of 24
Letters
https://doi.org/10.1038/s41562-018-0440-2
Choice overload reduces neural signatures of
choice set value in dorsal striatum and anterior
cingulate cortex
Elena Reutskaja
1,8
, Axel Lindner
2,3,4,8
*, Rosemarie Nagel
5
, Richard A. Andersen
4,6
and Colin F. Camerer
7
1
Marketing Department, IESE Business School, Barcelona, Spain.
2
Department of Psychiatry and Psychotherapy, University Hospital Tübingen, Tübingen,
Germany.
3
Department of Cognitive Neurology, Hertie-Institute for Clinical Brain Research, Tübingen, Germany.
4
Division of Biology and Biological
Engineering, California Institute of Technology, Pasadena, CA, USA.
5
Institució Catalana de Recerca i Estudis Avançats, Barcelona Graduate School of
Economics, Department of Economics and Business, Universitat Pompeu Fabra, Barcelona, Spain.
6
The Tianqiao and Chrissy Chen Brain-Machine Interface
Center, California Institute of Technology, Pasadena, CA, USA.
7
Division of the Humanities and Social Sciences and Computation and Neural Systems,
California Institute of Technology, Pasadena, CA, USA.
8
These authors contributed equally: Elena Reutskaja, Axel Lindner.
*e-mail: a.lindner@medizin.uni-tuebingen.de
SUPPLEMENTARY INFORMATION
In the format provided by the authors and unedited.
NA
tuRE HumAN BEHA
viouR
|
www.nature.com/nathumbehav
Supplementary Discussion
In this supplementary discussion we first consider alternative task designs before we
discuss
possible confounding variables that could have influenced our fMRI results.
In this study we used post
-
choice self
-
reported subjective ratings of the subjects
to determine the value of the set (see
m
ain manuscript). The exact question we asked
was thereby
borrowed from the seminal paper on choice
overload
1
. We relied on post
-
choice measure
s
because the integrated value of a set (i.e., the related benefits and
costs of choosing between items of a given set)
might only become
apparent
during the
ultimate pro
cess of choosing from the set
.
We also opted for this measure because
many studies in domains similar to ours have shown that subjective liking ratings of
individual
goods are highly correlated with inferred utility or monetary value (measured
by incentive
-
compatible Becker
-
DeGroot
-
Marschak procedures;
e.g.
see
2
,
which shows
parallel results from predicting ratings and inferred utility rankings
). Another study
showed
strong correlation between liking ratings and BDM
bids
3
. See
also
4
which found
strong correlations between ratings of health
and taste, and choices of foods
.
We,
however, recognize that there are other methods to elicit the estimation of the set value
and
each method has its own merit
s and drawbacks. One possible way
to determine set
value
in future research is to have
subjects pay in
an
incentivize
-
compatible
way to be
allowed to make choices from that set
,
or
to make
subjects select which of the three set
sizes
they prefer to choose from
.
As we already discuss in the main manuscript, it would be especially interesting
to know whether neural activity in dorsal striatum and ACC might
also
account for inter
-
individual differences in perceived set value. An alternative way to exhibit such an
interrelation would be to correlate individual amount ratings with fMRI activity. Moreover,
such approach could also be considered as an alternative mean
s to exhibit areas
representing set
-
value (instead of modelling the inverted
-
u shaped profile of set
-
value of
the overall subject group by a quadratic predictor).
While
our study
was not designed
for
such an analysis, we still have implemented it as per re
viewer request
. But it did not
show
any correlat
ions
that survive our statistical threshold (
a
second
-
level
regression
analysis was performed on
the
beta estimates of model 2 for the pooled choice
conditions of the exp
osure period and on
individual subject estimates of choice set
value;
P
<
0.05 FDR
-
corrected for multiple comparisons
).
This outcome is not particularly surprising as neither our design nor our data set
were created to perform such analysis on the individual level. We did no
t sample subjects’
set
-
value curves in a way that could estimate inter
-
individual differences. Before and during
the scanning, the subjects were not told the number of different choice sets or the number
of items included. This information was only provide
d as they learned, and was explicitly
told to them afterwards. Hence, subjects would have to provide post
-
hoc ratings about
three choice sets (small, medium, and large) which they did not necessarily notice during
the experiment.
