Scientic Reports | (2021) 11:8780 |
Choosing increases the value
of non‑instrumental information
Matthew Jiwa1*, Patrick S. Cooper1,2, Trevor T.‑J. Chong2,3,4 & Stefan Bode1
Curiosity pervades all aspects of human behaviour and decision‑making. Recent research indicates
that the value of information is determined by its propensity to reduce uncertainty, and the hedonic
value of the outcomes it predicts. Previous ndings also indicate a preference for options that are
freely chosen, compared to equivalently valued alternatives that are externally assigned. Here, we
asked whether the value of information also varies as a function of self‑ or externally‑imposed choices.
Participants rated their preference for information that followed either a self‑chosen decision, or an
externally imposed condition. Our results showed that choosing a lottery signicantly increased the
subjective value of information about the outcome. Computational modelling indicated that this
change in information‑seeking behaviour was not due to changes in the subjective probability of
winning, but instead reected an independent eect of choosing on the value of resolving uncertainty.
These results demonstrate that agency over a prospect is an important source of information value.
Individuals are required to choose whether to receive information about a vast range of topics. From the caloric
contents of our favourite snacks, to the misdeeds of unknown celebrities, and our own genetic make-up, we now
have more information available at the touch of a button—or swipe of a credit card—than ever before. erefore,
how we decide which information to view or avoid is of increasing personal, social, and commercial relevance.
Although information can be used to increase the likelihood or magnitude of future rewards, recent ndings
suggest that the value of information is not determined by this utility alone. Both human and non-human animals
demonstrate a willingness to exchange rewards for information that cannot be used to inuence the probability
or magnitude of future rewards1–7. Recent neurophysiological data have shown that such non-instrumental
information is encoded by similar neural circuits as primary reinforcers5,8–10, with unexpectedly informative
signals producing similar neural responses to unexpectedly positive outcomes1,8. Beyond its instrumental value
(the extent to which that information can be used to increase the magnitude or likelihood of future rewards), the
subjective value of information is further determined by both its hedonic value (the expected aective response
to the information), and its cognitive value (the degree of uncertainty that viewing the information is expected
Importantly, however, intrinsic biases and contextual factors may aect the contributions that each of these
factors make to the overall value of an informational prospect11. e hedonic value of information may be par-
ticularly susceptible to bias. Typically, it is found that prospects that oer a greater chance of a positive outcome
(or lesser chance of a negative one) elicit a greater willingness to pay to view that information than those with a
more negative outlook5,12,13. However, as ndings in the elds of behavioural economics and cognitive psychology
have repeatedly shown, individuals’ predictions of outcomes are oen open to systematic biases and heuristics
that may, in turn, aect the value of information pertaining to those prospects11,14,15. A common example is
choice-induced preference change—where the act of choosing an option increases its subjective value relative
to alternatives both during and aer the decision making process16–23. In addition, choice may not only increase
an the subjective value of a chosen option, but also an individual’s curiosity about it24. However, the evidence
suggesting this does not account for pre-choice preferences, nor can it comment on whether increases in curios-
ity are due to choice-induced modulation, or more indirectly through an increase in the subjective value of the
Critically, individuals predict more favourable outcomes for prospects over which they have agency, rather
than those that are assigned to them—a phenomenon termed the “illusion of control” (IOC)14,25,26. As the prob-
ability of outcomes is crucial to the valuation of prospects, with higher probability of favourable outcomes leading
to a higher valuation of a prospect27–29, there are clear theoretical implications of this subjective change for both
the behavioural and neural components of decision-making. As the neural responses to rewards are typically
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encoded as the signed dierence between an actual reward and an expected reward (reward prediction error;
RPE), we may expect that an increased subjective probability of positive outcomes would lead to an attenuated
RPE in the event of a positive outcome30. However, evidence suggests that neural responses in the striatum may
not be aected by the IOC31. is nding suggests that the probability of winning used in the computation of
the RPE may dier from the probability of winning reported by participants31,32.
e question of whether subjective information value is aected by biases in probability produced by the IOC
remains an open one. In this study, we aimed to test whether agency over an arbitrary choice between alterna-
tive lotteries with identical probabilities of winning systematically increased: (a) participants’ condence in a
winning outcome (measured through self-reported condence levels) and (b) the valuation of receiving early,
non-instrumental information about the outcome of that prospect (measured by participants’ willingness to
exchange rewards for the early knowledge of a lottery’s outcome). In addition, we used computational modelling
to test whether the potential increase in condence in winning the lottery could explain any observed increase
in the information value, or if the increase in information valuation was otherwise better explained by a distinct
eect of agency on the factors determining the subjective value of information.
To assess the inuence of choosing on information valuation, we manipulated participants’ perceived agency
during a simple lottery, in which the decision to play a specic “roulette wheel” could be approved or vetoed. In
a series of trials, participants were presented with three roulette wheels, which they were accurately instructed
each had the same probability of winning, and asked to choose their preferred prospect, similar to Kool etal.31
(see Fig.1a). e participant’s selection was either approved (granting agency over the trial) or vetoed (remov-
ing agency from the trial). ese lotteries utilised scrambled roulette wheels comprising segments of a winning
colour and a non-winning colour. e three wheels on each trial were rotated versions of the same conguration
of otherwise identical colour segments, with the probability to win 0.2, 0.4, 0.6 or 0.8 (see “Methods” for details).
Following the approval/veto stage, we probed the eects of agency on information value using two methods.
