisions been bracketed together. Whether someone who likes cigarettes ends up as a lifetime smoker may thus depend in part on how she brackets her choices. In recent years, the distinction between narrow and broad bracketing, under the guise of different more-or-less synonymous labels, has been a frequent object of research. Simonson (1990) used sequential and simultaneous choice; Kahneman and Lovallo (1993) used narrow and broad decision frames; Herrnstein and Prelec (1992a, 1992b) used isolated and distributed choice; Rachlin (1995) used decision making based on acts and patterns; and Heyman (1996) used local and overall value functions. Thaler (in press) argues that many choice errors are the result of myopic loss aversion which he contrasts to more global forms of utility maximization. All of these researchers have used these terms in the way that we use choice bracketing-to distinguish between choices made with an eye to the local consequences of one or a few choices (narrow bracketing), or with an eye to the global consequences of many choices (broad bracketing), We argue that bracketing effects are central to understanding a great deal of human choice. Moreover, the distinction between broad and narrow bracketing is one that is often overlooked, even by economists. Economic theory assumes that people bracket broadly by maximizing well-defined global utility functions. Yet, specific economic analyses often rationalize puzzling behavior by showing how it is rational within narrow brackets. For instance, most formal models of risk attitudes assume that they are defined over aggregate wealth levels, and hence that consumers judge each risky choice according to the impact it will have on aggregate long-term risk. Yet specific economic analyses of activities that involve risk such as insurance purchases, treat consumers' individual decisions as if they were the only decisions that they make. ## 2. Choice Bracketing in Context Choice bracketing can be distinguished from two closely-related forms of choice partitioning. Outcome editing refers to whether the outcomes associated with a particular alternative are aggregated or segregated. Joint versus separate evaluation refers to whether the alternatives of a particular choice are evaluated one-at-a-time or comparatively. After defining choice bracketing, we elaborate on each of these other types of partitioning effects. ## 2.1 Choice Bracketing Consider the choices: (x1, y₁) and (x2, y2). Under narrow bracketing, each choice is made separately. Under broad bracketing, a choice is made between the four y1y2). A bracketing effect occurs whenever the outcomes chosen under narrow bracketing differ from those chosen under broad bracketing. For instance, if x is chosen over y for both narrowly bracketed choices, then bracketing matters if anything other than x₁x₂ is chosen under broad bracketing. The special, but common, case of temporal bracketing applies when the sequencing of choices is important. In narrow temporal bracketing, the individual first chooses between x₁ and y, (subscripts now designate time) without consideration of the subsequent choice between x₂ and y₂, and then chooses between x₂ and y₂. Again, bracketing effects occur when narrow bracketing leads to a different final outcome than broad bracketing. In practice, choices are usually made sequentially, and therefore most bracketing effects are probably cases of temporal bracketing. Choice bracketing is illustrated by responses to the following classic problem, due to ***Tversky and Kahneman*** (1981): Imagine that you face the following pair of concurrent decisions. First examine both decisions, then indicate the options you prefer: **Choice (I) Choose between:** * A. a sure gain of $240. * B. 25% chance to gain $1000 and 75% chance to gain nothing. **Choice (II) Choose between:** * C. a sure loss of $750. * D. 75% chance to lose $1000 and 25% chance to lose nothing. When the two choices were presented in this way, a large majority of subjects chose A and D. This is because people are loss-averse-a loss of x is far more aversive than a gain of x is pleasurable-and because they give disproportionate weight to outcomes that are certain relative to those that are uncertain (***Kahneman and Tversky***, 1979). Consequently, subjects were risk averse when making Choice I (they chose the sure gain), and risk seeking when making Choice II (they chose the uncertain loss). When B and C are combined, however (giving a 25% chance to gain $250 and a 75% chance to lose $750), they dominate outcomes A and D (a 25% chance to gain $240 and a 75% to lose $760). Tversky and Kahneman's subjects apparently bracketed the two choices separately and treated each choice as if it had no connection to the other. That they would want something different if they had bracketed broadly was demonstrated when the outcomes from each choice pair were explicitly combined: nobody chose the dominated AD pair. ## 2.2 Outcome Editing Outcome editing (***Kahneman and Tversky***, 1979; ***Thaler***, 1985) refers to how outcomes (or attributes) are integrated or segregated when their utility