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Losses loom larger than gains in the brain:

Neural loss aversion predicts behavioral loss aversion

Sabrina M. Tom

, Craig R. Fox

1,2

, Christopher Trepel

, & Russell A. Poldrack

1,3

1. Department of Psychology, UCLA

2. Anderson School of Management, UCLA

3. Brain Research Institute, UCLA

Abstract

One of the most robust phenomena in behavioral studies of decision making is

loss aversion, the tendency for people to exhibit greater sensitivity to losses than to

equivalent sized gains. We measured brain activity while individuals decided whether to

accept or reject gambles without feedback. This design isolated activity reflecting

decisions without contamination by the anticipation or experience of impending monetary

gains or losses. A broad neural network (including midbrain dopaminergic regions and

their limbic and cortical targets) showed increasing activity as the potential gain

increased, whereas an overlapping set of regions showed decreasing activity as the

potential loss increased. Thus, potential losses did not engage a separate set of emotional

brain systems, but were instead represented by decreasing activity in several gain-

sensitive areas. Moreover, these regions exhibited neural loss aversion as shown by their

greater sensitivity to losses than gains. Finally, individual differences in behavioral loss

aversion were predicted by a measure of neural loss aversion in several regions including

ventral striatum and prefrontal cortex. These results provide the first neuroscientific

evidence that risk aversion is driven by the brain’s greater sensitivity to losses than gains.

Main text

Many decisions, such as whether to invest in the stock market or whether to

accept a new job, involve the possibility of either gaining or losing relative to the status

quo. When faced with such decisions, most people are strikingly risk averse. For

instance, when deciding whether to accept gambles that offer a 50/50 chance of gaining

or losing money, people typically only accept gambles in which the amount that could be

gained is at least twice the amount that could be lost (e.g., a 50/50 chance to either gain

$100 or lose $50) (1). Prospect theory, the most successful behavioral model of decision

making under risk and uncertainty (1, 2), explains risk aversion for “mixed” (gain/loss)

gambles using the concept of loss aversion: People are more sensitive to the possibility of

losing objects or money than they are to the possibility of gaining the same objects or

amounts of money (1, 3, 4). Thus, people typically require a potential gain of at least

$100 to make up for exposure to a potential loss of $50 because the subjective impact of

losses is roughly twice that of gains.

Loss aversion also applies to decisions that involve no risk (5). For example, in

one study, students who were randomly assigned to receive a coffee mug (so that giving

up the mug would be perceived as a loss) subsequently set a median selling price of $7.12

for that mug, whereas students who were randomly assigned an opportunity to receive

either an identical mug or money (so that acquiring the mug would be perceived as a

gain) valued the mug at only $3.12 (6). Outside the laboratory, loss aversion has been

invoked to help explain a wide range of economic behaviors, such as why consumer

demand for products is more sensitive to price increases than decreases (7) and why

investors require a much higher average return to invest in stocks than bonds (8).

Moreover, loss aversion has been documented in the trading behavior of children as

young as age five (9) and capuchin monkeys (10), suggesting that the tendency for losses

to loom larger than gains may reflect a fundamental feature of how potential outcomes

are assessed by the primate brain.

The neural basis of loss aversion has not been directly investigated to date.

Previous neuroimaging studies of responses to monetary gains or losses have focused on

activity associated with the anticipation of immediate outcomes (“anticipated” utility)

(11, 12) or the actual experience of gaining or losing money (“experienced” utility) (11,

13, 14). However, to our knowledge, no previous studies have addressed the question of

which brain systems represent potential losses versus gains when a decision is being

made (“decision” utility). Behavioral researchers have shown that evaluations of

outcomes at these different points in time (i.e., “decision”, “anticipated”, and

“experienced”, utilities) often diverge in dramatic ways, which raises the possibility that

the corresponding brain systems involved may also differ (15). In the current study we

aimed to isolate activity associated with the evaluation of a gamble when choosing

whether or not to accept it (i.e., “decision” utility). This allowed us to test whether the

neural response during the evaluation of potential outcomes is similar to patterns

previously reported in studies of anticipated and experienced outcomes.

One important question is whether loss aversion reflects cognitive or emotional

processes. Decisions have been shown to vary systematically depending on whether

options are described in terms of gains from one reference point or losses from another

(16), demonstrating that cognitive representations are involved in loss aversion.

However, this cognitive account alone does not explain why losses should loom larger

than gains. Alternatively, it has been suggested that enhanced sensitivity to losses is

driven by negative emotional responses, such as fear or anxiety (e.g, 17). This notion

predicts that exposure to increasing potential losses should be associated with increased

activity in brain systems involved in negative emotions (such as amygdala or anterior

insula, cf., (18, 19)). Alternatively, loss aversion could reflect an asymmetric response to

losses versus gains within a single system that codes for the subjective value of the

potential gamble, such as ventromedial/orbital prefrontal cortex and ventral striatum (11,

20, 21).

