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Neuroeconomics

Intertemporal choice – toward an integrative framework Gregory S. Berns1, David Laibson2 and George Loewenstein3

1 Department of Psychiatry & Behavioral Sciences, Emory University School of Medicine, Atlanta, GA 30322, USA

2 Department of Economics, Harvard University, Cambridge, MA 02138, USA

3 Department of Social and Decision Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA

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Intertemporal choices are decisions with consequences that play out over time. These choices range from the prosaic – how much food to eat at a meal – to life- changing decisions about education, marriage, fertility, health behaviors and savings. Intertemporal preferences also affect policy debates about long-run challenges, such as global warming. Historically, it was assumed that delayed rewards were discounted at a constant rate over time. Recent theoretical and empirical advances from economic, psychological and neuroscience perspectives, however, have revealed a more complex account of how individuals make intertemporal de- cisions. We review and integrate these advances. We emphasize three different, occasionally competing, mechanisms that are implemented in the brain: repres- entation, anticipation and self-control.

Economic, psychological and neuroscientific perspectives on intertemporal choice Intertemporal choices – decisions with consequences that play out over time – are important and ubiquitous. De- cisions about spending, investments, diet, relationships, fertility, crime and education all contain intertemporal tradeoffs. In this paper, we discuss interrelated perspect- ives on intertemporal choice from the fields of economics, psychology and neuroscience.

Until recently, the main contribution of economics to the study of intertemporal decisions was modeling. For nearly 80 years, economists have analyzed intertemporal de- cisions using the discounted utility (DU) model, which assumes that people evaluate the pleasures and pains resulting from a decision in much the same way that financial markets evaluate losses and gains, exponentially ‘discounting’ the value of outcomes according to how delayed they are in time. DU has been used to describe how people actually make intertemporal choices and it has been used as a tool for public policy. Policy decisions about how much to spend on research and development, health and education all depend on the discount rate used to analyze the decision. Indeed, recently the discount rate has proven to be a key parameter in the policy debate about global warming [1].

Corresponding authors: Berns, G.S. ([email protected]); Laibson, D. ([email protected]); Loewenstein, G. ([email protected]).

Available online 5 November 2007.

www.sciencedirect.com 1364-6613/$ – see front matter � 2007 Elsevier Ltd. All rights reserve

The main contribution of psychology has been to identify, through empirical research, psychological mech- anisms underlying intertemporal choice. For example, George Ainslie’s research on the structure of time discount- ing posed the first serious challenge to the DU model – specifically to the assumption that people discount the future exponentially [2,3]. The concept of ‘hyperbolic time discounting’ (explained below) can be considered the first observed pattern of behavior that is inconsistent with DU – a DU ‘anomaly’. Subsequent research by both psy- chologists and economists has identified a wide range of additional anomalies [4–12]. Economists have responded to these findings by constructing new models of intertem- poral choice, which incorporate psychological insights, to explain otherwise anomalous patterns of economic beha- vior [13].

Neuroscience is the most recent entrant into what was already a rich interdisciplinary mix of research. Although still in its infancy, neuroscience research on intertemporal choice has led to an enhanced understanding of how inter- temporal choices might be implemented in the brain [14– 17], and, as we document, has already begun to inform economic modeling and to provide new clues about pro- ductive empirical and theoretical avenues for future research.

Time discounting The great strengths of the DU model are its simplicity and generality. DU is easy to apply mathematically to any kind of intertemporal choice. According to DU, intertemporal choices are no different from any other type of choices except that some consequences are delayed, and hence must be anticipated and discounted (i.e. reweighted to take account of delay). Much of the research on intertemporal choice has, therefore, focused on the degree to which people anticipate and discount future events.

Numerous experiments in animals, notably rats and pigeons, have shown that under operant conditioning para- digms, the effectiveness of a reinforcer diminishes the further in time it is delayed [18]. In pigeons, for instance, the reinforcement value of three units of reward available in 11 s is approximately equal to the reinforcement value of eight units of reward available after 20 s [19]. The traditional model of intertemporal choice uses ‘exponential discounting’, in which a reward of magnitude x occurring at

d. doi:10.1016/j.tics.2007.08.011

Figure 1. Discount functions. Exponential discounting assumes a constant rate of

discounting, e.g. d t

where d is the discount rate (here, d = 0.95). Hyperbolic

discounting is generally greater for short time periods than long periods, and can

be described by a function of the form 1/(K * t + 1). Here, K = 0.1. Quasi-hyperbolic

discounting is a piecewise function that follows a form similar to exponential

discounting after the first discount period (i.e. the first year): 1, b�d, b�d2, . . ., b�dt. (Here, b = 0.792 and d = 0.96.)

