Exerting effort for non-instrumental information under risk

Abstract

People constantly invest effort to seek information in everyday life, even if the information is of no instrumental value for the decision at hand. However, the mechanism underlying people’s willingness to exert effort in exchange for information remains unclear. Previous work has suggested that desirability and uncertainty are two key factors influencing information-seeking, but few studies have tested if these factors are important when exerting physical effort in exchange for information. Additionally, it remains unknown whether different kinds of uncertainty, i.e., risk and ambiguity, have differential impacts. In the current study, we developed a novel information-seeking task to quantify the value of non-instrumental information using incentive-compatible physical effort to examine how effort changes as a function of desirability and uncertainty. Across two studies (N = 123), we found that people’s willingness to exert effort is positively associated with outcome expected value under both risk and ambiguity. Additionally, people exert more effort when outcome distribution uncertainty increases in risky situations, but are insensitive to ambiguity, except when facing extreme ambiguity. Our results demonstrate an unexpected dissociation. Humans will engage in effort-based information-seeking, even for non-instrumental information, when facing risk. In contrast, they show a much lower willingness to expend effort to resolve non-instrumental ambiguity.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-43803-2.

Working just to know: exerting effort for non-instrumental information under risk

Humans are infovores. From listening to the weather forecast to searching for answers to trivia questions, we gather information passively and actively in everyday life. In many cases, seeking information can help people learn about the world around them and guide them to make adaptive decisions^1–5. In other instances, people seek information with no instrumental value,people desire to be ‘in the know’ even when the information does not offer clear benefits or allow us to alter future outcomes^6–10. These observations highlight that, for humans, non-instrumental information is intrinsically valuable, valued enough that people are willing to pay^11–13, endure pain or uncomfortable situations^12–15 and exert effort^16,17 to obtain this kind of information.

Active information seeking in real life is often effortful and effort is usually viewed as aversive¹⁸. How much effort are people willing to invest to access information? In this study, we examine two key factors that might influence the willingness of individuals to exert physical effort to gain non-instrumental information. Previous information-seeking research using measurements other than physical effort, such as willingness to pay, has offered multiple accounts for the appetite of individuals for non-instrumental information, with the two major accounts focusing on desirability and uncertainty^6,19. The desirability-based argument - sometimes referred to as valence-based in the literature - suggests that people seek information more when they expect that a desirable outcome (e.g., winning a lottery) is more likely to occur²⁰. This is because gaining advanced information could change people’s belief state and people overall prefer to move into positive belief states associated with positive life experiences^21,22,also see²³and²⁴ for evidence against the desirability-based account). The desirability of information can be influenced by both the probability and the magnitude of the good outcome, however few studies have assessed the effect of the outcome magnitude and the conclusion remains elusive^26,27. Besides pursuing a positive belief state, people also seek non-instrumental information to reduce uncertainty^8,9,28,29. Given that people generally find uncertainty aversive³⁰, resolving uncertainty is rewarding. It has also been argued that the effects of desirability and uncertainty resolution are moderated by the time interval between information and outcome delivery and can result in either information seeking or avoidance behavior patterns depending on the delay length³¹. Though the majority of existing work suggests that both desirability and uncertainty drive information-seeking^32,33, some studies have only found supporting evidence for an uncertainty-based account^8,24.

The current study, therefore, aims to test whether desirability- and uncertainty-based motives coexist in effort-based information-seeking. Previous work in the effort domain has shown that people are willing to exert effort in exchange of social feedback from peers¹⁷ and information about lottery outcome¹⁶, supporting these two accounts. However, the existing work either did not examine both motives together¹⁷ or did not systematically vary parameters related to these motives¹⁶. Following previous research⁶, we construct a non-instrumental information-seeking scenario in which participants can exert effort for information about the outcome of a lottery that they are endowed with. Specifically, we examined physical effort exertion in the study. Previous literature on effort has suggested that physical and cognitive effort shares neural substrates³⁴ and people’s willingness to exert physical and cognitive effort correlates³⁵. Together, these findings suggest that our results may extend to the cognitive effort domain. To assess the desirability-based account, we examine the relationship between willingness to exert effort and the expected value of the lottery. Assuming that winning is associated with positive feelings as well as positive belief states, we expect to observe a positive association between expected value of the lottery and effort exertion. Specifically, we vary both winning probability (Experiments 1 and 2) and outcome magnitude (Experiment 2) to assess if people are sensitive to expected value of the outcome beyond the chance to win.