First, participants rated their condence to win that trial using a continuous scale. Second, participants were
administered a Becker–DeGroot–Marschak (BDM) auction33 in which they stated the maximum cost they would
be willing to incur in order to reveal the outcome of the lottery immediately. eir bid was then compared to
a random bid made by the computer, and, if the participant’s bid was higher than the computer’s bid, the latter
would be deducted from the participant’s points total, and they would learn the outcome of the trial. If their bid
was lower, they were instructed that the lottery would still be played out and winnings allocated; however, they
would not learn the outcome immediately. e magnitude of the participant’s bid therefore served to represent
the maximum value they would be willing to pay in order to view the non-instrumental information about that
trial’s outcome. is auction procedure guaranteed that the most realistic valuation of the non-instrumental
information was obtained on each trial.
To characterise participants’ preferences for acquiring this information, we also constructed a series of com-
putational models which were t to the participants’ trial-wise bidding patterns. ese models included a null
model, which assumed no eect of agency on information-seeking behaviour, as well as a series of models that
characterised dierences in information valuation across agentic and non-agentic trials as due to changes in the
subjective probability of winning, the subjective value of resolving uncertainty, the subjective value of anticipat-
ing a positive outcome, or simply to the desirability of information.
Agency increases win expectancy and information value. To assess whether participants’ subjec-
tive probability of a positive outcome was aected by their agency over the lottery, their condence ratings were
compared across agentic and non-agentic trials. A
repeated measures analysis of variance (ANOVA) with
within-subjects factors of agency (agentic or non-agentic) and win probability (0.2, 0.4, 0.6 or 0.8) indicated that
condence in positive outcomes was modulated both by the probability of winning,
F(3, 114)=949.90, p<0.001
and possession of agency,
F(1, 38)=30.78, p<0.001
. As shown in Fig.1b, condence ratings were an average
of 2.04% higher when participants had agency over which lottery they played, indicating that this paradigm suc-
cessfully elicited the IOC and replicated earlier ndings14,31.
Next, we examined the inuence of agency on the perceived value of information by assessing participants’
willingness to pay for non-instrumental information. A
repeated measures ANOVA with within-subjects
factors of agency (agentic or non-agentic) and win probability (0.2, 0.4, 0.6 or 0.8) indicated that participants’
bid magnitude was positively predicted by both win-probability,
F(3, 114)=49.92, p<0.001
F(1, 38)=14.27, p<0.001
, see Fig.1c. ere was also a signicant interaction eect between the win-probability
F(3, 114)=4.41, p=0.006
. A post-hoc comparison of bid-magnitude across probabilities revealed
that the dierence between agentic and non-agentic bids was only signicant for trials in which the probability of
winning was 0.4,
aer Bonferroni corrections were applied.
ese ndings suggest that participants were willing to sacrice a signicantly higher proportion of their
winnings in order to learn the outcome of a trial if they had agency over the selection of the prospect (compared
to when they did not have agency), with the strongest eect found in scenarios with relatively higher uncertainty.
Agency increases the value of resolving uncertainty. To assess whether the increase in information
desirability could be explained by the increase in the subjective probability of a positive outcome, we constructed
ve computational models. e rst model assumed no eect of agency on information preference. Based on
previous ndings, this null model instead constructed predictions only from a weighted combination of the win-
probability, the uncertainty of the prospect, and a subject-specic constant (see “Methods”).
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We also constructed a series of alternative models to assess dierent characterisations of the contributions
of agency to information value. In the probability-shied model, shis in the subjective probability of winning
across agentic and non-agentic trials were permitted, such that the probability of winning on agentic trials was
shied by the magnitude of an additional subject-specic free parameter.
In addition, we constructed three further models to test for changes in the subjective valuation of each con-
stituent parameter of the null model. ese models use an additional free parameter to allow the contributions
of reward probability (agency reward model), uncertainty (agency uncertainty model), and the constant value of
information (agency constant model) to vary across agentic and non-agentic trials.
To compare model ts, we used the Watanabe-Akaike Information Criterion (WAIC) measure of out-of-
sample prediction error34,35. WAIC calculation involves the subtraction of a measure of model complexity from a
goodness of t measure. It was chosen over other information criteria (e.g., the Deviance Information Criterion)
Figure1. Experimental design and results. (a) On each trial, participants made a selection between three
equivalent roulette wheels. eir choice was either approved or vetoed, in which case the cursor was moved to
and selected an alternative option. ey then rated their condence to win that trial and submitted a bid in a
Becker–DeGroot–Marschak (BDM) auction to determine whether the outcome would be revealed or hidden.
If their bid was successful, the outcome was shown, otherwise, it was hidden. (b) Mean condence ratings (on a
scale from 0 = “sure loss” to 100 = “sure win”) for each possible probability of winning. Condence ratings were
signicantly higher when participants’ selection of lottery was approved. Error bars represent the standard error
of the mean. (c) Mean bid size in points for each possible probability of winning. Bids were signicantly larger
when participants’ selection of lottery was approved. Error bars represent the standard error of the mean.
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as it has a higher power rate and does not assume the posterior distribution to be Gaussian36,37. e WAIC sug-
gests that the agency uncertainty model is preferred, with the null model underperforming compared to each of
the other models, suggesting that dierences in curiosity between chosen and non-chosen lotteries were best
accounted for by an increase in the value of resolving uncertainty, rather than due to the shi in the subjective
probability of a positive outcome (see Table1). Further, the probability-shi parameter of the probability-shied
model demonstrated poor adherence to the reported increase in subjective win probability, as shown by their
. Posterior predictive checks demonstrated an excellent t of the agency uncer-
tainty model to the data (Supplementary Fig.S1). e nal parameter estimates for the agency uncertainty model
are shown in Supplementary Fig.S2.