Imaging decision utility. To examine the neural systems that process decision

utility, we collected functional magnetic resonance imaging (fMRI) data while

participants decided whether to accept or reject “mixed” gambles that offer a 50/50

chance of either gaining one amount of money or losing another amount (see Figure 1)

(22). To encourage participants to reflect on the subjective attractiveness of each gamble

rather than revert to a fixed decision rule, we asked that they indicate one of four

responses to each gamble (strongly accept, weakly accept, weakly reject, and strongly

reject). In order to estimate the neural response to gains and losses separately, the sizes

of the potential gain and loss were manipulated independently, with gains ranging from

$10 to $40 (in increments of $2) and losses ranging from $5 to $20 (in increments of $1).

These ranges were chosen because previous studies indicate that people are, on average,

roughly twice as sensitive to losses as to gains (1, 23); thus, we expected that for most

participants this range of gambles would elicit the entire range of attitudes, from strong

acceptance to indifference to strong rejection. All combinations of gains and losses were

presented (see Figure 1), with trials distributed over three fMRI scanning runs. During

scanning, participants evaluated each gamble without receiving feedback. In addition to

allowing for the isolation of decision utility from anticipated or experienced utility, it

prevented early trial outcomes from influencing a participant’s decision making on later

trials.

Sixteen participants were endowed with $30 at least one week prior to the

scanning session. The endowment was provided during a separate behavioral testing

session in order to minimize the potential increase in risk seeking behavior that can occur

when individuals feel that they are gambling with “house money” (24). Participants were

asked to bring $60 in cash to the scanning session, and told they could win up to an

additional $120 or lose up to $60. At the outset of the scanning session, participants were

told that one of their decisions from each of the three scanning runs would be selected at

random, and each selected gamble would be played for real money if they had accepted it

during scanning. Outcomes were summed across all “played” trials and ranged from -$12

to +$70, with an average total gamble outcome of $23 (leading to an average payout of

$53, including the endowment).

---- Figure 1 about here ----

Behavioral loss aversion. Behavioral sensitivity to gains and losses was assessed

by fitting a logistic regression to each participant’s acceptability judgments collected

during scanning, using the size of the gain and loss as independent variables. Based on

this analysis, a measure of loss aversion (λ) was computed as the ratio of the (absolute)

loss response to the gain response. The observed level of loss aversion (median λ = 1.93;

range: 0.99-6.75) is consistent with the fact, shown in Figure 1B, that participants were

roughly indifferent to gambles in which the potential gain was twice the potential loss

(i.e., gambles that fall along the main diagonal of the gain/loss matrix in Figure 1). This

finding also accords well with results reported by other researchers (1, 23).

Neural response to potential gains and losses. The imaging data were first

analyzed to identify regions whose activation correlated with the size of the potential gain

or loss, using parametric regressors (for details on model specification, see

Supplementary Materials and Methods). This analysis found a network of regions

responsive to the size of potential gains when evaluating gambles (averaging over levels

of loss) (see Figure 2). The gain-responsive network included regions previously shown

to be associated with the anticipation and receipt of monetary rewards, including dorsal

and ventral striatum, ventromedial prefrontal cortex (vmPFC), ventrolateral PFC (vlPFC),

anterior cingulate (ACC), orbitofrontal cortex (OFC), and dopaminergic midbrain regions

(see Supplementary Figure 2). There were no regions that showed decreasing activation

as gains increased.

---- Figures 2 and 3 about here ----

If loss aversion is driven by a negative affective response (e.g., fear, vigilance,

discomfort), then one would expect increasing activity in brain regions associated with

these emotions as the size of the potential loss increases. Contrary to this prediction, no

brain regions showed significantly increasing activation during evaluation of gambles as

the size of the potential loss increased (averaging over all levels of gain). Instead, a

network of regions including the striatum, vmPFC, ventral ACC, and medial OFC, most

of which also coded for gains, showed decreasing activity as the size of the potential loss

increased (see Figure 2 and Supplementary Figure 3). A conjunction analysis between

increasing activity for gains and decreasing activity for losses demonstrated joint

sensitivity to both gains and losses in a set of regions, including the dorsal and ventral

striatum and vmPFC (see Figure 3 and Supplementary Table 1).

