1
nature research | reporting summary
April 2018
Corresponding author(s):
Lindner, Camerer
Reporting Summary
Nature Research wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency
and transparency
in reporting. For further information on Nature Research policies, see
Authors & Referees
and the
Editorial Policy Checklist
.
Statistical parameters
When statistical analyses are reported, confirm that the following items are present in the relevant location (e.g. figure lege
nd, table legend, main
text, or Methods section).
n/a
Confirmed
The exact sample size (
n
) for each experimental group/condition, given as a discrete number and unit of measurement
An indication of whether measurements were taken from distinct samples or whether the same sample was measured repeatedly
The statistical test(s) used AND whether they are one- or two-sided
Only common tests should be described solely by name; describe
more complex techniques in the Methods section.
A description of all covariates tested
A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons
A full description of the statistics including central tendency (e.g. means) or other basic estimates (e.g. regression coeffici
ent) AND
variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals)
For null hypothesis testing, the test statistic (e.g.
F
,
t
,
r
) with confidence intervals, effect sizes, degrees of freedom and
P
value noted
Give P values as exact values whenever suitable.
For Bayesian analysis, information on the choice of priors and Markov chain Monte Carlo settings
For hierarchical and complex designs, identification of the appropriate level for tests and full reporting of outcomes
Estimates of effect sizes (e.g. Cohen's
d
, Pearson's
r
), indicating how they were calculated
Clearly defined error bars
State explicitly what error bars represent (e.g. SD, SE, CI)
Our web collection on
statistics for biologists
may be useful.
Software and code
Policy information about
availability of computer code
Data collection
Compare Methods and Supplementary Methods: Stimuli were generated on a windows PC using custom made scripts under “Cogent
Graphics” (developed by John Romaya at the LON at the Wellcome Department of Imaging Neuroscience) in combination with Matlab
7.5. Eye movements of participants were monitored during fMRI using an MRI-compatible eye-camera and the ViewPoint Eye Tracker
software. Brain Imaging was performed on a Siemens Trio Scanner, as is further specified below.
Data analysis
Compare Methods and Supplementary Methods: Brain imaging data were analysed using SPM5 in combination with Matlab 7.5
(including the SPM2 Volumes Toolbox Code to extract Raw data from image files, such as beta values and signal intensity values
for fMRI
signal time courses). Eye movement analysis was performed based on previously established scripts in Matlab 7.5. Statistical a
nalyses
were performed using Matlab 7.5 and the Measures of Effect Size (MES) Toolbox V1.6, SPM 5, and SPSS 24.
For manuscripts utilizing custom algorithms or software that are central to the research but not yet described in published lit
erature, software must be made available to editors/reviewers
upon request. We strongly encourage code deposition in a community repository (e.g. GitHub). See the Nature Research
guidelines for submitting code & software
for further information.
2
nature research | reporting summary
April 2018
Data
Policy information about
availability of data
All manuscripts must include a
data availability statement
. This statement should provide the following information, where applicable:
- Accession codes, unique identifiers, or web links for publicly available datasets
- A list of figures that have associated raw data
- A description of any restrictions on data availability
Data availability. The data that support the findings of this study as well as the data underlying our power calculation are av
ailable from the corresponding author
upon reasonable request. Un-thresholded statistical maps of our main fMRI-results will be made available at NeuroVault.org.
Field-specific reporting
Please select the best fit for your research. If you are not sure, read the appropriate sections before making your selection.
Life sciences
Behavioural & social sciences
Ecological, evolutionary & environmental sciences
For a reference copy of the document with all sections, see
nature.com/authors/policies/ReportingSummary-flat.pdf
Life sciences study design
All studies must disclose on these points even when the disclosure is negative.