is evaluated. If an alternative has multiple outcomes, such as a compensation package that includes both a long-term raise in salary and a bonus, then decision makers can either evaluate each outcome separately, then compute the value of the alternative as the sum of these separate values, or they can first combine the outcomes and then compute the value of the composite outcome. Imagine an alternative x with two attributes, r and s. In a simple case, integrated outcomes are first combined and then valued, as in v(r + s), whereas segregated outcomes are first valued and then added, v(r) + v(s). The hedonic consequences of the set of outcomes can vary depending on which editing procedure is used. The distinction between choice bracketing and outcome editing can be illustrated using the example from ***Tversky and Kahneman*** described above. Decision makers can either treat each choice in isolation (narrow bracketing) or combine them (broad bracketing). Broad bracketing confronts the decision maker with four alternatives: AC, AD, BC and BD. Within these alternatives, the individual outcomes can be segregated or integrated. Thus, under broad bracketing the alternative AD could be expressed in a segregated form: * a sure gain of $240; combined with a 25% chance to lose $1000 and 75% chance to lose nothing, or in an integrated form: * a 75% chance to lose $760 and a 75% chance to gain $240. Choice bracketing and outcome editing are close relatives and in many cases, such as the example just presented, the distinction depends on the point at which editing occurs. If the effect reported by ***Tversky and Kahneman** is due to a failure to transform the problem into the four-alternative representation, then it is a bracketing effect. If people do achieve that representation, but then fail to integrate the outcomes, then it is an illustration of outcome editing. Many problems, such as this one, may turn out to be ambiguous concerning when the editing occurs. We suggest, however, that for the problem described above and for the great majority of other situations revealing a failure to integrate outcomes across choices, the problem is not that decision makers combine the choices into a composite choice and then fail to integrate the outcomes (i.e., broad bracketing followed by outcome segregation), but that the decision maker views each choice as a separate choice to be evaluated on its own merits (narrow bracketing). As will be seen in many of the examples cited below, when experimenters turn separate choices into single choice, subjects readily integrate the outcomes. ## 2.3 Joint versus Separate Evaluation of Alternatives A third type of partitioning effect, which ***Hsee et al.*** (in press) refer to as joint versus separate evaluation, occurs between the alternatives offered within a single choice rather than between choices. Separate evaluation occurs when each alternative in a choice is first evaluated without reference to its neighbors, and then one of the alternatives is chosen based on the outcome of these evaluations. In joint evaluation, people choose between alternatives by making explicit comparisons between them. Numerous studies show that whether people evaluate alternatives jointly or separately can have a major impact on choice (eg., ***Kahneman and Ritov***, 1994; ***Nowlis and Simonson***, in press). In one study (***Hsee***, 1996), for example, participants were asked to assume that as the owner of a consulting firm they were looking for a computer programmer who could write in a special computer language-KY language. The two candidates, who were both new graduates, differed on two attributes: experience with the KY language and undergraduate GPA (on a 5-point scale): **Candidate J:** * Experience: 70 KY programs in last 2 years * GPA: 3.0 **Candidate S:** * Experience: 10 KY programs in last 2 years * GPA: 4.9 In the joint evaluation condition, participants were presented with the information on the two candidates as listed above. In the separate evaluation condition, participants were presented with the information on only one of the candidates. In all conditions, respondents were asked what salary they would be willing to pay the candidate(s). The result revealed a significant preference reversal between the two modes of evaluation: the salary offered to candidate J was higher (Ms = $33.2k for J and $31.2k for S) in joint evaluation; but lower in separate evaluation (Ms = $32.7k for S and $26.8k for J). Since the evaluation scale was identical in both conditions, the reversal could only have resulted from the difference in evaluation mode. ## 3. A Review of Bracketing Effects Bracketing effects occur because broad bracketing facilitates the consideration of choice factors that are either not perceived or given relatively less weight in narrow bracketing. These include: * **Emergent properties.** Alternatives can combine into options that have features that are not part of the alternatives taken by themselves. Sets of options that give rise to such gestalts are more likely to be recognized in broad bracketing. * **Adding-up effects.