In fact, we do have some e
vidence about what subjects noticed during the
scanning. Before telling subjects about the different choice sets they had just seen, they
guessed how many choice set sizes were used and how large they were. The mean
estimate for the number of different cho
ice set sizes was 5.0 (standard deviation
SD
=3.2).
The average estimate of the number of images in the
smallest and
largest set was 6.4
(
SD
=4.0) and 24.5 (
SD
=8.7)
, respectively
. The latter set size estimates are accurate on
average but highly variable
across subjects. It is likely that even after knowing the actual
sizes, their subjective estimates had some influence on their ratings and made them noisy
.
Having noisier individual estimates could simply explain the null result of this alternative
analysi
s.
One
future
way
c
ould be to design
an
experiment
with a larger range of choice
set sizes, in which
subjects are asked
,
after each choice
,
how they felt about
the
particular
choice set encountered
before
.
We
did not implement such a design
for two
reasons
. First
, we did not intend to study inter
-
individual differences
. This is a pioneering
exploratory study of this complicated phenomenon and estimating inter
-
individual
differences is too challenging at this point (and also requires a larger sample size of
people if one plans, for example, to classify people into clusters,
as would be sensible).
A
group analysis
ignoring individual differences has often been a good starting point in
decision neuroscience and was sufficient to get information about
our
research
questions. Second,
the
measurement
time necessary to perform an
fMRI
experiment
like the one described before
asking
about set liking in several tr
i
a
ls
--
would be way
too long to comply with our
recommended
institutional
scanning time
guidelines (
a
nd
people get tired).
Finally,
we did not want to bias
our
subjects
responses: if subjects had
to answer such questions after each choice, they would
alter the
focus
of
their attention
also
on
the attributes under investigation
, which
,
in turn
,
could chan
ge their behavio
u
r
and our fMRI results
.
Instead, w
e
here particularly tried
to
avoid such biases by
ask
ing
subjects about the
ir perceived
value of the sets only
after
the
fMRI
experiment.
Next, we will discuss why t
he inverted
-
u shaped activity profile, su
pposedly
representing choice set value, is unlikely to be explained by
a number of
potential
confounding factors
:
First
, it seems unlikely that this pattern emerged simply because subjects would
have “given up” earlier in case of the largest choice sets. This is because the number of
saccades steadily increased up to the largest choice set (
Fig
.
3b
) and irrespective of the
choice condition (NF vs. CF).
This is likewise documented by the
distribution
of
large,
re
-
fixating saccades
across
the exposure period (
Supplementary
Fig
.
2
).
If subjects would
have given up early, we would have expected to observe a correlated drop in s
accade
frequency for the largest choice set. This was not the case. Moreover, if subjects had
aborted the decision process at an earlier point in time for the larger sets, the time
-
courses of fMRI
-
activity would have reflected that drop (
Fig
.
4c
). In fact,
visual
inspection of
the time
-
courses of fMRI
-
activity do
es
not
reveal
any obvious earlier drop
in exposure
-
related fMRI activity for the largest choice sets. In these and in all other
trials subjects seemingly “worked” on the choice sets until
the end of the exposure
period and only then the fMRI
-
signal dropped rapidly and simultaneously for all choice
set sizes (
Fig
.
4c
).
Second
, the inverted u
-
shaped pattern also cannot be directly explained by
decision confidence: confidence should steadily
decrease with S as the both the
difference in liking between the best and the second
-
best item in a set and the variance
in the liking of individual choice options decreased
numerically
with S
in both free choice
conditions
(
Supplementary
Fig
.
1d and 1b,
respectively
) while
, as
visual inspection of
Supplementary Fig
.
1c suggests,
the rating of the best image within
CF and NF
set
s
was
rather
constant. Note that this theoretical consideration thereby assumes that decision
confidence is separable from choice
satisfaction, as is captured by our amount rating.
The assumed interrelation between set size and decision confidence is also suggested
by our measures of choice performance, which likewise decreased with set size
(
Fig
.
3d
,
e
).