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some time t in the future is worth dtx, where d � 1 is a fixed constant (the discount factor). In other words, the value of the reward decays by the same proportion for each minute that its occurrence is delayed. Figure 1 plots three different discount functions, including an exponential function with d = 0.95.

However, the bulk of the evidence (primarily from rats and pigeons) suggests that animals discount the future in a non-exponential manner. The most commonly described discounting behavior is hyperbolic, which means that delayed rewards are discounted by functions that are inversely proportional to delay – for example, 1/t or gener- alizations thereof [18–21]. Hyperboloid discount functions decay at a more rapid rate in the short run than in the long run, so a hyperbolic discounter is more impatient when making short-run tradeoffs than when making long-run tradeoffs. Figure 1 also plots a hyperboloid [7] and a ‘quasi- hyperbolic’ discount function (Box 1) [13,22].

Humans also have been shown to discount the future hyperbolically [7,20], and many commentators have implicitly or explicitly drawn connections between the patterns of choice displayed by animals and by humans. However, whether the parallel between animals and humans is a matter of analogy or homology is unclear. Most humans care about, or at least are capable of caring about, costs and benefits that extend years or even decades. By contrast, our nearest evolutionary relatives have measured discount functions that fall in value nearly to zero after a delay of about one minute. For example, Stevens et al. report that cotton-top tamarin monkeys are unable to wait more than eight seconds to triple the value of an immediately available food reward [23].

Some researchers have speculated that the difference between humans and other animals lies in our ability to form a mental image of, and care about, delayed outcomes [24], and there is widespread agreement that the prefron-

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tal cortex, which is disproportionately large in humans relative to other species, has an important role in this capability. The first clues about the function of the pre- frontal cortex came from people who experienced damage to it, either through accident, stroke or frontal lobotomy [24–26]. Studies have traced the development of self-con- trol capabilities in children to the maturation of prefrontal areas [27], and still other studies have connected criminal- ity and violent out-of-control behaviors to childhood injury to prefrontal regions [28,29]. Humans undoubtedly share with other animals the mechanisms that produce rapid hyperbolic time discounting, but we also have the capacity, seemingly enabled by the prefrontal cortex, to make de- cisions that take account of a much longer span of time.

All of these pieces of evidence, as well as the common observance in humans of extremes in apparent regard (or disregard) for the future, have led to a perspective that is both new and old. According to this perspective, time discounting in humans results from the interaction of two systems, one which is capable of anticipating and caring about the distant future, and the other which is much more oriented toward the present. Empirical support for such a perspective comes from a recent study in which subjects’ brains were scanned while they made choices between smaller money amounts that could be received earlier and large amounts that could be received later [14]. Some of the choices were between an immediate and a delayed payment, and others were between delayed and even more delayed payments. The researchers found that prefrontal regions were involved in all intertemporal choices (relative to rest) but that the mesolimbic dopamine system and associated regions were involved only in choices with an immediate outcome. Moreover, when immediate payment was one of the options, the relative activation of the two regions (prefrontal or dopamine) was a significant predictor of choice. This research lends sup- port to the idea that hyperbolic time discounting results from the splicing of two systems with different perspectives toward the future, and that the prefrontal cortex has an especially important role in implementing more patient preferences. However, it does not provide definitive evi- dence of causal relationships, because the data are purely correlational.

Other dimensions of intertemporal choice Time discounting might be the most frequently studied aspect of intertemporal choice, but it is only one of several dimensions that come into play. In this section, we discuss three other mechanisms that, prior research suggests, have an especially important role in intertemporal choice: ‘anticipation’, ‘self-control’ and ‘representation’. Anticip- ation refers to an individual’s propensity to imagine, and experience pleasure and pain in anticipation of, a future event. Self-control refers to the tensions that people experi- ence when they attempt to implement a far-sighted decision in the presence of immediate temptation. Repres- entation refers to the way that the brain interprets or frames a set of choices. Representation often happens first in a decision time-line, but we discuss representation last because less is known about this component of intertem- poral decision making. Although these mechanisms, in

Box 1. Modeling preference reversals

Standard economic theory assumes that individuals (agents) have

preferences that are stable through time. In this context a preference

refers to a rank ordering of outcomes, or choices, that an individual

makes. For example, a person might be said to prefer tea over coffee.