In order to ensure that potential loss-related responses were not being obscured by

the overall positive expected value of the gambles, we compared activity evoked by the

worst possible gambles (gain $10-$16, loss $17-$20) and the best possible gambles (gain

$34-$40, loss $5-8). In a whole-brain analysis, there were no regions that showed

significantly more activity for the worst gambles compared to the best (corrected p > 0.4

in all voxels using randomization tests). Given the specific prediction regarding loss-

related activity in amygdala and insula based on prior studies of experienced utility and

risk aversion (11, 19), we performed further analyses focused on these areas. Even at a

very liberal uncorrected threshold of p < 0.01, there were no significant voxels in the

amygdala, and only two single unconnected voxels in the insula. By comparison, at the

same threshold there were large clusters of activation for the best versus the worst

gambles in the ventral striatum and vmPFC. These results strongly support the

conclusion that losses and gains are coded by the same mechanism rather than two

separate mechanisms. Moreover, this aggregate representation of decision utility appears

to be represented by the same neural circuitry that is engaged by experienced rewards

such as the receipt of money (11), the consumption of cocaine (25) or fruit juice (26), and

the viewing of attractive faces (27). These results are also consistent with previous

studies showing increased and decreased activity in striatum, respectively, for

experienced monetary gains and losses (11, 13).

Correlating behavioral and neural loss aversion. As noted above, there was

substantial variability in behavioral loss aversion (i.e., reluctance to gamble) across

individuals in the present study. We next investigated whether individual differences in

brain activity during decision making were related to these individual differences in

behavioral loss aversion, using whole-brain analyses to identify regions where the neural

response to gains or losses was correlated with behavioral loss aversion. Surprisingly,

greater loss aversion was associated with greater sensitivity to both not only losses but

also gains. For increasing gains, correlation with behavioral loss aversion was only

observed in the sensorimotor cortex and superior frontal cortex (see Supplementary

Figure 4). On the other hand, as potential losses increased, an extensive set of areas

showed a more rapidly decreasing response to mounting losses in individuals who were

more loss averse (see Supplementary Figure 5). Notably, these regions encompassed

many of the areas that showed an overall decrease in neural activity with increasing

potential loss. The association of decreased loss aversion with decreased neural responses

to losses and gains during decision making is consistent with the longstanding notion that

some forms of risk-taking may have their roots in sensation-seeking by individuals who

have a diminished physiological response to stimulation (28). It is also worth remarking

that previous work has shown that individuals with high levels of the “harm avoidance”

personality trait (who are presumably more loss averse) show greater activation of the

ventral striatum during risky decision making (cf., 29).

Initial examination of regions of interest in the striatum and vmPFC from the

gain/loss conjunction analysis (as shown in Figure 3) revealed that these regions exhibit a

pattern of “neural loss aversion”; that is, the (negative) slope of the decrease in activity to

increasing losses was steeper than the slope of the increase in activity for increasing gains

in a majority of participants (striatum: median loss/gain =1.88, loss > gain for 14/16

participants, sign test p = .004; vmPFC: median loss/gain = 1.82, loss > gain for 13/16

participants, p = .021). Therefore, whereas loss averse participants showed more neural

sensitivity to both potential gains and losses compared to less loss averse participants, it

appears that this neural sensitivity was disproportionately greater for losses than for

gains.

In order to more directly assess the relationship between behavioral loss aversion

and neural loss aversion, we defined a neural loss aversion measure as the difference

between the (negative) slope of the parametric loss responses and the slope of the

parametric gain responses at each voxel. Whole-brain analysis of the correlation between

neural and behavioral loss aversion (see Supplementary Figure 6 and Supplementary

Table 2) showed significant correlations in several regions, including bilateral lateral and

superior (pre-SMA) PFC, bilateral ventral striatum, right inferior parietal cortex, and

lateral occipital/cerebellum. Activation maps and scatterplots for a subset of these regions

are shown in Figure 4. These analyses show exceedingly strong correlations between

behavioral and neural loss aversion, and these associations are highly significant using

robust regression, which prevents undue influence of outliers.

---- Figure 4 about here ----

Loss aversion is mediated by sensitivity to losses. The foregoing analysis

demonstrates a direct relation between neural and behavioral loss aversion. We further

investigated whether this relationship was driven more by the neural processing of

potential gains or losses in each of the clusters identified in the foregoing analysis.

Whereas all of the regions had significant negative correlations between behavioral loss

aversion and the (negative) neural loss response, only one region showed a significant

relationship between behavioral loss aversion and the neural gain response (see

Supplementary Table 2). Thus, in agreement with the whole-brain analysis above,

participants who were less behaviorally loss averse (i.e., more risk seeking) were less

neurally sensitive to the size of the potential loss. In order to more directly characterize

the relative roles of gain and loss responses in behavioral loss aversion, the data from

each cluster were entered into a mediation analysis, which revealed that the effect of the

neural gain response on (log) behavioral λ was mediated by the neural loss response in

five of the eight clusters (including bilateral lateral PFC, pre-SMA, and ventral striatum).

Thus, differences in behavioral loss aversion across individuals seem to be driven

primarily by the degree to which those individuals show decreasing neural activity to

potential losses.