Together, these analyses show that subjective information value was increased in agentic, relative to non-
agentic contexts, particularly when uncertainty was maximal. Computational modelling contradicts the notion
that the increased value of information is simply an eect of the increase in the subjective probability of a positive
outcome for agentic prospects. Instead, it suggests that the value of resolving uncertainty is increased insitua-
tions involving agency.
In this study, we assessed how choosing a prospect aects information valuation. Each participant was given
the opportunity to bid money in exchange for immediate, but entirely non-instrumental, information about the
outcomes of lotteries. On each trial, the participant could possess agency over which lottery would determine
their winnings, or the lottery could be randomly assigned. First, we replicated earlier ndings that agency over
choosing one’s lottery increased the perceived condence in a positive outcome of the lottery31. Consistent with
previous ndings, we also demonstrated that participants showed a preference for information pertaining to
prospects with high likelihood of revealing positive outcomes, as well as those with high uncertainty5,10,12. Our
results further showed that participants were willing to place higher bids in order to learn the outcome of a trial
over which they had agency, suggesting that they valued the information more under those circumstances. is
was particularly so for trials with a higher degree of uncertainty about the outcome. Computational modelling
analyses indicated that the agency-related subjective change in the probability of a positive outcome did not
provide the best account for the increase in information valuation for agentic choices. e results were best
explained through an increase in the subjective value of resolving uncertainty for agentic prospects. ese nd-
ings are not directly explained by existing theories of information-seeking behaviour11.
e success of the agency uncertainty model over the other competing models may be explained by a tight,
automatic association between agency and the cognitive value of information. e cognitive value of an infor-
mation signal is determined by the extent to which that information signal is able to reduce the uncertainty sur-
rounding one’s own mental model of the world around them11. Outcomes of events produced through agentic
means may be perceived as possessing greater cognitive value for two primary reasons. First, they oen inform
us of the outcomes of our own decisions or actions, and therefore may aect our mental model of concepts
related to our self-perception, including our attitudes towards ourselves and towards other concepts38. More
generally, experiencing the outcomes of our actions may allow us to assess the accuracy of our existing predic-
tions of action-outcome contingencies present in our mental models by either validating or challenging these
predictions. Second, outcomes of our own actions may be associated with a higher cognitive value simply because
we are typically more likely to act upon or interact with objects or concepts that have a greater relevance to us
(and, therefore, have a more signicant presence in our mental model of the world and elicit more curiosity). In
support of this, research has demonstrated that information on topics that are selected by an individual lead to
higher levels of curiosity than those that are randomly selected24. Of course, participants in the current experi-
ment could not expect to extract more cognitive value from information about lotteries under agentic condi-
tions. However, the increased valuation of information arising from agentic decisions may be attributed to the
association between agency and cognitive value being “overlearned”; learned beyond the point of automaticity
such that it is applied dogmatically. e phenomenon of overlearning is typically associated with improvements in
memory retention39, but can also strengthen stimulus-response associations40. If this association between agency
and cognitive value were to be the subject of overlearning, this may result in the higher subjective valuation of
agentic outcomes observed in the present study.
Alternatively, the current ndings could be explained by an overlearning of the perceived contingency
between agency and the utility of information. Under normal, everyday circumstances, information about
decision outcomes can typically be used to inform future decisions41. Conversely, information learned in an
Table 1. Watanabe-Akaike Information Criterion (WAIC) for each of the discussed models. A smaller value
indicates a better t to the data. e WAIC for the best tting model is highlighted in bold.e dierence from
the best-tting model is represented as
Model Free parame ters (per participant) WAIC
Null 4 8065.11 31.60 (11.54)
Probability-shied 5 8040.51 7.00 (14.48)
Agency reward 5 8039.78 6.27 (15.29)
Agency uncertainty 5 8033.51 –
Agency constant 5 8038.90 5.39 (14.40)
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environment in which one does not possess agency may not be perceived as useful, because we cannot use such
information to inform future decisions. ough the association between agency and utility was not present in the
current experimental framework, an overlearning of this association may account for the relationship between
agency and the subjective value of resolving uncertainty.
Equally, the failure of the other competing models highlight key shortcomings in the ability of existing
accounts to explain the present ndings. For example, choice-induced preference change16–24 alone cannot
account for the present ndings, as it predicts that the value of information should increase uniformly across
agentic prospects (consistent with the agency constant model), or that the value of information should increase
due to the indirect eects of an increase in the subjective value of the associated rewards (consistent with the
probability-shied model). e underperformance of these models relative to the agency uncertainty model indi-
cates that we cannot attribute the present results to choice-induced preference change alone.
Other contemporary accounts argue that agency provides an opportunity for self-enhancement (the motiva-
tion to view oneself in a positive manner), which could supplement information value. Previous studies have
shown that the delivery of outcomes from agentic decisions activates neural circuits that process self-referential
information31,42–48. However, information-seeking with the goal of self-enhancement typically involves an active
search for attering (positively-valenced) information49,50. In the current experimental framework, this should
manifest in an increase in the perceived value of information pertaining to agentic prospects with a high prob-
ability of winning, as conceptualised by the agency reward model. e poor t of this model relative to that of
the agency uncertainty model indicates that a self-enhancement explanation alone cannot account for these data.