To examine a role for uncertainty, we further distinguish among types of uncertainty. Uncertainty is a multidimensional construct and can be broken down into two categories: risk and ambiguity^36,37. Risk refers to situations of uncertainty with known probabilities (e.g., the outcome of throwing a well-balanced die). Under risk, the degree of uncertainty refers to the dispersion of all the possible outcomes³⁸, and we expect to find a positive relationship between the amount of effort people are willing to exert and the standard deviation of a given lottery’s outcome distribution. Ambiguous situations, on the other hand, have unknown probabilities (e.g., the probability of rain in the next hour). Uncertainty level under ambiguity reflects how much probability is unknown. Therefore, we expect that the amount of effort increases as the amount of hidden probability increases. Although previous work on effort-based information-seeking has included ambiguous scenarios where information is partially hidden¹⁶, they did not examine the impact of ambiguity level or compare information-seeking under risk and ambiguity. Existing literature on economic decision-making has suggested that people’s attitude towards risk and ambiguity is dissociable³⁹, reflected in distinct developmental trajectories^40,41 and neural dissociations^42–44. Specifically, people tend to avoid options associated with ambiguity more than risk, implying that people are more averse to ambiguity than risk. Given the differential attitude towards risk and ambiguity, we hypothesize that people will be more willing to exert effort for information to resolve ambiguity to a greater extent than risk.

Experiment 1

Method

Transparency and openness

We report how we determined our sample size, all data exclusion (if any), and all manipulations in the study. Deidentified data and data analysis code are publicly available at https://osf.io/2mze4⁴⁵. Data were analyzed using R, version 4.4.0 (R Core Team, 2023) with packages lme4⁹⁵ and ggplot, and Python (version 3.11.9) with packages scipy, numpy, and pandas.

Participants

Seventy-one participants (20 participants reported their genders as male and 48 as female, 3 participants did not report their genders; 18 White, 2 Black, 41 Asian, 7 multiracial, 3 unreported; 4 Hispanic) were recruited from the Harvard study pool for students and the Cambridge, MA local area. Our sample size was decided by power analysis based on pilot data, which suggested that N >= 60 is needed to achieve a power of over 80%. Participants were excluded if they failed to pass the comprehension check questions administered at the end of the experiment, resulting in 62 participants included in the final data analysis (17 participants reported their genders as male and 42 as female, 3 participants did not report their genders; 17 White, 2 Black, 34 Asian, 6 multiracial, 3 Unreported; 3 Hispanic). Participants had no history of disease affecting cognitive function, normal or corrected vision, English fluency, and no alcohol or drug dependency. Participants were asked to refrain from drugs, alcohol, caffeine, or nicotine within the 2 hours prior to the lab visit. We restricted our participants to the young adult population (age range: 18-35; M = 24.28, SD = 4.32) to minimize the potential impact of age on effort exertion and information seeking^46–49. Participants were compensated with $30 or research credit for their visit in addition to a monetary bonus based on the selected endowed gamble outcome and a monetary bonus for the grip calibration. All participants gave written informed consent before the experiment and the study was approved by Harvard University Committee on the Use of Human Subjects (IRB19–0789). All methods were performed in accordance with Harvard’s guidelines and regulations.

Experiment design

Maximum 3-second grip force calibration

Before the beginning of the experiment, participants completed a calibration task to quantify their maximum grip force. They were instructed to squeeze a hand dynamometer to meet increasingly difficult benchmarks for three seconds. The calibration was conducted in a stepwise fashion (see Supplemental Materials for details). Participants were monetarily incentivized and could receive a monetary bonus ($2 max) proportional to their maximum grip force. The monetary incentive aims to keep participants engaged and motivated to exert near-maximal effort during the calibration phase. The same calibration procedure was repeated after the main experiment to measure any change in maximum grip force, which was identically monetarily incentivized.

Information-seeking task

After the initial grip force calibration, participants completed an information-seeking task, during which they saw a series of lotteries and reported how much effort they were willing to exert in exchange for the lottery outcome.