Conclusions. The present study replicates the common behavioral pattern of risk

aversion for mixed gambles that offer a 50/50 chance of gaining or losing money, and

shows for the first time that this pattern of behavior is directly tied to the brain’s relative

sensitivity to potential losses versus gains. These results provide striking evidence in

favor of one of the fundamental claims of prospect theory (1, 2), namely that the function

mapping money to subjective value is steeper for losses than gains. Importantly,

mediation analysis suggests that individual differences in risk attitudes (as measured by

the behavioral coefficient of loss aversion) are driven primarily by individual differences

in the degree to which activity in the brain’s reward circuitry is attenuated by potential

losses. Although the present study focused on loss aversion in the context of mixed

gambles, recent work has found that the coefficient of loss aversion (i.e., the ratio of

sensitivity to losses versus gains) is highly correlated across risky and riskless contexts

(30). Therefore, we surmise that a similar mechanism may contribute to other

manifestations of loss aversion.

Neural loss aversion was observed throughout, though not strictly limited to, the

targets of the mesolimbic and mesocortical dopamine (DA) systems (specifically, the

ventral striatum and orbital, medial, and lateral prefrontal cortices). Lesions to some of

these regions (particularly the core region of nucleus accumbens in the ventral striatum

and medial PFC) have been previously associated with increased risk aversion in animal

models (31), and disruption of the DA system can also result in shifts of risk attitudes in

humans (32). It is tempting to speculate that the individual differences in behavioral and

neural loss aversion observed in the present study may be related to naturally occurring

differences in dopamine function, perhaps due to genetic variability in dopamine

signaling or metabolism. This is an appealing hypothesis, though the relation between

genetic variation in the DA system and personality traits such as impulsivity and risk-

taking remains largely unknown (33), and it is possible that other neurotransmitter

systems (e.g., serotonin and noradrenaline) are also involved.

Previous studies have shown that anticipated or experienced losses give rise to

activation in regions that have been associated with negative emotions, such as amygdala

or anterior insula (11, 18, 19). In contrast, the present study demonstrates that, in the

context of decision making, potential losses are represented by decreasing activity in

regions that seem to code for subjective value rather than by increasing activity in regions

coding for negative emotions. This difference between present and prior results reinforces

the importance of distinguishing between experienced, anticipated, and decision utility in

economic theories of choice (15). It is possible that the engagement of the amygdala for

experienced losses reflects negative prediction error (11, 34) rather than negative value

per se, whereas the lack of immediate outcomes in the present study precludes the

computation of prediction errors.

The present results also illustrate how neuroimaging can be used to directly test

predictions stemming from behavioral theories, and thereby complement evidence

provided by behavioral studies and studies of lesion patients. Further, the diminished

neural sensitivity to losses among less loss averse (i.e., more risk seeking) individuals

may shed light on a number of neuropsychiatric and behavioral disorders, such as

substance abuse, pathological gambling, and antisocial personality disorder, that are

associated with increased risk-taking and impulsive behavior. The involvement of

dopamine in these disorders, and the overlap of our results with the dopamine system and

its targets, suggest that greater traction on these disorders could be obtained by

integrating the methods and models of behavioral economics with the tools of cognitive

neuroscience.

Acknowledgments

This work was supported by NSF DMI-0433693 (C. Fox & R. Poldrack, PIs), and by

NIH P20 RR020750 (R. Bilder, PI). The authors thank Adam Aron, Robert Bilder,

Michael Frank, Adriana Galvan, Marisa Geohegan, Eric Johnson, Matthew Lieberman,

Raj Raizada, and Elena Stover for helpful comments, Kristopher Preacher for assistance

with mediation analysis, and Ajay Satpute and Jessica Cohen for assistance in data

collection.

Figure Captions

Figure 1. A. An illustration of the event-related task design. During each trial, the

participant was presented for 3 seconds with a display showing the size of the potential

gain (in green) and loss (in red). After the acceptability response, a variable interval was

presented to allow for optimal deconvolution of fMRI responses to each trial (35).

Gambles were not resolved during scanning. The values of gain and loss for each trial

were sampled from the gain/loss matrix, as shown here for two example gambles; a

gamble from each cell in this 16×16 matrix was presented during scanning, but the data

were collapsed into a 4×4 matrix for analysis. B. Color-coded heatmap of probability of

gamble acceptance at each level of gain/loss (red: high willingness to accept the gamble,

blue: low willingness to accept the gamble). Participants’ willingness to accept gambles

increased as the size of the gain increased, and decreased as the size of the loss increased.

C. Color-coded heatmap of response times (red: slower response times, blue: faster

response times). Performance was slowest on trials that were closest to the point of

indifference between acceptance and rejection.

Figure 2. Whole-brain analysis of parametric responses to size of potential gain (left) or

loss (right). Statistical maps were projected onto an average cortical surface using

multifiducial mapping in CARET (36); coronal slices (y=+10) are included to show

ventral striatal activation. All maps are corrected for multiple comparisons at the whole-

brain level using cluster-based Gaussian random field correction (37) at p < .05.