It should be noted that our conclusions are somewhat limited by the small eect sizes. is highlights the
comparative importance of the primary information-seeking drivers, such as the anticipation of positive out-
comes. Further, in the present study, the agentic condition in which participants chose their own prospect was
contrasted to a condition in which their choice was vetoed31. Arguably, the veto might have evoked cognitive
processes beyond the experience of a lack of agency, for example the feeling of a loss of agency, or dissatisfac-
tion with losing control in general. Future studies could consider a truly passive control condition in which no
agency exists in the rst place; however, this might come with the danger of task disengagement. ese ndings
also leave open further questions about whether subjective changes in reward value and probability inuence
the value of non-instrumental information about those rewards. One example of this is eort discounting, in
which the value of a reward is reduced when it is earned through eortful, as opposed to non-eortful means51–55.
While evidence for the IOC has not been demonstrated in neural indices of reward31, the modulation of reward
signals has been demonstrated in tasks requiring eort53,54. Investigating information-seeking behaviour in this
context would provide insight into whether the ndings of the present study are unique to the IOC, or whether
they can be generalised to other, neurally observable subjective alterations to the expected value of a prospect.
Finally, though each of the alternative models outperformed the null model, this is likely because each is able
to make predictions that mimic the performance of the agency uncertainty model. is is exemplied by the poor
correlation between the probability-shi parameter of the probability-shied model and the subjective increase
in win-probability reported by participants. As such, though the success of each alternative model relative to the
null model would promote the conception of hybrid models that include combinations of the agency-modulated
parameters, the inclusion of combinations of these parameters would constitute redundancy. Consequently,
models that include more than one agency-modulated parameter produce divergent model ts, as very dierent
combinations of the parameters lead to similar model performance, making model identication dicult and
inferences about such models unreliable.
In sum, the ndings of the present study demonstrated an increase in the perceived value of resolving uncer-
tainty about the post-decisional outcomes of prospects when those prospects are selected through agentic means,
as opposed to when agency is removed. is increase in value was not explained by a change in the subjective
probability of a positive outcome. Instead, it may be attributed to an overlearning of the association between
choice and the instrumentality or cognitive value of information.
Participants. Forty-seven participants (30 female, 17 male,
M=23.47, SD =2.69
) completed the experi-
ment. Four were excluded from analyses for failing to meet the pre-determined accuracy threshold for con-
dence ratings of
% from the true probability across all four probability levels, indicating an insucient
understanding of the real probability of winning. A further four were excluded for failing to show any evidence
of information valuation, suggesting a general lack of interest in the lottery’s outcome. e remaining sample
of 39 participants (25 female, 14 male) were aged between 18 and 36 years of age (M = 23.21, SD = 2.65). Par-
ticipants received a reimbursement of AUD $15 for their participation, and were instructed that they could win
an additional reward of up to $5 available depending on the results of the experiment. However, at the end of
the experiment, all participants were awarded the full $20 reimbursement, regardless of performance. Informed
consent was provided by all participants, and research was conducted in accordance with the Declaration of
Helsinki. All study protocols were approved by e University of Melbourne Human Research Ethics Commit-
tee (ID 1954969).
Procedure. All stimuli were presented using the Psychophysics Toolbox56 running on MATLAB R2018a
(e Mathworks, Natick, MA) on a cathode-ray tube (CRT) monitor with a resolution of
a screen refresh rate of 60Hz.
Before commencing with the experiment, participants were provided with written and verbal instructions for
the task and were permitted to complete a series of practice trials (with a minimum of 20) until they felt condent
to continue to the main task. Participants were instructed that, on each trial, they were to choose from three
Scientic Reports | (2021) 11:8780 |
roulette wheels, each of which had an equal probability of producing a winning outcome. e roulette wheels
comprising segments of red and blue, with the either the red or blue connoting a winning outcome (counter-
balanced across participants). Importantly, participants were fully aware that there was no dierence in the
probability of winning for each of the wheels on each trial. ey were instructed that a spinner was going to be
rotated around one of the wheels and if it landed on their winning colour, they would win 50 points. Losses were
worth 0 points, with their overall total points at the end of the experiment determining the size of the monetary
payment at the end of the experiment. ey were further told that on some trials, their choice of wheel would be
“approved” while on other trials, the computer would “veto” their decision and select a dierent wheel.
e main experiment consisted of ten blocks, each containing twelve trials. In each block, three trials of each
of the four win probabilities (0.2, 0.4, 0.6, 0.8) were presented. On each trial, three possible roulette wheels were
initially shown. e wheels consisted of 40 segments of equal size. To construct the three roulette wheels, the
win probability was multiplied by the total number of segments, and the resultant number of segments were
shaded in the participant’s winning colour, with the remainder shaded in the alternate colour. e order of the
segments was randomly shued. To construct the other two wheels, this roulette wheel was then duplicated,
clockwise and counter-clockwise. is ensured that the wheels were structurally identical, such
that dierential segment distribution could not produce preferences based on perceived dierences in win prob-
ability. Participants were instructed that each of the three lotteries were equivalent. During the post-experiment
debrief, participants were also asked to describe their method of choosing a lottery, such that any participants
who indicated they believed the lotteries were not equivalent could be excluded. Two participants indicated
that they believed the lotteries had not been equivalent. Both also failed to meet the accuracy requirement for
condence ratings and were excluded.