Finally
,
we’d like to discu
ss whether the inverted u
-
shaped pattern could arise
from
eye movements or
visual search.
In fact,
the number of saccades rises with choice
-
set size
(
Fig
.
3b
) while, at the same time, saccade amplitudes get smaller (
Fig
.
3c
).
Could it be that the interplay of increasing saccade frequency and decreasing saccade
size (and a growing ease to find the next saccade target) explain the inverted u
-
shaped
activity profile?
For the following
reasons,
we do think that such a scenario i
s rather
unlikely: (i)
N
either the
right
ACC nor the
left dorsal
striatum
did
exhibit a correlation of
activity with the frequency of saccades across subjects (
Supplementary t
able 1). If the
sheer number of saccades would contribute to the observed signal
pattern, at least a
hint for such interrelation should be present.
(ii)
It is also questionable whether smaller
saccade amplitudes
per se
would lead to significant signal reductions for larger sets. In
fact, saccade amplitude
is chiefly topologically coded
in saccade
-
related areas above
the
brainstem level
, and this coding scheme results in saccade
-
related
fMRI
-
signals
,
which
are hardly influenced by saccade amplitude but
which
do
almost exclusively
reflect
saccade
frequency
5
.
Accordingly, we’d rather expect a linear signal increase in
saccade
-
related areas and, in fact, several of the
linear areas
that were revealed by our
study are also engaged in the control of saccadic eye movements.
(iii)
Finally, it is
questionable wheth
er the
ease of
the
visual search problem
, i.e. finding the next
saccade target, truly
grows with
the
number of options
available in a choice set
. To
come up wi
th a decision a subject has to search
all options (and not simply saccade
to
the nearest target
) and this search space is increasing with choice set size. Accordingly,
reaction times do increase for larger sets in visual search while performance decreases.
This effect is
also
referred to as “set
-
size effect” in visual search. Moreover, brain activit
y
typically increases (rather than decreases) with larger sets in visual
search
6
.
F
uture
research
should
include a ‘neutral’ control condition that mimics visual search and
saccadic performance in our experimental conditions. Yet, i
n conclusion, we do thin
k
that saccades and visual search are
at least
highly
unlikely to explain the observed
pattern of results
in our
current
study
.
The observed shift from a quadratic to a linear response profile in
right
ACC and
left
dorsal striatum is also clearly consiste
nt with the predictions of our simple model on
choice set value (
Fig
.
1a; compare green vs. blue curve, respectively). It is important to
stress, however, that there are multiple factors that could give rise to the observed
difference in activity between
CF and NF. This difference is consistent with a set
-
value
interpretation. It could, however, also refer to differences in decision difficulty, in decision
confidence, or in the value of the chosen item across conditions (
Fig
.
3d
). Yet, the latter
interpret
ation is unlikely, because hardly any of the ROIs associated with set value
showed a dependency of their (residual) activity on the value of the chosen item
at least
during the exposure stage
(
Fig
.
4e
).
Also,
the factor decision difficulty seems ineligible
as fMRI activity was greater in CF than in NF while difficulty should lead to the exact
opposite, namely higher activity in NF than in CF. Ultimately, decision confidence could
likewise
besides choice set value
-
explain the difference between CF and NF
. As was
pointed out above, however, decision confidence seems unable to explain our primary
marker of choice set
-
value
namely the inverted
-
u shaped activity profile as a function
of set size S.
In summary, we are convinced that explaining the overall p
attern of activity in
right
ACC and the
left
dorsal striatum within the framework of choice set
-
value is the
most parsimonious interpretation of our data.
Supplementary Methods
Sample Size
Sample size was guided by our previous behavioural study on
choice overload
7
and built
on a power
-
analysis (alpha=0.05, power=0.8) performed on amount rating data obtained
on a scale equivalent to ours (Fig
.