** Alternatives that are chosen repeatedly have trivial or even non-noticeable costs or benefits when considered individually. When choices are bracketed together, however, the aggregated costs or benefits can exceed a threshold so that they play a greater role in choice. * **Taste change.** What we choose now can change our tastes, and thus influence what we will want in the future. When choices are bracketed together, we are more likely to recognize how a choice of one alternative will influence our desire for future alternatives. Taste change effects are specific to temporal bracketing. * **Trade-offs.** When making many choices between multidimensional alternatives, it may be possible to find 'integrative solutions' in which the good parts of some alternatives compensate for the bad parts of others. Again, these trade-offs are easier to see when choices are bracketed together. These factors embrace what we believe to be the majority of bracketing effects. They are not, however, mutually exclusive, and even in the examples we discuss below there is scope for controversy about where they fit into the framework. The first two factors are the most general, and describe the 'essential' differences between broad and narrow bracketing. Broad bracketing reveals global patterns and magnifies local consequences that can be missed or ignored under narrow bracketing. Taste change can be viewed either as a special kind of emergent property that unfolds over time, or as an adding-up effect involving endogenous changes. Trade-offs are also emergent properties, but these are unique to situations in which choices involve allocating limited resources to alternatives. In the remainder of this section we elaborate on these four factors, and give examples of their operation. ## 3.1 Emergent Properties When combined, alternatives can have set-level or emergent features that do not exist as features of any single alternative. An illustrative emergent feature is representativeness. A representative sample (the result of a sequence of sampling decisions) has properties that reflect those of its population, yet no single element in the sample can be said to be representative; nor can the representativeness of the sample be inferred from one element. Analogously, in some situations the outcome of many choices must be combined for emergent features to be recognized, and this can only be accomplished through broad bracketing. We consider three ways in which broad bracketing can highlight properties of alternatives that might otherwise not be apparent. First, people often prefer sets of goods (e.g., clothes, books, movies) that are diverse rather than homogeneous. They are more likely to pay attention to this diversity when they bracket multiple choices together (e.g., by purchasing several books in one trip to the bookstore) than when they bracket them separately (e.g., in a series of single-book purchases). Second, people like to have their pleasures and pains distributed over time in specific ways: they like to spread them out rather than getting them all at once, and they like things to improve over time rather than to get worse. They can only know which choices will achieve these goals when they schedule many experiences simultaneously. Finally, people like to avoid risk-especially the risk of loss-and one way to reduce risk is to combine many risky choices. Consequently, the attractiveness of a portfolio of gambles, when perceived with the benefit of broad bracketing, may be greater than the sum of the attractiveness of its constituents. ## 3.2 Adding-Up Effects Bracketing effects due to adding-up occur when the perceived costs of alternatives accumulate at a different rate than their benefits. The costs or benefits from a single act may be so low as to fall below a threshold of consideration, while the cumulative costs or benefits of many such acts can be momentous. Consider, for example, the health consequences of one cigarette, the girth added by one slice of cake, or the effects on one's grades of a single decision to 'skip class.' In each of these examples, the anticipated cumulative benefit from indulging on multiple occasions seems to increase much more slowly than the cumulative costs. We suspect, for example, that the magnitude of the anticipated pleasure from 100 desserts does not even approach 100 times the pleasure from a single dessert, whereas the anticipated growth in your waistline is (if anything) greater than that from a single dessert. The same is true for cigarettes and skipping class. If people bracket narrowly and consider the costs and benefits of a single action, then the balance of costs and benefits will likely favor the benefits, while if they bracket broadly the balance can be reversed. The failure to take tiny but cumulative effects into account has been implicated in many apparently suboptimal patterns of choice. Sabini and Silver (1982), for example, attribute procrastination to a combination of narrow bracketing and the apparently trivial amount of work that can be accomplished on a project in a short period: Imagine you have two days to write a paper. You