On each trial, the centre-point of each wheel was positioned along the circumference of an imaginary circle
centred at the mid-point of the screen. e rst wheel was placed randomly along this circumference, with the
remaining two positioned at
clockwise, respectively. e mouse was initially positioned at the centre
of the screen. Participants were instructed to select one of the three options by clicking on it with the mouse
within 2.5s of stimulus onset. If the participant did not respond in time, they received the feedback, “too slow”,
and the trial was restarted with dierent stimuli (with the same win probability).
If the participant’s selection was approved, their selected wheel was highlighted with a green circle. If their
selection was vetoed, the cursor would ash, and was then automatically moved to one of the other two options
by the computer. e newly computer-selected option was then highlighted with the green circle. Approved
and vetoed selections were pseudo-randomised, such that each occurred on half of the trials in each block. e
proportion of approved/vetoed trials was kept equal across all win probabilities, and it was ensured that equal
numbers of approved and vetoed trials resulted in winning outcomes.
Following their selection, there was a 2s delay, aer which participants completed a condence rating to
indicate how likely they perceived a winning outcome to be31. is was completed by moving the mouse along
a continuous scale with markings of “sure loss” and “sure win” at either end. Cursor position was randomised
prior to the appearance of the scale on each trial. Participants were given 4s to complete this rating, with the
position of the mouse at the end of the 4s period recorded as their condence rating.
Aer this, participants completed a procedure that allowed us to assess the value they placed on receiving
immediate information about the outcome of the trial. We used a Becker–DeGroot–Marschak (BDM) auction33
to determine whether they would learn the outcome of the trial or not. In this procedure, the position of the
cursor was randomised before participants had 5s to make a bid of between 0 and 5 points (with increments of
0.1). e size of their bid was then compared against a randomly generated “price” of between 0.1 and 5 points.
If the participant’s bid was equal to or higher than this price, that price would be deducted from their score,
and they were shown the outcome of the lottery at the end of the trial. Otherwise, no points were deducted, but
the outcome of the lottery was kept secret. Participants were explicitly instructed that the outcome of the bid
had no bearing on whether they won or lost on any given trial, only whether they would nd out the outcome
immediately. Any winnings were added to their total score. All bids were made by moving the mouse along a
horizontal scale, with the position of the mouse at the end of the 5s duration determining the size of the bid.
If their bid was successful (i.e., if it was greater than the price), a green bar ashed on the screen for 1s. e
initial three roulette wheels were then redisplayed, with a spinner placed on the (self- or computer-) selected
wheel. e spinner rotated around the selected wheel for 2.5s, stopping on either a winning or losing segment.
If the spinner stopped on a winning segment, the feedback “$$$” was shown. If it stopped on a losing segment,
the feedback “XXX” was shown.
If the participant’s bid was unsuccessful, a red bar ashed on the screen for 1s. e wheels were not shown
with their original segments, but were instead replaced by uniformly grey wheels. e spinner rotated around
the wheel for 2.5s, returning to the top of the wheel, and the feedback “???” was shown, indicating that the
outcome of the trial remained unknown. Participants were explicitly instructed that, when the grey wheel was
shown, the nal position of the spinner in no way reected its position on the selected wheel and was intended
as a ller screen only.
Each trial was followed by an inter-trial interval of 0.4s. Participants were provided with an un-timed break
aer each block of 12 trials.
Computational models. We constructed a series of computational models to characterise the value that
individuals placed on each lottery. All models were t using Hamiltonian Monte Carlo sampling as implemented
in Stan57. Each model was t using four parallel chains with a warm-up period of 1500 samples each followed by
5000 samples drawn from the converged chains.
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Null model. Based on the previously established ndings in this area5,10,12, the null model operationalised the
prediction that participants’ bids were dependent on: (1) the likelihood of a positive outcome, and (2) the uncer-
tainty of the current prospect. Uncertainty was dened as the entropy of the prospect, with entropy calculated
by the Shannon function58, see Eq. (1). To maintain uncorrelated model parameters, this entropy was centred by
subtracting the mean level of entropy across all trials, as shown in Eq. (2).
As a result, the null model predicts that the value of information is determined by the weighted, linear combina-
tion of win probability, uncertainty, and a constant to capture any other sources of information valuation (Eq.3).
Here, the free parameter
dictates the extent to which the probability of winning (P(W)) modulates the subjec-
tive value of information, with greater values of
leading to greater increases in subjective information value
with increasing win probability. Similarly,
corresponds to the magnitude of change in the subjective value of
information associated with the level of uncertainty on the given trial. Finally, the free parameter
is a subject-
specic constant that modulates the value of information uniformly across all trials.
To estimate this set of parameters, we employed a hierarchichal Bayesian estimation strategy that assumes that
each subject’s parameters are drawn from a joint group-level distribution such that the parameters for subject i
are constrained to being drawn from the prior distributions:
Each of these prior distributions was weakly informative, restricting the model to reasonable areas of the possible
parameter space. e half-Cauchy distribution was used as a prior for standard deviations as it restricts away
from large values while still oering some prior information59.
Finally, the outcome variable was also assigned weakly informative group-level hyperparameters and restricted
to a truncated normal distribution with limits of 0 and 5, to match the lower and upper bid limits. e mean of
, was given by Eq. (3).