Figure 3. Conjunction analysis results. Map in left panel shows regions with conjointly

significant positive gain response and negative loss response (p < .05, whole-brain

corrected, in each individual map). Heatmaps on right were created by averaging

parameter estimates versus baseline within each cluster in the conjunction map for each

of the 16 cells (of 16 gambles each) in the gain/loss matrix; color-coding reflects strength

of neural response for each condition, such that dark red represents the strongest

activation and dark blue represents the strongest deactivation.

Figure 4. Correspondence between neural and behavioral loss aversion. Left panel

presents statistical maps of the correlation between neural and behavioral loss aversion in

whole brain analysis (whole brain false discovery rate corrected at q < 0.05 [t > 3.7] and

cluster extent > 100 voxels) (see also Supplementary Figure 6 and Supplementary Table

2). Right panel presents scatterplots of behavioral versus neural loss aversion in several

clusters. Regression lines and p-values were computed using robust regression by

iteratively-reweighted least squares, to prevent influence of outliers. MNI coordinates

(X/Y/Z center of gravity in mm) for plotted clusters: B ventral striatum (3.6, 6.3, 3.9), L

inferior/middle frontal (-48.5, 24.7, 17.0), R inferior frontal (50.2, 14.3, 7.6), R inferior

parietal (47.9, -45.6, 49.4).

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+12

-14

+30

-7

response

interval

(3 secs)

variable

ISI

(mean 2.6 secs)

Gain/loss matrix

Potential gain

Potential loss

-5

-20

Time

Potential Loss ($)

Potential Gain ($)

1.3

1.4

1.5

1.6

Potential Loss ($)

Potential Gain ($)

0.2

0.4

0.6

0.8

1.0

0.0

Probability of acceptance

Response time (secs)

LH RH

2.3

Z-value

4.0-2.3-4.0

Potential gains Potential losses

Potential Gain ($)

Potential Loss ($)

10 20 30 40

Potential Gain ($)

Potential Loss ($)

10 20 30 40

−25

−20

−15

−10

−5

Striatum

Ventromedial prefrontal cortex

z = -12

y = 12

y = 40

B ventral striatum

L inferior/middle frontal

R inferior frontal

R inferior parietal

y=+10

z=+18

y=+16

z=+42

RRLL

−50 0 50 100 150

−0.5

0.5

1.5

Neural loss aversion (-βloss - βgain)

Behavioral loss aversion (ln(λ))

r = 0.85, p < 0.001

−50 0 50 100

−0.5

0.5

1.5

r = 0.90, p < 0.001

Neural loss aversion (-βloss - βgain)

Behavioral loss aversion (ln(λ))

0 50 100

−0.5

0.5

1.5

r = 0.86, p < 0.001

Neural loss aversion (-βloss - βgain)

Behavioral loss aversion (ln(λ))

−50 0 50 100 150

−0.5

0.5

1.5

r = 0.83, p < 0.001

Neural loss aversion (-βloss - βgain)

Behavioral loss aversion (ln(λ))

Supplementary materials for:

Losses loom larger than gains in the brain:

Neural loss aversion predicts behavioral loss aversion

Sabrina M. Tom

, Craig R. Fox

1,2

, Christopher Trepel

, & Russell A. Poldrack

1,3

1. Department of Psychology, UCLA

2. Anderson School of Management, UCLA

3. Brain Research Institute, UCLA

Supplementary Methods

Participants: Sixteen right-handed, healthy, English-speaking participants (nine females;

mean age, 22 ± 2.9 years) were recruited through advertisements posted on the UCLA

campus. All participants were free of neurological and psychiatric

history and gave

informed consent to participate according to a protocol approved by the University

California, Los Angeles Institutional Review Board.

Pre-testing and endowment session. Prior to fMRI scanning, participants were endowed

with a $30 cash payment for their participation in an initial pre-testing session. The

payment was made at least a week in advance of the scanning session in order to

minimize the potential risk-seeking that can occur in response to windfall gains (i.e.,

when one is “playing with the house money”) (cf. Thaler and Johnson, 1990). During

this session, they were presented with a questionnaire regarding gambling attitudes and

made a number of choices involving hypothetical gambles.

Scanning session. In order to convince participants that this was a real gambling

experiment in which they would be exposed to a real possibility of losing their own

money, we asked them to bring $60 in cash with them on the day of the scan and told

them that this was the maximum amount that they could possibly lose. In actuality, due to

the positive expected value of the gambles that participants evaluated, such a negative

outcome was highly unlikely, and in fact no participant lost more than $12 from these

gambles. The average amount won was $23. Ten participants won money (max gain=

$70) and three participants lost money (max loss= $12) from gambling. The remaining

three participants rejected all three trials that were selected, and thus received no

additional money. Due to the initial $30 endowment, all participants left the experiment

with a net gain, ranging from $18 – $100.