believe it will take about six hours. To avoid being rushed, you decide to get to work. Now suppose you had to decide what to do for the next five minutes-either work on the paper or play one game of pinball... In the short run, five minutes of pinball is far more pleasurable than five minutes of paper writing, and after all, how much of a paper can you do in five minutes? Pinball is the obvious choice. The game is over so you must decide about the next five minutes. The situation is only trivially changed, so you will reach the same result. Once you've fragmented your night into five minute intervals, you may be doomed to play until you run out of money, the machine breaks, or someone meaner than you wants to play.... One of the ways of being irrational and procrastinating is to act on rational calculations for intervals that are irrationally short.... A model that would capture rational action must not only show how means are fit to goals, but also how appropriate intervals for calculation are picked (***Sabini and Silver***, 1982, p. 1.33). ## 3.3 Taste Change Taste change occurs when choosing an option at one time affects that option's future utility, and hence the likelihood of choosing it again. Bracketing is important because if individuals bracket narrowly, taking each choice separately, they will not take into account these internalities (***Herrnstein et al.***, 1993)-i.e., impacts of earlier choices on the utilities associated with later choices. ***Herrnstein*** (1982; ***Herrnstein and Prelec***, 1992a) argues that the tendency to ignore internalities, which he calls **melioration**, can account for a wide range of suboptimal patterns in repeated choice. The most important taste change effects are **habit formation** and **satiation**. ## 3.4 Tradeoffs Across Choices When two parties negotiate over many issues simultaneously they can look for **integrative agreements**, which are settlements in which one party concedes on a dimension that it values less than the other in exchange for a reciprocal concession on a dimension that it values more. A union, for instance, may be willing to concede on wage increases (which management values more) in exchange for job security (which the union values more). In this way both sides end up with an agreement which they prefer to the one which would have come from making separate concessions on wages and job security. Integrative agreements are possible only when more than one issue is negotiated simultaneously. Analogously, individual decision makers can reach integrative agreements with themselves if they take into account the possibility of trade-offs across the many choices that they face. Just as with union and management, such an intrapersonal integrative solution can only be reached if the decision maker brackets more than one choice together. In this section we examine cases that illustrate the impact of bracketing on the exploitation of opportunities for intrapersonal tradeoffs. First, we look at how people trade off the amount of the time they spend working across days that offer different wage rates; then we examine how people trade off across categories of consumption; and finally we consider people's notions of a just division of resources, and how they allocate resources between different people who value those resources differently. ## 3.4 Tradeoffs Across Choices When two parties negotiate over many issues simultaneously they can look for **integrative agreements**, which are settlements in which one party concedes on a dimension that it values less than the other in exchange for a reciprocal concession on a dimension that it values more. A union, for instance, may be willing to concede on wage increases (which management values more) in exchange for job security (which the union values more). In this way both sides end up with an agreement which they prefer to the one which would have come from making separate concessions on wages and job security. Integrative agreements are possible only when more than one issue is negotiated simultaneously. Analogously, individual decision makers can reach integrative agreements with themselves if they take into account the possibility of trade-offs across the many choices that they face. Just as with union and management, such an intrapersonal integrative solution can only be reached if the decision maker brackets more than one choice together. In this section we examine cases that illustrate the impact of bracketing on the exploitation of opportunities for intrapersonal tradeoffs. First, we look at how people trade off the amount of the time they spend working across days that offer different wage rates; then we examine how people trade off across categories of consumption; and finally we consider people's notions of a just division of resources, and how they allocate resources between different people who value those resources differently. ## 4. Determinants of Bracketing In the previous section, we summarized the results of numerous studies that document the important consequences of bracketing choices narrowly or broadly. We did not directly address