## Introduction

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. Therefore, 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 findings 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 influence the probability or magnitude of future rewards1,2,3,4,5,6,7. Recent neurophysiological data have shown that such non-instrumental information is encoded by similar neural circuits as primary reinforcers5,8,9,10, 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 affective response to the information), and its cognitive value (the degree of uncertainty that viewing the information is expected to resolve)5,10,11,12.

Importantly, however, intrinsic biases and contextual factors may affect the contributions that each of these factors make to the overall value of an informational prospect11. The hedonic value of information may be particularly susceptible to bias. Typically, it is found that prospects that offer 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 findings in the fields of behavioural economics and cognitive psychology have repeatedly shown, individuals’ predictions of outcomes are often open to systematic biases and heuristics that may, in turn, affect 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 after the decision making process16,17,18,19,20,21,22,23. 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 curiosity are due to choice-induced modulation, or more indirectly through an increase in the subjective value of the chosen information.

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 probability of outcomes is crucial to the valuation of prospects, with higher probability of favourable outcomes leading to a higher valuation of a prospect27,28,29, 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 encoded as the signed difference 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 affected by the IOC31. This finding suggests that the probability of winning used in the computation of the RPE may differ from the probability of winning reported by participants31,32.

The question of whether subjective information value is affected 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 alternative lotteries with identical probabilities of winning systematically increased: (a) participants’ confidence in a winning outcome (measured through self-reported confidence 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 confidence 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 effect of agency on the factors determining the subjective value of information.

## Results

To assess the influence of choosing on information valuation, we manipulated participants’ perceived agency during a simple lottery, in which the decision to play a specific “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 et al.31 (see Fig. 1a). The participant’s selection was either approved (granting agency over the trial) or vetoed (removing agency from the trial). These lotteries utilised scrambled roulette wheels comprising segments of a winning colour and a non-winning colour. The three wheels on each trial were rotated versions of the same configuration 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 effects of agency on information value using two methods. First, participants rated their confidence 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. Their 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. The 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. This 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 computational models which were fit to the participants’ trial-wise bidding patterns. These models included a null model, which assumed no effect of agency on information-seeking behaviour, as well as a series of models that characterised differences 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 anticipating a positive outcome, or simply to the desirability of information.

### Agency increases win expectancy and information value

To assess whether participants’ subjective probability of a positive outcome was affected by their agency over the lottery, their confidence ratings were compared across agentic and non-agentic trials. A $$2 \times 4$$ 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 confidence 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, confidence ratings were an average of 2.04% higher when participants had agency over which lottery they played, indicating that this paradigm successfully elicited the IOC and replicated earlier findings14,31.

Next, we examined the influence of agency on the perceived value of information by assessing participants’ willingness to pay for non-instrumental information. A $$2 \times 4$$ 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, $$F(3, 114) = 49.92, p < 0.001$$ and agency, $$F(1, 38) = 14.27, p < 0.001$$, see Fig. 1c. There was also a significant interaction effect between the win-probability and agency, $$F(3, 114) = 4.41, p = 0.006$$. A post-hoc comparison of bid-magnitude across probabilities revealed that the difference between agentic and non-agentic bids was only significant for trials in which the probability of winning was 0.4, $$t(38) = 3.96, p = 0.001$$ or 0.6, $$t(38) = 2.92, p = 0.023$$ after Bonferroni corrections were applied.

These findings suggest that participants were willing to sacrifice a significantly 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 effect 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 five computational models. The first model assumed no effect of agency on information preference. Based on previous findings, this null model instead constructed predictions only from a weighted combination of the win-probability, the uncertainty of the prospect, and a subject-specific constant (see “Methods”).

We also constructed a series of alternative models to assess different characterisations of the contributions of agency to information value. In the probability-shifted model, shifts in the subjective probability of winning across agentic and non-agentic trials were permitted, such that the probability of winning on agentic trials was shifted by the magnitude of an additional subject-specific free parameter.

In addition, we constructed three further models to test for changes in the subjective valuation of each constituent parameter of the null model. These 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 fits, 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 fit measure. It was chosen over other information criteria (e.g., the Deviance Information Criterion) as it has a higher power rate and does not assume the posterior distribution to be Gaussian36,37. The WAIC suggests that the agency uncertainty model is preferred, with the null model underperforming compared to each of the other models, suggesting that differences 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 shift in the subjective probability of a positive outcome (see Table 1). Further, the probability-shift parameter of the probability-shifted model demonstrated poor adherence to the reported increase in subjective win probability, as shown by their weak correlation, $$r(38) = -0.10$$. Posterior predictive checks demonstrated an excellent fit of the agency uncertainty model to the data (Supplementary Fig. S1). The final 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 effect 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 in situations involving agency.

## Discussion

In this study, we assessed how choosing a prospect affects 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 findings that agency over choosing one’s lottery increased the perceived confidence in a positive outcome of the lottery31. Consistent with previous findings, 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. This 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. The results were best explained through an increase in the subjective value of resolving uncertainty for agentic prospects. These findings are not directly explained by existing theories of information-seeking behaviour11.

The 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. The cognitive value of an information signal is determined by the extent to which that information signal is able to reduce the uncertainty surrounding 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 often inform us of the outcomes of our own decisions or actions, and therefore may affect 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 predictions 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 significant 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 experiment could not expect to extract more cognitive value from information about lotteries under agentic conditions. 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. The 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 findings 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 environment in which one does not possess agency may not be perceived as useful, because we cannot use such information to inform future decisions. Though 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 findings. For example, choice-induced preference change16,17,18,19,20,21,22,23,24 alone cannot account for the present findings, 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 effects of an increase in the subjective value of the associated rewards (consistent with the probability-shifted model). The underperformance of these models relative to the agency uncertainty model indicates 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 motivation 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 information31,42,43,44,45,46,47,48. However, information-seeking with the goal of self-enhancement typically involves an active search for flattering (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 probability of winning, as conceptualised by the agency reward model. The poor fit 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 effect sizes. This highlights the comparative importance of the primary information-seeking drivers, such as the anticipation of positive outcomes. 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 dissatisfaction with losing control in general. Future studies could consider a truly passive control condition in which no agency exists in the first place; however, this might come with the danger of task disengagement. These findings also leave open further questions about whether subjective changes in reward value and probability influence the value of non-instrumental information about those rewards. One example of this is effort discounting, in which the value of a reward is reduced when it is earned through effortful, as opposed to non-effortful means51,52,53,54,55. 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 effort53,54. Investigating information-seeking behaviour in this context would provide insight into whether the findings 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. This is exemplified by the poor correlation between the probability-shift parameter of the probability-shifted 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 fits, as very different combinations of the parameters lead to similar model performance, making model identification difficult and inferences about such models unreliable.

In sum, the findings of the present study demonstrated an increase in the perceived value of resolving uncertainty about the post-decisional outcomes of prospects when those prospects are selected through agentic means, as opposed to when agency is removed. This 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.