In the scanner, participants were presented with 3 runs of 85-86 trials, each of which

proposed a mixed gamble entailing a 50/50 chance of gaining one amount of money or

losing another amount. Possible gains ranged from $10-$40 (in $2 increments) and

possible losses ranged from $5-$20 (in $1 increments). All 256 possible combinations of

gains and losses were presented across the three runs. Participants were asked to evaluate

whether or not they would like to play each of the gambles presented to them. They were

told that one trial from each of the runs would be selected at random, and if they had

accepted that gamble during scanning, the outcome would be decided with a coin toss; if

they had rejected the gamble, then the gamble would not be played.

In order to encourage participants to reflect on the subjective attractiveness of each

gamble rather than revert to a fixed decision rule (e.g., accept only if gain ≥ 2 × loss), we

asked them to indicate one of four responses to each gamble (strongly accept, weakly

accept, weakly reject, and strongly reject) using a four-button response box. We also

instructed them to respond as quickly as possible within the 3-second trial duration.

Stimulus presentation and timing of all stimuli

and response events were achieved using

Matlab and the Psychtoolbox

(www.psychtoolbox.org) on an Apple PowerBook running

Mac OS

9 (Apple Computers, Cupertino, CA). Visual stimuli were presented using MRI-

compatible goggles (Resonance Technologies, Van Nuys, CA). The timing and order of

stimulus presentatation was optimized for estimation efficiency using optseq2

(http://surfer.nmr.mgh.harvard.edu/optseq/) (Dale, 1999).

Behavioral analysis. Statistical analyses of behavioral data were performed using the R

statistical package (http://www.r-project.org). Logistic regression was performed on the

behavioral data after collapsing strong/weak responses into accept and reject categories,

with the size of the potential gain and loss as independent variables and

acceptance/rejection as the dependent variable. This analysis was performed separately

for each participant, collapsing over scanning runs. Behavioral loss aversion (λ) was

computed as:

= -

loss

gain

where

loss

and

gain

are the unstandardized regression coefficients for the loss and gain

variables, respectively. This parameter is similar to the

parameter in prospect theory

(Tversky and Kahneman, 1992) but makes the common simplifying assumptions of a

linear rather than curvilinear value function, and identical decision weights for a 0.5

probability to gain or lose money.

MRI data acquisition. Imaging was performed using a 3T Siemens AG (Erlangen,

Germany)

Allegra MRI scanner at the UCLA Ahmanson-Lovelace Brain Mapping

Center. We acquired 240 functional

T2*-weighted echoplanar images (EPI) [slice

thickness, 4 mm;

34 slices; repetition time (TR), 2 s; echo time (TE), 30 ms;

flip angle,

90°; matrix, 64 x 64; field of view (FOV), 200 mm]. Two additional volumes were

discarded at the beginning of each run to allow for T1 equilibrium effects.

In addition, a

T2-weighted matched-bandwidth high-resolution

anatomical scan (same slice prescription

as EPI) and magnetization-prepared

rapid-acquisition gradient echo (MPRAGE) were

acquired for each

subject for registration purposes (TR, 2.3; TE, 2.1; FOV, 256; matrix,

192 x 192; sagittal

plane; slice thickness, 1 mm; 160 slices). The orientation for matched-

bandwidth and EPI

scans was oblique axial so as to maximize full brain

coverage and to

optimize signal from ventromedial prefrontal regions.

Imaging preprocessing and registration. Initial analysis was performed using the FSL

toolbox from the Oxford Centre for

fMRI of the Brain (www.fmrib.ox.ac.uk/fsl). The

image timecourse was first realigned to compensate for small head movements

(Jenkinson et al., 2002). Translational movement parameters

never exceeded 1 voxel

(3.125 mm inplane, 4 mm throughplane) in any direction for any subject or session.

cases where translational motion of more than 1 mm was detected in any direction,

images were denoised using MELODIC independent components

analysis within FSL

(this was performed for 22 runs in 9 participants). Motion-related components were

identified manually using a set of heuristics (Poldrack, Aron, & Tom, 2005, Human Brain

Mapping Abstracts), and the data were then reconstituted after removing the motion-

related components. Data were spatially smoothed using a 5

mm full-width-half-

maximum Gaussian kernel. Registration was conducted through a 3-step procedure,

whereby EPI images were first registered to the matched-bandwidth

high-resolution

structural image, then to the MPRAGE structural image, and

finally into standard

[Montreal Neurological Institute (MNI)]

space (MNI avg152 template), using 12-

parameter affine transformations (Jenkinson and Smith, 2001). Statistical analyses were

performed in native space, with the statistical maps normalized to standard space prior to

higher-level analysis.

Statistical analysis. Whole-brain statistical analysis was performed using a multi-stage

approach to implement a mixed-effects model treating participants as a random effect.

Statistical modeling was first performed separately for each imaging run. Regressors of

interest were created by convolving a delta function representing trial onset times with a

canonical (double-gamma) hemodynamic response function.