However, actions speak louder than words and simply professing

such a preference is no guarantee that, given a choice, such an

individual would actually choose tea. Because of the hidden nature of

preferences, eliciting choices (e.g. through forced-choice or will-

ingness-to-pay) is the only reliable way to measure preferences. Even

so, individuals often exhibit reversals in their apparent preferences

when it comes to delayed outcomes. Dieting, for example, often falls

into this trap of preference reversals. An individual makes a New

Year’s resolution to lose weight (a temporally remote outcome), but

when confronted with the deliciousness of food, changes his mind (a

temporally immediate outcome). Such preference reversals can be

modeled in terms of a non-exponential discount function. Assume

that an economic agent has a quasi-hyperbolic discount function: 1,

b�d, b�d2, b�d3, . . .. (Figure 1). In general, this discount function is parameterized with 0 < b < 1 and 0 < d < 1, but to simplify the illustrative example, set b = 1/2 and d = 1, so the discount function takes the form 1, 1/2, 1/2, 1/2, . . .., Immediate payoffs have a weight of

one and all future payoffs have a weight of 1/2. Assume that an

investment activity has an immediate cost of four and a delayed

benefit of six. When the investment opportunity is distant in time, the

agent plans to undertake the investment because 1/2(�4) + 1/2(6) = 1. However, when the moment of action arises, the agent changes her

mind because 1(�4) + 1/2(6) = �1. If agents anticipate such preference reversals [57], they might find

ways to commit themselves in advance – for instance, scheduling an

appointment to exercise with a trainer or putting their saving into

illiquid accounts [13]. If agents fail to anticipate their preference

reversals, they might engage in patently self-defeating behaviors,

such as perpetually paying monthly dues at a gym that they never

attend [54] or, more generally, procrastinating [58,59].

The predictions of the basic hyperbolic discounting model have

been experimentally and empirically validated [20,60]. But the basic

hyperbolic discount function provides only a partial account of

intertemporal preferences [6]. Most importantly, temporal immediacy

of rewards is only one of many factors that seem to produce

impulsivity. Other factors include sensory proximity – the sight,

sound, smell or touch of a desired reward – and the activation of drive

states, such as hunger, thirst or sexual arousal. Thus, for example,

mild opioid deprivation in a population of heroin-addicted outpatients

produces greater discounting of monetary rewards [61]. Likewise,

nicotine deprivation among smokers also produces greater monetary

discounting [62,63]. People often lose control in the ‘heat of the

moment’ or when willpower is depleted [64].

Although preference reversals are often attributed to hyperbolic

time discounting, they can also result from other mechanisms (which

themselves, in some cases, can help to explain hyperbolic time

discounting). Three (overlapping) categories of mechanisms are

visceral influences, cue-contingent influences and temptation prefer-

ences.

Visceral influences are associated with emotion and affect, and are

directly related to changes in drive state. Visceral preferences are

generated by immediate biological imperatives – for instance, thirst,

hunger, sexual arousal, exhaustion, pain, the need to physically

dominate an opponent, or fear for physical safety. Loewenstein has

argued that visceral needs often overwhelm other goals and produce

short-sighted behavior [65]. This assumption has also been adopted

in a two-state decision-making model [66]. In the cold state, the

decision-maker is guided by forward-looking rational deliberations. In

the hot state, the decision-maker is completely controlled by her

myopic visceral needs. Hence, highly impatient behavior would be

associated with time periods in which the visceral preferences are

dominant, explaining many addictive behaviors, including excess use

of an addictive substance and relapse after detoxification.

Cue-contingent preferences have been studied since Pavlov’s

feeding experiments [67]. Cue-contingent preferences are formed

when a neutral stimulus is repeatedly paired with a non-neutral

stimulus, such as a consumption event. The end result is a change in

drive state, even though the eliciting stimulus was, at one point,

neutral. For instance, a heroin user might come to associate the visual

stimuli of a certain environment with ingestion of heroin. Such

pairings might be strong enough to elicit cue-contingent drug

cravings and cue-contingent tolerance, so that the user’s desire to

take heroin becomes much stronger when the cues are present [68].