Probability-shied model. e probability-shied model allowed for the adjustment of the subjective probability
of a winning outcome depending on whether or not participants could choose the lottery, as expected under
the illusion of control. is was achieved by allowing probability to be adjusted by an additional free parameter,
, such that the probability of winning used in the calculation of entropy and information valuation was
given by Eq. (4). Here, A is a binary variable that equals 1 on trials in which the participant has agency (i.e., when
their selection is approved) and 0 when the participant does not have agency (i.e., when their selection is vetoed).
e entropy equation used to calculate uncertainty was also updated to employ the use of the shied prob-
ability such that it was calculated using Eqs.5 and 6.
e distribution of the
parameter was truncated at
, to prevent the subjective probability of winning
from exceeding 0 or 1. e model otherwise followed the same format as the null model. e full notation for
the probability-shied model is provided below:
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Agency modulation models. Finally, a series of models were constructed that allowed the magnitude of each of
the factors used to compute the value of information in the null model to vary based on the presence or absence
of agency. ese models explored the possibility that agency modulates the value of information via a modula-
tion of the value of the anticipation of a positive outcome, the resolution of uncertainty, or the constant underly-
ing value of information.
e agency reward model predicts that the value of information in agentic contexts diers from that in non-
agentic contexts due to a dierence in the valuation of the anticipation of a positive outcome. is was achieved
by adding the product of a binary parameter, A, and an additional free parameter,
, to the existing free
. e full notation for the agency reward model is provided below:
Similarly, the agency uncertainty model predicts that agency aects information valuation due to a modulation
of the value of resolving uncertainty for agentic prospects. is was achieved by adding the product of a binary
parameter, A, and an additional free parameter,
, to the existing free parameter
. e full notation for the
agency uncertainty model is provided below:
Finally, the agency constant model predicts that agency aects information valuation equally across all levels
of probability and uncertainty. is model conceptualised the possibility that the desirability of information
is modulated equally by the possession of agency irrespective of the probability of winning and uncertainty of
the outcome of the prospect itself. is was achieved by adding the product of a binary parameter, A, and an
additional free parameter,
, to the existing free parameter
. e full notation for the agency constant model
is provided below:
βprob ∼TruncNormal(µβprob ,σβprob ),∈(−0.2, 0.2
µβprob ∼Normal(0.02, 0.05)
βaW ∼Normal(µβaW ,σβaW )
µβaW ∼Normal(0, 1)
βaU ∼Normal(µβaU ,σβaU )
µβaU ∼Normal(0, 1)
Scientic Reports | (2021) 11:8780 |
Received: 12 January 2021; Accepted: 7 April 2021
1. Bromberg-Martin, E. S. & Hikosaka, O. Midbrain dopamine neurons signal preference for advance information about upcoming
rewards. Neuron 63, 119–126. https:// doi. org/ 10. 1016/J. NEURON. 2009. 06. 009 (2009).
2. Bromberg-Martin, E. S. & Hikosaka, O. Lateral habenula neurons signal errors in the prediction of reward information. Nat.
Neurosci. 14, 1209–1216. https:// doi. org/ 10. 1038/ nn. 2902 (2011).
3. Blanchard, T., Hayden, B. & Bromberg-Martin, E. Orbitofrontal cortex uses distinct codes for dierent choice attributes in deci-
sions motivated by curiosity. Neuron 85, 602–614. https:// doi. org/ 10. 1016/J. NEURON. 2014. 12. 050 (2015).
4. Bennett, D., Bode, S., Brydevall, M., Warren, H. & Murawski, C. Intrinsic valuation of information in decision making under
uncertainty. PLOS Comput. Biol. 12, e1005020. https:// doi. org/ 10. 1371/ journ al. pcbi. 10050 20 (2016).
5. Charpentier, C. J., Bromberg-Martin, E. S. & Sharot, T. Valuation of knowledge and ignorance in mesolimbic reward circuitry.
Proc. Natl. Acad. Sci. 115, E7255–E7264. https:// doi. org/ 10. 1073/ pnas. 18005 47115 (2018).
6. Vasconcelos, M., Monteiro, T. & Kacelnik, A. Irrational choice and the value of information. Sci. Rep. 5, 13874. https:// doi. org/ 10.
1038/ srep1 3874 (2015).
7. Bennett, D., Sutclie, K., Tan, N.P.-J., Smillie, L. D. & Bode, S. Anxious and obsessive-compulsive traits are independently associ-
ated with valuation of noninstrumental information. J. Exp. Psychol. Gen. https:// doi. org/ 10. 1037/ xge00 00966 (2020).
8. Brydevall, M., Bennett, D., Murawski, C. & Bode, S. e neural encoding of information prediction errors during non-instrumental
information seeking. Sci. Rep. 8, 6134. https:// doi. org/ 10. 1038/ s41598- 018- 24566-x (2018).
9. Kobayashi, K. & Hsu, M. Common neural code for reward and information value. Proc. Natl. Acad. Sci. US Am. https:// doi. org/
10. 1073/ pnas. 18201 45116 (2019).
10. van Lieshout, L. L. F. et al. Induction and relief of curiosity elicit parietal and frontal activity. J. Neurosci. 38, 2579–2588. https://
doi. org/ 10. 1523/ JNEUR OSCI. 2816- 17. 2018 (2018).
11. Sharot, T. & Sunstein, C. R. How people decide what they want to know. Nat. Hum. Behav. 4, 14–19. https:// doi. org/ 10. 1038/
s41562- 019- 0793-1 (2020).
12. Kobayashi, K., Ravaioli, S., Baranès, A., Woodford, M. & Gottlieb, J. Diverse motives for human curiosity. Nat. Hum. Behav. https://
doi. org/ 10. 1038/ s41562- 019- 0589-3 (2019).