1c). Namely, it builds on the results from a previously
published study which found that satisfaction from c
hoice followed an inverted
-
U shape
pattern with the highest satisfaction experienced by subjects when choosing from
intermediate
-
sized sets (vs larger or smaller sets
7
). In that study 120 subjects were
choosing a gift box to pack a present for their friend
s from different sized sets of boxes
containing either 5, 10, 15 or 30 alternatives. Specifically, in our power
-
analysis we
considered the rating difference between the small choice set [5 items, M = 4.17, SD =
1.80, N=30] and an intermediate choice set [1
0 items = twice the size of the small set, M
= 5.53, SD = 1.57, N=30] and the difference between an intermediate choice set [15
items, M = 4.90, SD = 2.25, N=30] and the large choice set [30 items = twice the size of
the intermediate set, M = 6.77, SD = 1.
87, N=30] (results from
7
). Note that the effective
sensitivity of the current study should be even higher due to our within
-
subject design
and due to task repetitions (as compared to the between
-
subjects design and the lack of
repetitions
7
). Both our curre
nt study and study
7
used visual stimuli. However, as study
7
suggests, the definition of “optimal”, “too small”, and “too large” choice set should
depend on the costs and benefits of each choice setting and is different in varying
environments.
Task 1
-
L
iking Rating.
Participants were shown 312 landscape images one by one on
a computer screen. All the images were obtained from www.terragal
l
e
ria.com with the
permission
from the website
. Subjects stated how much they wanted to have each of
those pictures printe
d on the product of their choice by setting a bar on a 11
-
point scale
(with “0” stating “I would not like at all to have the picture on my selected item” and “10”
stating “I would like to have the picture on my selected item very much.”; step size: 0.2)
,
a
procedure adopted from
8
and adjusted to the stimuli of our study.
Landscape images
were assigned to 6 categories: mountains, lakes, dunes, waterfalls, forests and
beaches. Each category included 52 pictures. All 312 images were presented in a
random order within a round and subjects had to rate each image twice in two
s
uccessive rounds. The final rating of each image was determined by the average rating
calculated across the two rounds. Subjects had stable preferences for a particular
picture and rated the same image similarly in both rounds: the individual linear
correl
ation of ratings of the first and second round revealed high correlation coefficients,
ranging from 0.37 [CI 95%: 0.270, 0.462] to 0.84 [0.804, 0.870] (0.6 on average).
Moreover, liking ratings did not differ significantly in the first and second round (2
-
way
repeated measures ANOVA with the factor ‘round’ [1 vs. 2] and the factor ‘image’ [1
-
312]; round: F(1,18)=
2.726, p=0.116;
η
2
p [
CI
95%
]=
0.132 [0.000, 0.357]; image:
F(311,5598)=
3.504, p<0.001,
η
2
p [
CI
95%
]=
0.163 [0.024, 0.025]; interaction:
F(311,5598)
=
0.962, p=0.673,
η
2
p [
CI
95%
]=
0.051 [0.000, 0.006]).
Task 2
fMRI Experiment/Choice Task.
During the choice task of the experiment
participants examined the sets of images and decided which of the landscape pictures
they wanted to have printed on the pr
oduct of their choice. The choice sets differed on
two dimensions: the number of alternatives and the availability of a clear favourite item
in the set. Choice sets included 6, 12, or 24 landscape images of the same category
(Fig
.
2b). In 2/3 of the random
ly interleaved trials subjects could select a photograph by
themselves (“free” choice trials, CF and NF). In the remaining 1/3 of trials, a landscape
picture from a particular set was selected for the participant by the computer (“forced”
choice trials, FO
). Within a FO trial the computer would always select a highly valued
picture, ranked by the subject in task 1 either as 1st or 2nd best. All forced choice sets
were sets without a clear favourite picture, and were therefore similar to NF sets, without
cle
ar favourite item.
To create CF, NF and FO sets we used the subjective ratings of images made by
participants in the liking rating task of the experiment. Choice sets were always
composed of images from the same landscape category. Specifically, to create
within
-
category choice sets with 6, 12 and 24 items, respectively, we first selected images from
the 42 lower
-
rated pictures within each of our six landscape categories (each category
had a total of 52 images). Then we assigned the resulting sets to the CF
, NF and FO
condition in a way that should minimize differences in the overall mean and variance of
ratings across all NF and FO sets (and the prototypes for the final CF sets) (see
Supplementary Fig
s
1a
and
1
b). In CF sets we additionally replaced the
best
-
rated
image out of the sub
-
selection of the 42 lower
-
rated images of a respective category
with either the best or the 2
nd
-
best rated image from the overall sample of 52 pictures
within that category. These replacements guaranteed that maximal image r
ating
(Supplementary Fig
.