There were two types of lotteries: risk and ambiguity, both of which have possible outcomes of $0 and $10. Risky lotteries showed the exact probability of winning $10, represented by a bar with different ratios of red and blue parts (Fig. 1 ‘Lottery Display’ column). Ambiguous lotteries were represented by a bar with equal parts of red and blue shown and a gray bar hiding the rest of the lottery, with equal probability of being any combination of red and blue. Participants were endowed with the lotteries (i.e., they could not opt out) and were told that one of them would be randomly selected to be realized at the end of the experiment. For example, if the selected trial is a lottery with 50% of winning $10 and 50% of getting $0, the computer will determine the lottery outcome by generating a random number between 0 and 1 and compare it with the winning probability. If the random number is larger than the winning probability, the participant wins the lottery and receives a $10 bonus, otherwise they receive $0 from this part of the experiment. This incentive structure is referred to as random lottery incentive system⁵⁰ and has been widely used in decision-making studies^44,51–54 to ensure participants treat each decision independently and as a decision with real consequences⁵⁵.

Fig. 1.

Information-seeking task schematics. The information-seeking task is composed of five stages. During the lottery display, participants are presented with the trial-unique lottery, which can be either risky or ambiguous (occluded by a gray bar). Participants then use the hand dynamometer to indicate how much effort they are willing to exert in exchange of information about the lottery outcome. Their highest effort level during this phase is recorded and is termed as their effort bid. After placing the bid, the computer runs the BDM auction by generating a random number (i.e., price) and comparing it with participants’ effort bid. If the price is higher than the bid, the bid is executed – the participant will exert the amount of effort indicated by the price for a consecutive 3 seconds and see the lottery outcome after the bid execution phase. If the price is lower than the bid, the participant loses the bid and have to wait for a short period of time before the delivery of no-information. See Methods section for a detailed explanation of experiment stages.

On each trial, participants saw a unique lottery and had the opportunity to then ‘bid’ on seeing the lottery outcomes using the hand dynamometer (Fig. 1 ‘Effort Bid’ column). This bidding process started with 5 seconds to squeeze the dynamometer as hard as they would be willing to then hold for three seconds in exchange for the information. The highest effort level during the 5 second period was recorded as their bid, shown on the screen as a gray line.

We adapted the Becker–DeGroot–Marschak (BDM) auction⁵⁶, Fig. 1 ‘BDM Auction’ and ‘Bid Execution/Waiting’ columns) to ensure that we elicit the true preference of effort exertion in pursuit of non-instrumental information. To determine whether the bid is successful, a random effort price, uniformly distributed between 0 and their maximum 3-second grip force, was generated by the computer and is compared to the participant’s bid. If the bid was lower than the effort price, the participant lost the bid and would not receive the information. If the bid was higher than the effort price, the participant won the bid and would receive the information after paying the price (i.e., holding the effort price for consecutive 3 seconds). The information was delivered as a square filled with the outcome color (blue/red) and text indicating outcome amount ($0/$10; Fig. 1 ‘Outcome Display’ Column). If the participant didn’t win, they would receive no information on the outcome, which was presented as a square filled with noninformative color (purple) and text indicating no-information ($?). When losing the bid, the participant needed to wait for a short period of time before the delivery of no-information to match the time spent on effort exertion in successful bidding trials. It is worth emphasizing that the outcomes of all lotteries presented to the participant were predetermined and were independent of participants’ effort. Therefore, participants’ willingness to exert effort to receive the outcome in advance has no bearing on the final payoff i.e., the information is non-instrumental.