Cue-contingent cravings might produce preference reversals, transi-

tory efforts to achieve immediate gratification, and forward-looking

efforts to modify cue exposure [65,66,69]. Indeed, several brain-

imaging experiments have demonstrated the powerful effect of

showing pictures of drug-related paraphernalia to people who are

addicted to these substances [70–75]. Although craving, in and of

itself, does not represent a breakdown in self-control, it does

represent an emotional state that places the individual at risk for a

preference reversal. The biological substrates of craving, however,

are complex and recruit a wide range of circuits in the brain that

include memory regions such as the hippocampus, executive control

regions in the prefrontal cortex, and visceral regions such as the

insula. However, no single brain region has been demonstrated to be

singularly responsible for self-control. Instead, multiple systems

process different psychological dimensions of competing prefer-

ences.

Temptation preferences arise in two-system models and are

another way of describing the temporal immediacy effect of rewards

by invoking the cost of self-control [66,76–78]. Rather than postulating

a non-exponential discount function, temptation preferences are

typically modeled as a drive for immediate gratification, which can

be cognitively overridden with some utility cost generated by mental

effort (self-control). In the models cited here, the cost is associated

with the degree to which the impatient preference is violated. The end

result, however, is the same as a non-exponential discount function.

For example, imagine that an agent has a craving to eat a (full) bowl of

ice cream sitting in front of him, but allows himself to eat only some

fraction of that bowl. Temptation models assume that the cost of

temptation is falling in the amount that the agent eats. If the agent

eats nothing, then temptation costs are maximal. If the agent eats the

whole bowl, then temptation costs are zero. Temptation preferences

are one way of formally modeling the interaction between the patient

(cortical) system and the impatient (mesolimbic dopamine reward

related) system. Little is known about the nature of the interaction of

these two putative systems, but one brain region, the anterior

cingulate cortex (ACC), is thought to have a role in mediating the

conflict between competing actions [79,80]. The exertion of self-

control requires the suppression of either cravings or temptations,

which are the types of competing responses that the ACC modulates.

Another region, the inferior prefrontal cortex, seems to be involved in

achieving self-control by inhibiting one of these responses [81].

Importantly, how the ACC processes these conflicts and how the

inferior prefrontal cortex inhibits one or another depends on the

context in which these temptations occur, which leads to the third

aspect of intertemporal choice: representation.

484 Review TRENDS in Cognitive Sciences Vol.11 No.11

some situations, come into competition with time discount- ing, in other situations they contribute to it. Indeed, as touched upon above, there is some question of whether these are the mechanisms underlying time discounting.

Anticipation

The classical economic model of intertemporal choice assumes that choices have no utility consequences other

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than the consumption events that result from those choices. For example, the pleasure of a decadent meal is assumed to arise from the meal itself and not the aware- ness, before the event, that it will take place. In practice, however, when a plan is made in advance – for instance a dinner reservation – there is a waiting period during which the future outcome is anticipated. Moreover, this period of anticipation might have its own affective consequences for

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the actor. The period between decision and outcome has received relatively little consideration from economic researchers because economic models typically do not treat purely mental events as intrinsic sources of utility [30].

From a behavioral perspective, however, both animals and humans experience subjective changes in mental state associated with this continuous period of anticipation. When rats are conditioned to associate a neutral stimulus with a noxious outcome (a loud noise), they enter a state of physiological arousal between the stimulus and outcome. The degree of arousal is associated with their tendency to ‘startle’ in response to the noise. Hence, the startle response serves as a measure of the degree of learning that has occurred [31,32]. Humans display similar states of arousal, which can be indexed by the galvanic skin con- ductance response (GSR) [33]. When the anticipation period is extended, the arousal level can assume complex forms, including an initial surprise effect when the indi- vidual first becomes aware of the impending outcome and a ramp-up to the time when the outcome is expected to occur [34,35].

The anticipation of an outcome can lead to physiological arousal, but does this state of anticipation enter into the decision-making process? Under certain circumstances it does. Consideration of the anticipation of a particularly pleasurable event, such as the promise of a kiss from a movie star, or the dread of something painful, such as an electric shock, often enters into the decisions that people make; for example, causing them to get unpleasant out- comes over with quickly to eliminate what otherwise would be an aversive period of waiting [36,37], behavior that is contrary to the most basic prediction of the DU model, assuming that people discount the future. A concise expla- nation of this phenomenon is that anticipation can confer utility (or disutility) in, and of, itself. Human neuroimaging data demonstrate that activity in regions associated with the experience of pain increases in anticipation of delayed painful stimuli [38–44], and the degree of this anticipatory activity correlates with the degree to which an individual chooses to expedite unpleasant outcomes [36].