1c) as well as the difference in rating between the first and second
best image (Supplementary Fig
.
1d) were numerically larger in CF than in the NF and
FO sets. No choice set included identical alternatives. Moreover, within each
experimental run an item was shown once, only, and, across sessions, choice sets
would always comprise different items.
Visual stimuli were back
-
projected onto a translucent screen (22° x 16° visual
angle) by using a video projector (800x600 pixels, 60 H
z). Subjects viewed the visual
stimuli via a mirror that was mounted on the head coil of the MRI scanner (viewing
distance 1150mm). Stimuli were generated on a windows PC using “Cogent Graphics”
developed by John Romaya at the LON at the Wellcome Departmen
t of Imaging
Neuroscience and in combination with
Matlab 7.5
.
Choice sets were presented on an
otherwise black screen with a central, white fixation cross (Fig
.
2b). Items of the choice
sets could be randomly placed at 15 possible positions to each side of
the fixation cross.
On both sides these positions were arranged in five rows and three columns. Depending
on the condition, a certain number of landscape images were placed at these positions
(with an equal number placed to the right and to the left sides
of the fixation cross).
Scrambled images were presented at the remaining locations in order to diminish global
visual differences between sets of different size (luminance, colour, image density, etc.).
Individual image size was 3.5° x 2.6° visual angle.
Each trial in the choice task consisted of three main stages: an exposure stage
(10s+0.5s mask), a delay stage (13
-
14s), and a response stage (3s, Fig
.
2c). During the
latter stage, subjects had to indicate the chosen item using the thumb of their right ha
nd
on an MRI
-
compatible button
-
box. In contrast to the free choice conditions CF and NF,
in FO, subjects had to select an object that was chosen by the computer and highlighted
by a yellow frame during the response stage. To distinguish the FO from free ch
oice
tr
i
a
ls, the forced choice trials were cued during the exposure stage by brackets around
the fixation cross (“[+]” instead of “+”; Fig
.
2c). The response time in the exposure
phase of all conditions was very short (3 sec) in order to prevent subjects
from delaying
their decision in CF and NF trials to the response stage. This was confirmed by our
analysis of reaction times. Before each trial, subjects had to maintain fixation on a
central white cross, presented on an otherwise dark background (duration
: 13 s). This
initial fixation period served as a baseline for our fMRI analysis.
The choice task of the experiment consisted of four runs with short breaks
between runs (< 5 min). Each participant went through 72 trials (3 conditions x 3 set
sizes x 8 rep
etitions) with 18 trials in each run (3 conditions x 3 set sizes x 2 repetitions).
All trials were presented to each participant in randomized order. To familiarize
themselves with the task, subjects went through a training run (18 trials) in which we
pres
ented only choice sets that were not used in the actual experiment.
Task 3
Questionnaire task.
After scanning, participants filled in a paper
-
based
questionnaire. Participants reported whether they felt that each choice set size
contained the “right” amount of alternatives (on a 9
-
point scale centred at 5 “Yes, I had
just the right amount of choice
options”, with lower numbers meaning too few options
and higher numbers meaning too many; also see Fig
.
1c)
, the measure borrowed from
1
.
Based on this estimate we derived the normalized set value as
1
-
| 5
Average Amount Rating | / 4
In other words, a
set size is perceived as optimal if this index is 1 while a set size is
perceived as least optimal if this index is 0 (Figure 1d). Subjects also reported their
difficulty of choosing from each set size (from 1 “Not difficult at all” to 10 “Extremely
diffi
cult”; see Fig
.
1b). Questionnaires further revealed that subjects liked the selection of
images that they were choosing from (mean = 7.16, SD = 1.57; range: 1 = not at all
10
= very much) and found the process of choosing enjoyable (mean = 7.32, SD = 1.33;
range: 1 = not at all
10 = very much). Several subjects also indicated verbally or in
written comments that the experiment was “engaging”, “cool”, and “interesting”. These
data confirm that subjects were not indifferent to the images they were exposed to, and
that the choice task was engaging.