Sample size
Compare Supplementary Methods: Sample Size. Sample size was guided by our previous behavioural study on choice overload7 and bu
ilt 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 choice followed an inverted-U shape pattern
with the
highest satisfaction experienced by subjects when choosing from intermediate-sized sets (vs larger or smaller sets7). In that s
tudy 120
subjects were choosing a gift box to pack a present for their friends from different sized sets of boxes containing either 5, 1
0, 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 [10 items = twice the size of the small set, M = 5.53, SD = 1.57, N=30] and the diff
erence 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 int
ermediate set, M
= 6.77, SD = 1.87, N=30] (results from7). 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 repetitions7). Both our
current study
and study7 used visual stimuli. However, as study7 suggests, the definition of “optimal”, “too small”, and “too large” choice s
et should depend
on the costs and benefits of each choice setting and is different in varying environments.
Data exclusions
Compare Methods: Initially we recruited 20 subjects. One subject reported verbally that he was indifferent about landscape imag
es, was not
interested in choosing any of them, and even rejected the customized item as a reward at the end of the experiment. His ratings
of the
landscape indicated the same: there was no variability in the liking ratings of different images that he reported. Over 84% of
images were
given a rating of “0” (meaning, the subject did not like the images at all), and the rest 16% of ratings were distributed betwe
en 0 and 1.8 on
the 11-point scale (M = 0.1, SD = 0.28). The data clearly indicated that the task was not engaging for that particular subject.
Therefore, the
data from that subject were not included in further analysis (behavioural or fMRI).
Replication
No replication tests were performed. Yet, in our study an array of independent conditions had to be fulfilled (task-related act
ivity, inverted-u
shaped activity, CF>NF, and less quadratic response in FO than in NF), only then a brain area would be considered to contribute
to a
representation of choice set value. The use of multiple independent criteria should increase the robustness of our findings.
Randomization
Our study used a within-subject design and subjects were not allocated to different treatment groups. All experimental conditio
ns were
presented randomly interleaved.
Blinding
Our within-subject design and our standardized computer-based analyses (which were the same for all individuals) did not requir
e blinding.
Reporting for specific materials, systems and methods
3
nature research | reporting summary
April 2018
Materials & experimental systems
n/a
Involved in the study
Unique biological materials
Antibodies
Eukaryotic cell lines
Palaeontology
Animals and other organisms
Human research participants
Methods
n/a
Involved in the study
ChIP-seq
Flow cytometry
MRI-based neuroimaging
Human research participants
Policy information about
studies involving human research participants
Population characteristics
Nineteen individuals (12 males; mean age 26.2 years +/- 4.9 SD) completed the study. All subjects were right-handed and had
normal or corrected to normal vision.
Recruitment
Participants were recruited through mailing lists. Recruitment should not have an impact on the results of our within-subject
study.
Magnetic resonance imaging
Experimental design
Design type
event-related task-design
Design specifications
Each subjects completed four runs with 18 trials each (three randomly interleaved choice conditions [CF,NF,FO] x three
choice set sizes [6,12,24]). Trial duration: ~27sec. Baseline: ~13.5sec.
Behavioral performance measures
Measures: Preference ratings, choice [action sequence], reaction time, eye movements. Detailed statistical analyses of
all respective measures are provided in the results section to characterize subjects' engagement in our task. In addition,
eye movement measures and preference ratings entered our fMRI analyses.
Acquisition
Imaging type(s)
T1-weighted MP-rage, T2*-weighted gradient-echo planar imaging
Field strength
3 Tesla (Siemens Trio)
Sequence & imaging parameters
T1: '176 slices, slice thickness = 1 mm, gap = 0 mm, in-plane voxel size = 1x1 mm, TR = 1500 ms, TE = 3.05 ms, FOV =
256x256, resolution = 256x256'; EPI: 'EPIs: slice thickness = 3.5 mm, gap = 0 mm, in-plane voxel size = 3x3 mm, TR =
2000 ms, TE = 30 ms, flip angle = 90°, FOV = 192x192, resolution = 64x64, 32 axial slices'
Area of acquisition
Compare Supplementary Methods: 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 inferior aspects of temporal cortex (see Figure 4a for additional information about the
actual volume covered).
Diffusion MRI
Used
Not used
Preprocessing
Preprocessing software
SPM 5 (Wellcome Department of Cognitive Neurology, London).