what causes people to bracket the way they do, in part because very few studies have addressed this question. Undoubtedly, many bracketing choices result from a wide range of subtle and unconscious factors that influence the way we categorize the world. For example, putting on one's shoes could be construed as: putting on each of two shoes; putting on a pair of shoes; part of getting dressed; part of preparing to leave the house; or, perhaps somewhat far-fetched, part of furthering one's career. Our lack of insight into the factors that influence bracketing even in mundane choices suggests that developing a theory of how people bracket is a crucial direction for future research. Despite our comparative ignorance on this issue, we provide a preliminary analysis of four factors that we suspect are important. * **Cognitive capacity limitations**. Cognitive limitations-in perception (***Miller***, 1956), attention (***Kahneman***, 1973), memory (***Baddeley***, 1986), and analytical processing (***Simon***, 1957), etc.-are one important determinant of bracketing. Such limitations sharply constrain our ability to simultaneously consider multiple decisions. As the number of choices or the number of alternatives per choice-in-creases, the cognitive cost of broad bracketing will undergo a combinatorial explosion. To take an abstract example, narrowly bracketing two choices (x1, y1) and (x2, y2) involves two binary comparisons; broadly bracketing the choice so that it is made between the composite alternatives (x1x2, x1y2, y1x2, y1y2) involves at least three and as many as six binary comparisons. If there are three choices, the composite choice can involve up to 28 binary comparisons. This does not take into account the resources needed to evaluate what will rapidly become exceedingly complex alternatives. * **Cognitive inertia**. Cognitive limitations are probably very important in the real world, and even in some experimental demonstrations of bracketing. In ***Kahneman and Tversky's** (1981) twin-gamble dominance violation illustration, described earlier, subjects might not integrate the gambles (despite being advised that the decisions are concurrent) because doing so would be cognitively taxing. But not all bracketing effects can be explained in this way. Many are due simply to the fact that people usually deal with problems in the way that they are presented to them. If choices come to them one at a time, they will bracket them narrowly, and if choices come to them collectively, they will bracket more broadly. This was elegantly illustrated by ***Redelmeier and Tversky*** (1992) in the domain of gambles. Given a choice, people will usually prefer a larger number of gambles (assuming they have a positive expected value and are independent) to a smaller number (e.g., ***Keren and Wagenaar***, 1987). Their study involved two groups, each of whom chose between five or six gambles. Most of the first group, who made a direct choice, took six gambles A second group made two choices. First they chose between zero gambles or five. Most chose the five. Then they were offered one more gamble, which amounted to a choice between the original five gambles or six gambles. Most refused the sixth gamble. Indeed, the proportion taking the sixth gamble was identical to that taking a single gamble when the choice was between one or zero. The second group had bracketed narrowly, by treating the single gamble choice as separate from the earlier choice of five gambles. Only when the choices were explicitly bracketed together, as they were in the first group, did subjects recognize that the five gambles influenced the desirability of the sixth. In a modification of ***Redelmeier and Tversky's*** study, we asked 143 Carnegie Mellon students to: Imagine that on each of 5 days you will be allowed to choose between the following: * A): 50-50 chance of losing $25 or winning $40; * B): Do not gamble. The students then made separate choices for each day. In the narrow bracketing condition, subjects chose for only the first day, while in the broad bracketing condition subjects made the decision for all 5 days. All subjects knew that they would be making five choices, so the only difference between groups was that single-day subjects would have more flexibility in their choices since they weren't precommitted to a pattern of gambles. They did not, however, take this view. While 50% of the broad-bracketing subjects gambled on the first day, only 32% of the narrow-bracketing subjects did (x²(1) = 4.57, p < .05). Note that cognitive limitations cannot account for results such as these. Rather, the difference between broad and narrow bracketing apparently involves a shift-in-viewpoint, and not more processing power. Narrow bracketing attributable to cognitive inertia may also contribute to the **embedding effect** (***Kahneman and Knetsch***, 1992)-the tendency for respondents in contingent valuation studies to report approximately equal willingness to pay to correct problems that differ dramatically in scope. Respondents, for example, might agree to pay as much to clean the pollution from one lake