Analysis of the post
-
scanning questionnaire further revealed that our subjects
generally preferred to choose by themselves (n = 14).
The remaining five subjects (out
of the 19 subjects that were included in our analysis) sometimes preferred the computer
to choose for them. Four of these subjects stated (without being explicitly asked) that
they wanted the computer to choose for them wh
en the set size was large or whenever
they had no clear favourite image. This implies that when subjects experience choice
overload, they might prefer the computer to select for them (as in FO trials).
Performance Monitoring.
Eye movements of participant
s were monitored during fMRI
using an MRI
-
compatible eye
-
camera and the ViewPoint Eye Tracker software. Our
procedure was identical to that applied in earlier studies
9
. Eye position was sampled at a
frequency of 60Hz. Further processing of the behaviour wa
s performed off
-
line using
Matlab 7.5. Eye position samples were filtered using a 10Hz low
-
pass filter. Saccades
were detected using an absolute velocity threshold (20deg/s), while blinks were
identified as gaps in the eye position records due to lid closu
re.
Image selection was realized by moving a button
-
controlled cursor on top of the
item of choice within the 3s time
limit of the response stage. Subjects used the thumb of
their right hand on a MRI
-
compatible diamond
-
shaped four
-
button response
-
box
(Curr
ent Designs Inc., Philadelphia, USA). Subjects could move the cursor (i.e., the
green frame; see Fig
ure
2c) up, down, left or right by pressing the corresponding
buttons. Reaction time was defined by the amount of time that elapsed from the
appearance of t
he response screen until subjects first started to move the cursor
towards the item choice (i.e., until the time of the first button press).
Statistical analyses.
Analyses were performed using Matlab 7.5 and the Measures of
Effect Size (MES) Toolbox V1.6,
SPM 5 and SPSS 24. Subjects ratings (Task 3) were
analysed by means of one
-
way repeated measures ANOVAs with the factor set size.
Additional post
-
hoc comparisons directly contrasted the effects for sets of different size
S (6 vs. 12; 12 vs. 24; 6 vs 24; B
onferroni
-
corrected for multiple comparisons).
Behavioural performance (i.e. reaction time, saccade frequency, value of the chosen
item, and percentage of trials with best image chosen) was analysed by means of 2
-
way
repeated measures ANOVAs to reveal the
influence of the factors choice set size S and
task condition. Separate ANOVAs were performed for conditions CF vs. NF, which only
differed with respect to the availability of a dominant option, and for conditions NF vs.
FO, which only varied in terms of
subjects’ decision intent, namely “choosing” vs.
“browsing”, respectively. We tested for sphericity (Mauchly’s test) and adjusted the F
statistic according to the procedure of Greenhouse and Geyser whenever the
assumption of sphericity was not met.
In all
aforementioned cases the assumption of normality was confirmed by Shapiro
-
Wilk
tests (p>0.01; no correction for multiple comparisons). Please note that in case of our
fMRI
-
data we used a canonical analytical approach in SPM 5, which assumes normality.
fMR
I Image Volume Coverage.
The EPI volume provided an almost entire coverage of
the cerebral cortex and of most sub
-
cortical structures: only the posterior part of the
cerebellum was not covered, and there were signal dropouts in orbito
-
frontal cortex and
in
ferior aspects of temporal cortex (see Fig
.
4 for additional information about the actual
volume covered). While the orbito
-
frontal cortex is often a region of interest in studies of
valuation, partial dropout had to be tolerated because the imaging sequen
ce was
optimized to cover the whole brain.