We spatially smoothed the normalized functional images using a Gaussian kernel (7x7x7 mm³ full-width at half-
maximum). Furthermore, we applied a high pass filter (cut-off period 128 ms).
Normalization
All images of each subject were realigned to the first scan of the first run. Next, we co-registered the mean image of the
realigned functional scans to the anatomical image. The latter was then normalized to the SPM T1-template in MNI
space (Montreal Neurological Institute, mean brain). The resulting non-linear 3D-transformation was applied to all EPI
images.
Normalization template
SPM 5 T1 template image (MNI space)
Noise and artifact removal
n.a.
Volume censoring
n.a.
Statistical modeling & inference
Model type and settings
Compare Methods:
4
nature research | reporting summary
April 2018
Model type and settings
fMRI-analyses were first performed at the individual- and then at the group- level. On the individual level we used two
different models.
In model 1, nine experimental conditions were modeled separately [three tasks (CF, NF, and FO choice) x 3 task stages
(exposure and mask, delay, and response periods)] in the general linear model (GLMs) for a given subject. Each model
also included 6 motion correction parameters obtained from a rigid-body transformation during image realignment, as
well as three further parameters which served as additional parametric modulators for each of the 3x3 condition-by-
stage regressors of the GLMs: (i) a linear predictor, (ii) a quadratic predictor (orthogonalized to the linear term), as well
as (iii) the liking rating of the chosen item. Parametric modulators are explained in more detail in the results section.
Thus, there were a total of 6 motion regressors and 27 parametrically modulated condition-by-stage regressors (3x3x3 =
3 tasks x 3 task stages x 3 parametric modulators).
In model 2 the individual subjects’ GLMs included regressors for each of our 3x3 experimental conditions [3 tasks (CF,
NF, and FO choices) x 3 choice sets S (6-, 12-, and 24-item sets)] and for each stage of the task (exposure and mask,
delay, and response period), amounting to 27 regressors per session. As in model 1, the 6 motion correction parameters
obtained from the rigid-body transformations during realignment were included as additional regressors in order to
capture any residual movement artifacts.
Effect(s) tested
Compare Methods: For analysing model 1 on the group-level, we restricted our calculations to task-related areas
(across-subject activity increases in the exposure phase in either of the choice conditions, CF or NF, at P < 0.01
uncorrected [one-tailed t-test; H0:
μ
>0]). Then, contrast images for the various regressors of the exposure phase were
analysed using one-tailed t-tests, allowing us to map brain regions which displayed an activity pattern in the pooled
choice conditions NF & CF that was positively correlated with the quadratic predictor (H0:
μ
>0; P < 0.05 FDR-corrected
for multiple comparisons) or with the linear predictor (P < 0.01 uncorrected; note that this liberal threshold was chosen
to ensure high sensitivity for detecting any additional presence of a positive linear signal component in “quadratic
areas”). Areas revealed by the latter contrast were considered potential candidates for being a neural correlate of
choice set value. The beta estimates revealed for these areas were further subjected to region of interest (ROI) analyses.
[...] The respective beta estimates, which were assessed by model 2, were subjected to additional ROI analyses. Also
compare 'ROI analyses' in our methods section.
Specify type of analysis:
Whole brain
ROI-based
Both
Anatomical location(s)
Areas were functionally defined according to the procedure described above (compare effect(s) tested).
Also compare chapter on ROI analyses in Methods: We used the SPM2 Volumes Toolbox V 1.21 by
Volkmar Glauche to extract the normalized beta weights for the exposure-period regressors of both
model 1 and model 2 for a 3mm-radius sphere that was centred on our functionally defined regions of
interest.
Statistic type for inference
(See
Eklund et al. 2016
)
voxel-wise
Correction
FDR (main contrast: quadratic predictor>0; also see 'Effect(s) tested' above)
Models & analysis
n/a
Involved in the study
Functional and/or effective connectivity
Graph analysis
Multivariate modeling or predictive analysis