For the primary whole-brain analyses, two modeling approaches were used. In the first

(referred to as the “parametric analysis”), all trials were modeled using a single condition

(i.e., overall task-related activation; see Supplementary Figure 1), and three additional

orthogonal parametric regressors were included representing: (a) the size of the potential

gain (see Supplementary Figure 2), (b) the size of the potential loss (see Supplementary

Figure 3), and (c) the Euclidean distance of the gain/loss combination from the diagonal

of the gamble matrix (i.e., distance from indifference assuming lambda=2 and a linear

value function). This latter variable was included because of behavioral evidence

suggesting greater difficulty making a decision for trials in which participants had the

weakest preference (See Figure 1C in main text), however, these results are not discussed

in the present paper; a fuller account of this latter analysis will be presented elsewhere.

In the second approach (referred to as the “matrix analysis”), the gain/loss matrix was

collapsed from 16 × 16 into a 4 × 4 matrix (see Figure 1 in the main text), and trials from

each of the 16 resulting cells were modeled as separate conditions. This allowed separate

estimation of the evoked response for each of these cells at each voxel; the primary use of

the matrix analysis was to create the heatmaps of activation presented in Figure 2, and to

perform the comparison between best versus worst gambles described in the main text.

For all analyses, time-series statistical analysis was carried out using FILM (FMRIB's

Improved Linear Model) with local autocorrelation correction (Woolrich et al., 2001)

after highpass temporal filtering (Gaussian-weighted LSF straight line fitting, with

sigma=33.0s).

For each of these lower-level analyses, a higher-level analysis was performed that

combined all sessions for each participant using the FMRIB Local Analysis of Mixed

Effects (FLAME) module in FSL (Beckmann et al., 2003; Woolrich et al., 2004), and a

one-sample t-test was performed at each voxel for each contrast of interest. Z

(Gaussianised T) statistic images were thresholded using clusters determined by Z > 2.3

and a (whole-brain corrected) cluster significance threshold of p < .05 using the theory of

Gaussian Random Fields (Worsley et al., 1992). For the comparison between best versus

worst gamble conditions, control for multiple comparisions was implemented using

randomization tests (Nichols and Holmes, 2002) with the FSL randomize tool in order to

allow correction limited to small regions of interest.

For whole-brain analyses of correlations between neural activity and behavioral

parameters across participants (see Supplementary Figures 4-6), voxelwise robust

regression was used to in order to reduce the influence of outliers on the analysis (cf.

Wager et al., 2005). Because Gaussian random field results were not available for these

analyses, whole-brain correction for multiple comparisons was implemented by

controlling the false discovery rate (FDR) at q < .05 (Genovese et al., 2002) along with a

cluster extent threshold of 100 voxels. Because FDR is adaptive, the t-threshold that

controls FDR at q < 0.05 varies between analyses.

Renderings. All statistical maps are presented at a whole-brain corrected significance

level of p < .05, either using GRFT or FDR corrections, and are overlaid on a group mean

structural image. Cortical renderings were performed using CARET software

(http://brainmap.wustl.edu). Group statistical maps were mapped into to the Probabilistic

Average Landmark and Surface-based (PALS) atlas using the multifiducial mapping

technique described by Van Essen (2005). For the purposes of presentation, data are

overlaid on the average atlas surface.

Conjunction analysis. Conjunction analysis for gains and losses (see Figure 2 in the main

text and Supplementary Table 1) was performed by multiplying binarized versions of the

thresholded statistical maps obtained for the parametric gain and loss analyses. Because

each of these maps is itself whole-brain corrected at p < .05, this conjunction tests against

the conjunction null at p < .05 (Nichols et al., 2005).

Computation of neural loss aversion. Because the neural gain and loss coefficients were

broadly distributed and spanned zero, it was not possible to compute a stable loss

aversion coefficient in the same way used for the behavioral data (i.e., the ratio of loss to

gain responses). Instead, we computed neural loss aversion at every voxel by subtracting

the slope of the gain response from the (negative) slope of the loss response. Whole-

brain analyses using the resulting images were performed using robust regression with

false discovery rate correction (see Figure 6 and Table 2).

Region-of-interest (ROI) analyses. For the purposes of exploratory analysis, ROIs were

created based on the significant clusters of activation in the voxelwise analyses. Using

these regions of interest, ROI analyses were performed by extracting parameter estimates

(betas) from the fitted model and averaging across all voxels in the cluster for each

subject. For analyses of correlations between behavioral and ROI data, robust regression

was used to minimize the impact of outliers in the behavioral data, using iteratively re-

weighted least squares implemented in the robustfit command in the MATLAB Statistics

Toolbox. Reported r-values reflect (non-robust) Pearson product-moment correlation

values, whereas the reported p-values and regression lines are based on the robust

regression results.

Mediation analysis. Simple mediation analysis was performed on a data from each of the

significant clusters in the neural loss aversion analysis (listed in Supplementary Table 2)

as described by Preacher and Hayes (2004). Because of the small sample size, 95% bias-

corrected and accelerated confidence intervals were generated for the indirect effect using

bootstrapping with the R software package.