Anticipatory responses to appetitive stimuli are also common in neural systems, although these tend to be in different regions than for aversive stimuli. Anticipatory activity in the ventral striatum and orbitofrontal cortex has been associated with the prospect of receiving a finan- cial windfall [45–47], beautiful faces [48] and pleasant- tasting drinks [49–51]. Because of the relatively short interval between the cue and the outcome in these exper- iments, it is difficult to ascertain whether the activity is in response to the initial cue or the waiting period.

Self-control

It is often difficult to wait for a delayed reward when an immediately gratifying alternative is available. For instance, quitting smoking is difficult because cigarettes are available at every news-stand and drug store. Situ- ations such as this can lead to ‘preference reversals’, wherein people initially decide to take a far-sighted course of action – quitting smoking – but subsequently succumb to temptation [20]. Preference reversals are observable phenomena that point to the weaknesses of standard

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DU theory, and they occur in a wide variety of circum- stances. Although it is possible, as we shall see, to modify the discount function in a way that explains preference reversals, the core mechanism might be generated by phenomena other than the discount function.

Successful implementation of a far-sighted plan of beha- vior, such as ending a bad habit, thus involves at least two distinct components. First, the individual needs to make an initial far-sighted decision, which is likely to depend on the ability to anticipate future consequences. Second, she needs to resist short-run temptations, which will under- mine her ability to implement that decision. Any successful model of intertemporal choice should incorporate features that accurately describe the tug of war between long-run (‘virtuous’) intentions and short-run temptations.

As a benchmark, the DU model fails this descriptive challenge. As Samuelson [52] noted, the DU model (with exponential discounting) implies that resolutions once made are never broken. Economists refer to this property as dynamic consistency. Anyone who follows the exponen- tial discounting model will be dynamically consistent – they will never change their state-contingent preferences. Plans or preferences made for the future will be the same as decisions executed at the moment of action. In this framework, resolutions to quit smoking or stick to a diet are always carried out (unless new decision-relevant infor- mation arrives).

Real people don’t have such exquisite self-command [20,53]. Most people experience preference reversals: plans made at one date are broken at some later date. For instance, estimates of relapse rates exceed 50% during the first year after quitting smoking. Many other types of behavior illustrate this tendency to backslide, including credit card spending, exercise and nutrition [54–56]. Beginning with the groundbreaking work of Ainslie [2,20], these types of effects have been integrated into models of time discounting.

The exponential discounting model counterfactually rules out preference reversals. However, any other dis- counting behavior has the potential to generate preference reversals, which economists refer to as dynamic inconsis- tency. This potential was first discussed by Samuelson [52] and then developed by others [22,57]. Most research has focused on the class of hyperbolic [2,7] and quasi-hyper- bolic discount functions [13], which predict that agents will make patient plans and then break them at the moment of execution (Box 1).

Representation

Economic analysis assumes that how a choice is represented is an objective matter. But, in fact, it is possible to mentally represent the same situation in a variety of different ways [82]. People use a wide range of choice heuristics to make the decisions they face and which heuristics come into play depends crucially on how they construe these decisions [83,84]. As a result, differences in context or in the way that a decision is ‘framed’ or cogni- tively construed can have an impact on the intertemporal tradeoffs that people make.

A child’s ability to delay gratification depends on the manner in which the child is instructed to mentally

Box 2. Directions for future research

How can neurobiological data be used to develop and test models of

intertemporal choice? In the past, the tautology of choice and

preference has excluded analysis of neurobiological mechanisms. In

recent years, a growing body of data based on brain imaging is

enabling researchers to link intertemporal decisions to neural

activation patterns, producing both new empirical regularities and

new controversies [14,90,91]. The challenge will be to marry

neurobiological descriptions with theoretical ones.

Can a single model account for the large range of timescales over

which intertemporal choices are made? Such choices range from

intervals of milliseconds to decades. Is there a unifying framework

for all such intertemporal choices or do different mechanisms apply

at different timescales?