13. Iigaya, K., Story, G. W., Kurth-Nelson, Z., Dolan, R. J. & Dayan, P. e modulation of savouring by prediction error and its eects
on choice. Elife 5, e13747. https:// doi. org/ 10. 7554/ eLife. 13747. 001 (2016).
14. Langer, E. J. e illusion of control. J. Pers. Soc. Psychol. 32, 311–328. https:// doi. org/ 10. 1037/ 0022- 3514. 32.2. 311 (1975).
15. Kahneman, D. & Tversky, A. On the psychology of prediction. Psychol. Rev. 80, 237–251. https:// doi. org/ 10. 1037/ h0034 747 (1973).
16. Voigt, K., Murawski, C. & Bode, S. Endogenous formation of preferences: Choices systematically change willingness-topay for
goods. J. Exp. Psychol. Learn. Mem. Cogn. 43, 1872–1882. https:// doi. org/ 10. 1037/ xlm00 00415 (2017).
17. Voigt, K., Murawski, C., Speer, S. & Bode, S. Hard decisions shape the neural coding of preferences. J. Neurosci. 39, 718–726. https://
doi. org/ 10. 1523/ JNEUR OSCI. 1681- 18. 2018 (2019).
18. Izuma, K. et al. Neural correlates of cognitive dissonance and choice-induced preference change. Proc. Natl. Acad. Sci. 107,
22014–22019. https:// doi. org/ 10. 1073/ pnas. 10118 79108 (2010).
19. Ariely, D. & Norton, M. I. How actions create—Not just reveal—Preferences. Trends Cogn. Sci. 12, 13–16. https:// doi. org/ 10. 1016/j.
tics. 2007. 10. 008 (2008).
20. Brehm, J. W. Postdecision changes in the desirability of alternatives. J. Abnorm. Soc. Psychol. 52, 384–389. https:// doi. org/ 10. 1037/
h0041 006 (1956).
21. Sharot, T., Martino, B. D. & Dolan, R. J. How choice reveals and shapes expected hedonic outcome. J. Neurosci. 29, 3760–3765.
https:// doi. org/ 10. 1523/ JNEUR OSCI. 4972- 08. 2009 (2009).
22. Sharot, T., Velasquez, C. M. & Dolan, R. J. Do decisions shape preference? Evidence from blind choice. Psychol. Sci. 21, 1231–1235.
https:// doi. org/ 10. 1177/ 09567 97610 379235 (2010).
23. Lee, D. & Daunizeau, J. Choosing what we like vs liking what we choose: How choice-induced preference change might actually
be instrumental to decision-making. PLoS ONE 15, e0231081. https:// doi. org/ 10. 1371/ journ al. pone. 02310 81 (2020).
24. Schutte, N. S. & Malou, J. M. Increasing curiosity through autonomy of choice. Motiv. Emot. 43, 563–570. https:// doi. org/ 10.
1007/ s11031- 019- 09758-w (2019).
25. Presson, P. & Benassi, V. Illusion of control: A meta-analytic review. J. Soc. Behav. Pers. 11, 493–510 (1996).
26. ompson, S. C., Armstrong, W. & omas, C. Illusions of control, underestimations, and accuracy: A control heuristic explana-
tion. Psychol. Bull. 123, 143–161. https:// doi. org/ 10. 1037/ 0033- 2909. 123.2. 143 (1998).
27. Caplin, A. & Leahy, J. Psychological expected utility theory and anticipatory feelings. Q. J. Econ. 116, 55–79. https:// doi. org/ 10.
1162/ 00335 53015 56347 (2001).
28. Starmer, C. Developments in non-expected utility theory: e hunt for a descriptive theory of choice under risk. J. Econ. Lit. 38,
332–382. https:// doi. org/ 10. 1257/ jel. 38.2. 332 (2000).
29. von Neumann, J. & Morgenstern, O. eory of Games and Economic Behavior (Princeton University Press, 1944).
30. Schultz, W., Dayan, P. & Montague, P. A neural substrate of prediction and reward. Science 275, 1593–1599 (1997).
βaC ∼Normal(µβaC ,σβaC )
µβaC ∼Normal(0, 1)
Scientic Reports | (2021) 11:8780 |
31. Kool, W., Getz, S. J. & Botvinick, M. M. Neural representation of reward probability: Evidence from the illusion of control. J. Cogn.
Neurosci. 25, 852–861. https:// doi. org/ 10. 1162/ jocn_a_ 00369 (2013).
32. Tobler, P. N., Christopoulos, G. I., O’Doherty, J. P., Dolan, R. J. & Schultz, W. Neuronal distortions of reward probability without
choice. J. Neurosci. 28, 11703–11711. https:// doi. org/ 10. 1523/ JNEUR OSCI. 2870- 08. 2008 (2008).
33. Becker, G. M., DeGroot, M. H. & Marschak, J. Measuring utility by a single-response sequential method. Behav. Sci. 9, 226–232.
https:// doi. org/ 10. 1002/ bs. 38300 90304 (1964).
34. Watanabe, S., & Opper, M. Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular
learning theory.J. Mach. Learn. Res.,11(12) (2010).
35. Gelman, A., Hwang, J. & Vehtari, A. Understanding predictive information criteria for Bayesian models. Stat. Comput. 24, 997–
1016. https:// doi. org/ 10. 1007/ s11222- 013- 9416-2 (2014).
36. McElreath, R. Statistical Rethinking: A Bayesian Course with Examples in R and Stan (Chapman and Hall/CRC, 2018).
37. Luo, Y. & Al-Harbi, K. Performances of LOO and WAIC as IRT Model Selection Methods (Psychol. Test Assess, 2017).
38. Albarracín, D. & Wyer, R. S. e cognitive impact of past behavior: Inuences on beliefs, attitudes, and future behavioral decisions.