in Ontario as to clean all of the lakes in Canada. In a verbal protocol study, ***Schkade and Payne*** (1994) found that when people estimate their willingness to pay to correct a particular environmental problem, they spend almost no time thinking about other uses for the money. Rather, they take the problem as it comes and think about how much they can afford to pay in general, and do not think about things like what proportion of their scarce resources they can spend on this cause as opposed to other causes. When respondents in ***Schkade and Payne's*** study were reminded that there were other causes as well, many indicated that their earlier statements of willingness to pay were too high. * **Pre-existing heuristics**. Bracketing decisions can also be determined by socially acquired heuristics and decision rules. For example, in our work-oriented society, it is common to divide the week into two intervals of unequal length-the work-week, and the weekend; periods of eating are labeled "meals," and food intake occurring between these designated times is referred to as "snacking"; and so on. All of these conventions, many or most of which exist for good reasons, influence the way that people bracket decisions. * **Motivated bracketing**. People sometimes adopt a particular bracket to accomplish some goal-most typically to overcome problems of self-control. Much of social guidance regarding bracketing is clearly motivated to counteract otherwise-tempting misbehavior. For example, abstinent alcoholics are instructed to take it one day at a time," presumably because taking it one year at a time makes their task seem overly daunting. Narrow bracketing may also facilitate self-control when people are budgeting time, money, or calories. Eating only 14,000 calories per week is a rule that is much easier to fudge on than 2,000 calories per day, even if, or perhaps precisely because, the former allows for more flexible and thus efficient scheduling. Those who get the urge to binge, for example, might be able to persuade themselves that today is the beginning of a new week. Similarly, spending is much easier to restrict on an entertainment budget of $10 per day rather than $70 per week, and spending two hours with one's child per day is more difficult to shirk on than spending at least 14 hours per week. This might be one reason why the taxi drivers in ***Camerer et al.'s*** (1997) study employed a daily earnings target; if they had, for example, picked a weekly target they might have been tempted to quit early on any given day while assuring themselves that they could make up the deficiency later in the week. Because narrow bracketing can make goals seem easier to attain, it can also increase motivation. This may be an additional reason for a lot of seemingly short-sighted behavior, such as that shown by the cab drivers. By setting a goal of earning a fixed amount per day, they had something realistic to work toward. Indeed, such a feasible performance-based goal may have enabled them to get more work done in less time than an alternative strategy such as 'work 8 hours per day.' ***Anthony Trollope*** (1883/1980, p. 119) attributed his remarkable productivity to a work schedule that explicitly recruited severe narrow-bracketing in the service of long-term goals: When I have commenced a new book, I have always prepared a diary, divided into weeks, and carried on for the period which I have allowed myself for the completion of the work. In this I have entered, day by day, the number of pages I have written, so that if at any time I have slipped into idleness for a day or two, the record of that idleness has been there, staring me in the face, and demanding of me increased labour, so that the deficiency might be supplied.... In the bargains I have made with publishers I have undertaken always to supply them with so many words, and I have never put a book out of hand short of the number by a single word. Trollope's strategy was exactly the same as the one used by the cab drivers. On days when he was very productive he was able to quit early, and on days when the writing was slow he worked longer hours-or else, as indicated in the text, paid a price. Trollope produced at least three major novels a year, many of which are still widely read, while successfully holding a responsible position in the English postal service. It is difficult to fault him for bracketing too narrowly. Broad bracketing can also serve motivational purposes. Both ***Rachlin's*** (1995) and ***Heyman's*** (1996) accounts of self-control and addiction are based on the premise that broad bracketing leads to superior choices and that people have some control over the type of brackets they adopt. ***Ainslie and Haslam*** (1992, p. 188) likewise posit that people may use broad bracketing of choices as a self-control device: Imagine a person on a weight-reducing diet who has been offered a piece of candy. The person knows that the calories in one piece of candy will not make any noticeable difference in weight, and yet he is apt to feel that he should not eat the candy. What would it cost him? Common