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Supplementary Table 1. Locations of significant activation in conjunction analysis for

potential loss and gain effects (Z > 2.3, whole-brain corrected p<.05 in each map, extent

in conjunction map ≥ 8 voxels). MNI coordinates denote the 3-dimensional center of

gravity of each cluster. Mean Z statistics were created by averaging statistical maps over

all voxels in cluster for parametric gain and loss analyses.

Location

Cluster

extent

(voxels)

MNI X

(mm)

MNI Y

(mm)

MNI Z

(mm)

Mean Z

statistic

(gains)

Mean Z

statistic

(losses)

B striatum (nuc. Accubens,

caudate), thalamus

1639

-0.4

6.1

-1.5

2.97

2.89

B VMPFC/OFC

1001

-6.0

39.3

-8.4

2.69

2.83

L frontal pole

154

-15.9

66.7

7.4

2.77

2.87

L middle frontal gyrus

116

-20.4

30.3

49.8

2.62

2.78

R middle/superior frontal gyrus

23.2

36.2

28.0

2.66

2.71

R frontal pole

7.0

63.9

18.1

2.58

2.65

R posterior cingulate

8.5

-38.3

32.5

2.66

R midbrain

10.2

-13.8

-16.0

2.59

2.68

Supplementary Table 2. Locations of significant relation between ln(λ) and neural loss

aversion (NLA) using robust regression (whole brain false discovery rate corrected at q <

0.05 [t > 3.7] and cluster extent > 100 voxels). Reported Pearson r-values were computed

between ln(λ) and parametric gain and loss responses and NLA averaged across all

voxels in each cluster; p-values for these correlations were computed using robust

regression. Confidence intervals (CI) for indirect effect were estimated using the bias-

corrected and accelerated bootstrap method described by Preacher & Hayes (2004). For

all columns, asterisk denotes significant effects at p < 0.05.

Location

Voxels

MNI

r(ln(l),

gain)

r(ln(l),

loss)

r (ln(l),

NLA)

Indirect effect CI

L inferior/middle

frontal

284

-48.5

24.7

17.0

0.11

-0.82*

0.9*

( 0.0013, 0.0308 ) *

R inferior/middle

frontal

175

47.5

22.4

26.0

0.28

-0.81*

0.88*

( 0.0102, 0.0342 ) *

L inferior frontal

(opercular)/

anterior insula

104

-39.5

19.8

-8.2

0.44

-0.82*

0.87*

( 0.0070, 0.0213 )*

R inferior frontal

(opercular)

122

50.2

14.3

7.6

0.36

-0.91*

0.86*

(-0.0122, 0.0218 )

B Ventral striatum

332

3.6

6.3

3.9

0.38

-0.85*

0.85*

( 0.0071, 0.0279 ) *

R inferior parietal

358

47.9

-45.6

49.4

0.29

-0.87*

0.83*

(-0.0011, 0.0201 )

B pre-SMA

110

-0.2

22.0

48.1

0.50*

-0.83*

0.81*

( 0.0011, 0.0170 )*

L lateral occipital/

cerebellum

963

-29.4

-74.3

-25.5

0.17

-0.55*

0.46*

(-0.0262, 0.0211 )

Supplementary Figure 1. Regions with significant activation for task vs. baseline (Z >

2.3, whole-brain cluster-corrected at p < .05 using GRFT). Red-yellow scale reflects

positive activation, blue-white scale reflects negative activation.

Supplementary Figure 2. Regions with significant parametric increase in fMRI signal to

increasing potential gains (Z > 2.3, whole-brain cluster-corrected at p < .05 using GRFT).

No regions showed decreasing activity for increasing potential gains.

Supplementary Figure 3. Regions with significant parametric decrease to increasing

potential losses (Z > 2.3, whole-brain cluster-corrected at p < .05 using GRFT). No

regions showed increasing activity for increasing potential losses.

Supplementary Figure 4. Regions with significant positive correlation between the

parametric response to potential gains and behavioral loss aversion (ln(λ)) across

participants (whole brain false discovery rate corrected at q < 0.05 [t > 4.3] and cluster

extent > 100 voxels). No regions showed significant negative correlation.

Supplementary Figure 5. Regions with significant positive correlation between the

parametric response to potential losses and behavioral loss aversion (ln(λ)) across

participants (whole brain false discovery rate corrected at q < 0.05 [t > 3.1] and cluster

extent > 100 voxels). No regions showed significant positive correlation.

Supplementary Figure 6. Regions showing significant positive correlation between ln(λ)

and neural loss aversion (difference between slopes of neural loss and gain responses)

(whole brain false discovery rate corrected at q < 0.05 [t > 3.7] and cluster extent > 100

voxels). No regions showed significant negative correlation.