J. Pers. Soc. Psychol. 79, 5–22. https:// doi. org/ 10. 1037/ 0022- 3514. 79.1.5 (2000).
39. Driskell, J. E., Willis, R. P. & Copper, C. Eect of overlearning on retention. J. Appl. Psychol. 77, 615–622. https:// doi. org/ 10. 1037/
0021- 9010. 77.5. 615 (1992).
40. Grol, M. J., De Lange, F. P., Verstraten, F. A., Passingham, R. E. & Toni, I. Cerebral changes during performance of overlearned
arbitrary visuomotor associations. J. Neurosci. 26, 117–125. https:// doi. org/ 10. 1523/ JNEUR OSCI. 2786- 05. 2006 (2006).
41. Sutton, R. & Barto, A. Reinforcement Learning: An Introduction 2nd edn. (MIT Press A Bradford Book, 2018).
42. Fossati, P. et al. In search of the emotional self: An fMRI study using positive and negative emotional words. Am. J. Psychiatry 160,
1938–1945. https:// doi. org/ 10. 1176/ appi. ajp. 160. 11. 1938 (2003).
43. Johnson, S. et al. Neural correlates of self-reection. Brain 125, 1808–1814. https:// doi. org/ 10. 1093/ brain/ awf181 (2002).
44. Johnson, M. et al. Dissociating medial frontal and posterior cingulate activity during self-reection. Soc. Cogn. Aect. Neurosci.
1, 56–64. https:// doi. org/ 10. 1093/ scan/ nsl004 (2006).
45. Rd, L., Gr, F., Pm, C. & Rj, D. Neural activation during selective attention to subjective emotional responses. NeuroReport 8, 3969
46. Lane, R . et al. Neural correlates of levels of emotional awareness: Evidence of an interaction between emotion and attention in the
anterior cingulate cortex. J. Cogn. Neurosci. 10, 525–535. https:// doi. org/ 10. 1162/ 08989 29985 62924 (1998).
47. Lou, H. C. et al. Parietal cortex and representation of the mental self. Proc. Natl. Acad. Sci. 101, 6827–6832. https:// doi. org/ 10.
1073/ pnas. 04000 49101 (2004).
48. Maddock, R. J. e retrosplenial cortex and emotion: New insights from functional neuroimaging of the human brain. Tre nds
Neurosci. 22, 310–316. https:// doi. org/ 10. 1016/ S0166- 2236(98) 01374-5 (1999).
49. B eer, J. & Hughes, B. Self-enhancement: A social neuroscience perspective. In Handbook of Self-Enhancement and Self-Protection,
chap 2 1st edn (eds Alicke, M. D. & Sedikides, C.) 49–65 (e Guilford Press, 2020).
50. Strube, M. & Roemmele, L. Self-enhancement, self-assessment, and self-evaluative task choice. J. Pers. Soc. Psychol. 49, 981–993
51. Kivetz, R. e eects of eort and intrinsic motivation on risky choice. Market. Sci.https:// doi. org/ 10. 1287/ mksc. 22.4. 477. 24911
52. Apps, M. A., Grima, L. L., Manohar, S. & Husain, M. e role of cognitive eort in subjective reward devaluation and risky decision-
making. Sci. Rep. https:// doi. org/ 10. 1038/ srep1 6880 (2015).
53. Botvinick, M. M., Hustetler, S. & McGuire, J. T. Eort discounting in human nucleus accumbens. Cogn. Aect. Behav. Neurosci.
9, 16–27. https:// doi. org/ 10. 3758/ CABN.9. 1. 16 (2009).
54. Croxson, P. L., Walton, M. E., O’Reilly, J. X., Behrens, T. E. & Rushworth, M. F. Eort-based C ost-benet valuation and the human
brain. J. Neurosci. 29, 4531–4541. https:// doi. org/ 10. 1523/ JNEUR OSCI. 4515- 08. 2009 (2009).
55. Atkins, K. J., Andrews, S. C., Stout, J. C. & Chong, T.T.-J. Dissociable motivational decits in pre-manifest Huntington’s disease.
Cell Rep. Med. https:// doi. org/ 10. 1016/j. xcrm. 2020. 100152 (2020).
56. Brainard, D. H. e psychophysics toolbox. Spatial Vis. https:// doi. org/ 10. 1163/ 15685 6897X 00357 (1997).
57. Carpenter, B. et al. Stan: A probabilistic programming language. J. Stat. Sow. https:// doi. org/ 10. 18637/ jss. v076. i01 (2017).
58. Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423. htt ps:// do i . org/ 10. 1002/j. 1538- 7305. 1948.
tb013 38.x (1948).
59. Gelman, A. Prior distributions for variance parameters in hierarchical models (Comment on Article by Browne and Draper).
Bayesian Anal.https:// doi. org/ 10. 1214/ 06- BA117A (2006).
T.C. and S.B. were supported by the Australian Research Council (DP 180102383 to T.C. and S.B., DE 180100389
M.J., P.C., T.C. and S.B. conceived the experiment. M.J. conducted the experiment, analysed the results and wrote
the manuscript. All authors discussed the results and reviewed the manuscript.
e authors declare no competing interests.
Supplementary information e online version contains supplementary material available at https:// doi. org/
10. 1038/ s41598- 021- 88031-y.
Correspondence and requests for materials should be addressed to M.J.
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