How does the representation of time itself influence intertemporal

choice? The representation of time is typically assessed in a

retrospective manner (i.e. how much time has passed). Intertem-

poral choices are fundamentally prospective. How does the

representation of the past affect the representation of the future?

486 Review TRENDS in Cognitive Sciences Vol.11 No.11

represent a reward [9,85]. When given a choice between an immediate single pretzel or two delayed pretzels, children were more likely to wait if instructed to represent the pretzel in pallid or unappealing terms – for instance, as ‘little brown logs’ – than if they were to represent the pretzel in consumatory terms – ‘yummy, tasty’. In research with adults, Wilson and Daly [86] found that showing male subjects photographs of attractive females raises the male subjects’ monetary discount rates. Wilson and Daly’s results show that reproductively salient stimuli change the way that individuals evaluate time-dated monetary rewards, possibly by creating a general sense of urgency or by generating emotional arousal, which increases the relative strength of the impatient affective reward systems.

A variety of studies have shown that framing an inter- temporal choice in a fashion that draws more attention to the need to wait during the delay interval tends to produce steeper time discounting – less willingness to delay. For example, subjects are much less willing to delay gratifica- tion when they made a choice that was expressed in terms of delay than when the same choice was expressed in terms of speed-up or simply as a choice between outcomes at two different points in time [37]. More recently, several studies have shown that people tend to display flatter time discounting when the delay interval of an intertem- poral choice is presented in terms of dates – for example, x today or y on a particular date – than when expressed in terms of a delay interval – for example, x today or y after a wait of z days (where the interval in the two choices is equal) [87].

Given the complexities of many decisions, people often simplify the process of decision making by drawing from a toolbox of different choice heuristics – simple rules of choice that dictate what to do in a particular situation [83]. Examples of choice heuristics might include ‘pick what the last person picked’ or ‘pick what you picked last time (unless it turned out bad)’. If the representation of the choice affects the selection of choice heuristics, then repres- entation will have an impact on decision making.

One important choice heuristic that people seem to employ is to choose sequences of outcomes that improve over time – a pattern of choice that effectively results in ‘negative time preference’: subjects prefer to have the smaller rewards early and the larger rewards later, con- trary to what the DU model would predict. However, whether a particular intertemporal choice is represented as a sequence, and hence whether this heuristic is applied, can depend on relatively subtle factors. In the first demon- stration of this point, Prelec and Loewenstein [88] asked some subjects to hypothetically choose whether to consume a fancy French dinner on the following weekend or on a weekend one month later. Most subjects chose to have the French dinner on the earlier date. However, when the decision was represented as a sequence of two events on fixed dates, where subjects could choose to eat at home on one weekend and eat the fancy dinner on the other, a majority of subjects now chose to delay the fancy French dinner to the later date. Later research found that the more coherent a sequence was made to seem, the more probable subjects were to opt for improving sequences [89].

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Conclusion The research reviewed above identifies three operations that affect intertemporal choice. Anticipation produces immediate hedonic consequences, even when the anticip- ated consumption event is delayed in time. Self-control is used to resist temptations to reverse patient plans. Repres- entations evoke specific choice heuristics that increase or decrease the salience of delayed rewards and make waiting more or less aversive. Any comprehensive account of inter- temporal choice should incorporate all of these mechan- isms. At the moment, we know little about how these mechanisms interact, which should be a priority for future research. At the most general level, it is important to determine whether the brain has one all-purpose time discounting mechanism or whether the brain draws upon different systems, each with its own occasionally compet- ing time perspective.

Although the new models of intertemporal choice are more realistic than the DU model they are intended to replace, the increased realism has come at the expense of simplicity. Researchers face a familiar conflict between parsimony and realism. We hope that the interactions among economists, psychologists and neuroscientists will identify basic neural mechanisms that explain a wide range of empirical regularities. We believe that models with multiple interacting/competing neural mechanisms represent the most promising research frontier (Box 2). Such models are characterized by at least two classes of neural systems – patient systems that implement cool, analytic preferences and impatient systems that imple- ment hot, affective preferences.

Acknowledgements We would like to gratefully acknowledge discussions of these issues with Jonathan Cohen, Keith Ericson and Sam McClure, the input of our editor and three anonymous referees, and the support of the National Institute on Drug Abuse (R01 DA016434 and R01 DA20116 to G.S.B.) and the National Institute on Aging (P30 AG012810 and P01 AG005842. to D.L.).

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