Interrelation of main GLM regressors, subjective difficulty and performance
. While
there was obviously no correlation between our main GLM regressors of interest,
namely the linear predictor and the
orthogonalized quadratic predictor in model 1, both
correlated to different extend with subjective ratings of perceived difficulty and average
saccade frequency. Significant positive correlation with the linear predictor was obtained
for both subjects’ dif
ficulty ratings (F(1,55)=22.792, p<0.001, r [95% CI]=0.541 [0.326,
0.703]) and subjects’ average number of saccades per second in choice trials
(F(1,112)=41.656, p<0.001, r [95% CI]=0.521 [0.373, 0.643]). Importantly, these
correlations demonstrate that th
e “linear predictor” is a good description of the objective
and subjective costs of choosing, namely the number of saccades and perceived
difficulty, respectively. In addition, the number of saccades and the difficulty ratings were
also positively correlat
ed (F(1,112)=9.028, p=0.003, r [95% CI]=0.273 [0.094, 0.435]). In
contrast, the orthogonalized quadratic predictor was neither correlated with the number
of saccades (F(1,112)=3.451, p=0.066, r [95% CI]=
0.173 [
-
0.011, 0.346]) nor with the
difficulty ratin
gs (F(1,55)=0.178, p=0.675, r [95% CI]=
0.057 [
-
0.207, 0.313]).
Supplementary References
1.
Iyengar, S. S. & Lepper, M. R. When choice is demotivating: can one desire too much of
a good thing?.
J. Pers. Soc. Psychol.
79,
995
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1006 (2000).
2.
Smith, A.,
Bernheim, B. D., Camerer, C. F., & Rangel, A. Neural activity reveals
preferences without choices.
Am Econ J
-
Microecon
6
(2), 1
-
36 (2014).
3.
Harris, A., Adolphs, R., Camerer C.F. & Rangel A.
Dynamic construction of stimulus
values in the ventromedial prefro
ntal cortex.
PLoS One
6
(6) e21074 (2011).
4.
Hare, T. A., Camerer, C. F., & Rangel, A. Self
-
Control in Decision
-
Making Involves
Modulation of the vmPFC Valuation System.
Science
324,
646
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648 (2009).
5.
Kimmig, H. et al. Relationship between saccadic eye movements and cortical activity as
measured by fMRI: quantitative and qualitative aspects.
Exp. Brain Res.
141,
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194
(2001).
5
6.
Jerde, T. A., Ikkai, A. & Curtis, C. E. The search for the neural
mechanisms of the set
size effect.
E. J. Neurosci.
,
33
,
2028
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2034 (2011).
6
7.
Reutskaja, E., & Hogarth, R. M. Satisfaction in choice as a function of the number of
alternatives: When ‘goods satiate.
Psychol. Market.
26,
197
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203 (2009).
8.
Reutskaja, E., Camerer, C., Nagel, R. & Rangel, A. Search dynamics in consumer choice
under time pressure: an eye
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tracking study.
Am. Econ. Rev.
101,
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9.
Lindner, A., Iyer, A., Kagan, I. & Andersen, R. A. Human posterior parietal cortex plans
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Supplementary Figures
Supplementary
Fig.
1
|
Descriptive Statistics of Choice sets
(N=19)
.
In this figure the attributes of the choice sets
for the different conditions are depicted, averaged across 19 subjects (+
/
-
95% confidence intervals):
a
shows
the m
ean
image rating of each set,
b
the standard deviation o
f image ratings within a set,
c
the rating of the be
st image within the
set, and
d
the difference in rating between the first and second best image in the set. Note that this distance was always
>0 in all subjects and in all condit
ions.
Please refer to the paragraph on ‘Task 2
fMRI Experiment/Choice Task’ in our
supplementary methods for further details.
Supplementary
Fig.
2
|
Distribution of re
-
fixating saccades across the exposure phase
(N=19)
.
The nine
histograms show the
m
ean number
(+/
-
95% confidence intervals)
of
large, re
-
fixating
saccades
(amplitude larger than
image width, i.e. >3.5deg visual angle)
throughout the 10s exposure phase of the fMRI task for each condition (CF, NF,
FO) and for each set size (bin width:
2s).
As is obvious
when visually inspecting
the figure, subjects use the full length
of the exposure period to
explore
the choice sets
not only in free choice but also in FO
conditions
(all bins >0)
.
Importantly,
the
way that the
number of re
-
fixating sacc
ades decreases across the exposure phase
is indistinguishable
between
conditions. Specifically, three
-
way repeated measures ANOVA
s
with factors condition [CF vs. NF
or NF vs.