experience tells us: his expectation of sticking to the diet. He will face many chances to eat forbidden foods, and if he sees himself eating this one, it will not seem likely to him that he will refuse the others. By bracketing dieting choices together, and by viewing rejection or acceptance of the single piece of candy as a larger choice between diet versus no diet, this person increases the chance of adherence to his diet. Although the evidence is not clear concerning whether bracketing as a framing strategy is a successful means of self-control, the widespread existence of rigid rules of conduct and the explicit claims that these rules are self-control devices suggest that it has some beneficial effect. ## 5. Is Broad Bracketing Always Better Than Narrow Bracketing? The underlying premise of this article is that broad bracketing usually leads to better outcomes than narrow bracketing. By "better" we mean that people will usually gain more happiness from making the choices dictated by the broader bracketing than the narrow one. An examination of the studies cited above should make this clear: people who buy stocks will be wealthier than those who buy bonds; dieters who bracket their dining decisions broadly will eat fewer desserts than those who consider each day separately; and consumers who bracket all their purchases together without setting up inviolable budgets will be able to make efficient trade-offs across purchase categories. The general principle is that broad bracketing allows people to pursue maximization of their global well-being. However, broad bracketing is not an unalloyed good, and there may be cases where it is actually better to bracket narrowly. We see at least four caveats to the broader-is-better view of bracketing. First, as is no doubt clear from many of our examples, choices made under broad bracketing often involve putting up with small discomforts or annoyances in order to achieve long-term gains. For example, people who invest all of their retirement funds in stocks, as they might do if they bracket broadly, may be wealthier when they retire, but at the cost of ongoing anxiety during the intervening period. A priori, it is impossible to determine whether the expected gain is adequate compensation for the anxiety. Likewise, for cab drivers to attempt to bracket more broadly-e.g., by attempting to maximize their weekly earnings while minimizing hours driven-might require more self-control and more careful record-keeping, burdens which could offset the benefits derived from greater efficiency. In order to be able to determine whether broadly or narrowly bracketed choices are better in a particular situation, we need some way of comparing the overall or total utility (***Kahneman, Wakker and Sarin's*** (1997) term) of a lifetime of small annoyances against the big gains from broad bracketing. Ironically, it may turn out that narrow bracketing is sometimes better because it enables us to take little annoyances into account (such as the pain of record keeping) that have a significant effect on total utility but which can be ignored when one takes the long view. The second caveat is that, because broad bracketing facilitates the consideration of factors that are given little weight during narrow bracketing, it can exacerbate errors people make in anticipating the role these factors play in their experienced well-being. A possible case in point is the diversification bias, already discussed. Although people like diversity when they choose sets of goods, it is by no means certain that they are always more satisfied with diverse experiences. That is, diversity may influence their choices, but not the pleasure they get from what they choose. In one study, ***Read and Loewenstein*** (1995) found that people who chose a diverse set of snacks under broad bracketing often wanted to change their minds if given a chance-and usually changed their minds in the direction of less diversity. In another study, ***Read et al.*** (1999) found that people who chose more variety, whether under broad or narrow bracketing, retrospectively evaluated their choices as being less enjoyable than did those who chose less variety, suggesting that the tendency to diversify under broad bracketing may lead people to make poor choices. We suggest that the larger principle is that broad bracketing can lead to superior choices only when there are genuine and important preference interactions between alternatives. Broad bracketing will be worse than narrow bracketing when it leads people to either exaggerate trivial preference interactions or to imagine nonexistent ones. The third caveat to the superiority of broad bracketing has already been discussed under the heading of 'motivated bracketing' When people have self-control problems, broad bracketing might undermine the motivation to embark on a long chain of difficult choices. Broad bracketing, in this situation, can make the task seem overwhelming. In such cases, treating each choice in isolation may be the best strategy. In negotiation, this is known as a "salami tactic" (***Fisher***, 1969), in which a big problem