FO
], set size [S], and quantile [bins 1
-
5], which
were
calculated across the free
choice conditions, revealed
no
significant
influence of the relevant effects of interest, namely the
interaction between
quantile
and condition
(CF vs NF: F(4,72)=
0.139, p=0.967; η
2
p [CI95%]= 0.0
[0.0
, 0.0]; NF vs FO: F(4,72)= 0.409, p=0.801; η
2
p
[CI95%]= 0.0
[0.0
, 0.0])
and the
interaction
between quantile, condition and set size
(CF vs NF: F(8,144)= 0.286, p=0.970; η
2
p [CI95%]= 0.0
[0.0
, 0.0];
NF vs FO: F(8,144)= 0.4
22
, p=0.
906
; η
2
p [CI95%]= 0.0
[0.0
, 0.0])
.
Supplementary Fig. 3 |
Additional
quadratic ROIs
.
Figure
a
depicts the mean beta estimates of choice
-
related fMRI
activity in the exposure phase for each experimental condition as a function of set size S (6, 12, and 24). Error bars
denote SE.
The a
sterisk indicate
s a
significant differenc
e in
the
betas between CF and NF
for left MFG,
as w
as
revealed
by a 2
-
way repeated measures ANOVA with the factors condition
(F(1,18)=6.290, p=0.022*, η²p [95% CI]=0.259 [0.136,
0.386]
) and set size (factor of no interest).
A trend for the same effect was present in left POG (F(1,18)=4.233, p=0.054,
η²p [95% CI]=0.190 [0.000, 0.415]).
Each ROI’s corresponding fMRI
-
signal time
-
courses (subjects’ average % signal
change +/
-
SE), calculated across the pooled free choice conditio
ns, are depicted in
b.
Separate curves represent
different choice set sizes. Bar graphs in
c
exhibit the beta estimates for the linear (li) and quadratic (qu) predictor of
each condition during the exposure stage.
In both ROIs there was a tendency for a
re
duction of the quadratic signal
component in FO as compared to NF (one
-
tailed paired t
-
tests;
POG
l:
t(18)=1.532; p=0.071; g
1
[95% CI]=0.351 [
-
0.117,
0.811]
;
MFG l
:
t(18)=1.485; p=0.077; g
1
[95% CI]=0.341 [
-
0.127, 0.799]
). The subjects’ z
-
scored average beta
values of
the quadratic predictor and the chosen
-
value regressor of the pooled free choice conditions are shown separately for
each task stage in
d
(E: exposure; D: delay; R: response). Beta
-
values significantly larger than 0 are indicated (one
-
tailed t
-
t
ests; ***
P
< 0.001; detailed statistics are provided in supplementary table 2). N=19.
Supplementary
Fig.
4
|
Inter
-
individual differences in brain activity.
Based on the individual amount ratings (Figure
1c) we split our subjects into two groups that
exhibited a weaker modulation of the amount rating as a function of set
size (low slope group
, N=11
) vs. a stronger modulation (high slope group
, N=8
), respectively.
a
Mean amount rating of
low vs. high slope group (+/
-
SE
). We performed a 2
-
way mixed model ANOVA with the between
-
subject
factor
slope
(high vs. low
slope
) and the within
-
subject factor set size (S) for descriptive purposes: in agreement with our splitting
criterion, we revealed a significant effect for the fa
ctor set size (
F(
2,34
)=
103.936
, p
<
0.0
01**
*, η²p [95% CI]=0.
859
[
0.766
0.894
]
) and its interaction with the factor
slope
(
F(2,34)=10.394, p<0.001***, η²p [95% CI]=0.379 [0.144 0.519]
). The
interaction effect is
chiefly
driven by a higher amount rating for l
arge choice sets in the high slope group
. T
he overall
amount rating does, however
, not statistically differ between both sub
-
groups (
F(1,17)=2.043, p=0.171, η²p [95%
CI]=0.107 [0.00 0.336]
).
b
Mean difficulty rating of low vs. high slope group (+/
-
SE
). A c
orresponding 2
-
way mixed model