Experiment procedure

Upon arrival, participants first went through the calibration task, during which they were not aware of the upcoming information-seeking task to prevent them from strategically exerting lower effort than their maximum capacity. Grip force was recorded using a hand dynamometer (Biopac TSD121B-MRI) at a sample rate of 60 Hz. Real-time visual feedback of the force level was provided during the task using custom script in Python and Biopac Hardware API. After finishing the calibration, each participant had their hand wrapped to the dynamometer using soft stretchy wrap to ensure that their hand position on the dynamometer stayed constant for the duration of the experiment. Comprehension checks and practice trials were used to ensure that participants fully understood the task (see Supplemental Material for details). During the information-seeking task, participants encountered risky and ambiguous lotteries. To avoid potential learning across trials, each unique lottery is seen once during the entire experiment. A unique risky lottery is defined by its winning amount ($10), winning color (red or blue) and winning probability. The winning probability spans from 20% to 80% with a step size of 2% and excludes 30%, 40%, 50%, and 60%, which were used during practice. This resulted in 54 unique risky lotteries. As for ambiguity, a unique lottery is defined by its winning amount ($10) and occluded probability. The occluded probability follows the same distribution as the winning probability of the risky lotteries. Instead of showing two lotteries with the same occluded probability and different winning colors, we choose to include only one lottery per occluded probability because we want to prevent participants from learning the underlying probability of the ambiguous lotteries from previous outcome (e.g., if participants have won a 80% occluded red-winning ambiguous lottery and received the outcome information, they may increase their estimate of the occluded winning probability and behave differently next time they see the 80% blue-winning occluded lottery). This resulted in 27 unique ambiguous lotteries. The participants completed 81 lottery trials (54 risky and 27 ambiguous) split into three blocks and could rest as long as they want between blocks. After the information-seeking task, the participants completed the maximum 3-second grip force calibration again. Following the entire task procedure, participants completed a post-task survey and were debriefed. In the post-task survey, participants reported their gender by choosing among options male, female, and other. They reported their race by responding to the question ‘Which of the following describes your race? (Please select all that apply)’ and chose among options American Indian/Alaska Native, Asian, Black/African American, Native Hawaiian/Other Pacific Islander, and White/Caucasian. They reported their ethnicity by responding yes or no to the question ‘Are you Hispanic/Latino?’

Analytical plan

We quantified the value of outcome information via physical effort by measuring the peak grip force participants exerted during the bidding phase. This indicates how much effort participants indicate that they are willing to exert in exchange for the information resolving uncertainty irrespective of whether the bid is realized. To account for measurement bias (e.g., the hand dynamometer readout may drift across blocks and be slightly non-zero when no effort is exerted), we recorded the readout of the dynamometer at the beginning of each block (i.e., block baseline) and subtracted it from the peak grip force to correct for the baseline drift. To account for individual differences in strength, we calculated normalized effort bid by dividing the baseline-corrected peak grip force with the maximum 3-second effort measured in the calibration phase prior to the information-seeking task.

Based on previous literature^6,33, we consider a list of factors related to desirability and uncertainty that are likely to influence information-seeking behavior, including expected value (EV), outcome uncertainty, and ambiguity level. EV is calculated as p(win)*10, since all trials are associated with two possible outcomes: $0 and $10. Outcome uncertainty is operationalized as the standard deviation of the outcome Bernoulli distribution and is calculated as sqrt(p(win)*(1-p(win)))*10 i.e., reflecting the outcome dispersion. The distribution follows an inverted U shape, reaching maximum when p(win) = 0.5 i.e., when there is equal probability of getting $0 and $10. There is no linear relationship between EV and outcome uncertainty (r = 0, Supplemental Figure 1), which is designed to minimize collinearity when entering these two regressors into the same model. For all risky gambles, the ambiguity level is held at 0. For ambiguous gambles, EV and outcome uncertainty are held at $5 and 5 because the expected winning probability is 0.5 across all ambiguous situations. We also compared the willingness to exert effort under risk and ambiguity by predicting bid using a categorical variable indicating trial type (risk/ambiguity). To allow a fair comparison, this analysis includes all ambiguous trials and a subset of risky trials where the winning probability is equal to 50%. To account for the potential effect of fatigue, trial number was included in all analyses as a covariate. Age was also included as a covariate to control for the potential impact of age on effort exertion. The regression analyses focus on non-opt-out trials, defined as normalized effort bid >= 0.2 (n = 3661; 72.9% of all trials). This definition of opt-out trials is consistent with prior work^17,57.

All regression analyses were conducted using linear mixed-effects models allowing for subject-specific random intercept and slopes. Dependent variables were log transformed to account for their non-negative nature and correct for non-normality of model residuals⁵⁸.

Results

Overall, people are willing to exert 55.9% (SD = 30.0%) of their maximum 3-second effort for information about lottery outcomes. We compared people’s normalized effort bid to 0.2, which is the cutoff used to classify opt-out trials, and found that the normalized effort bid is significantly higher than 0.2 (one sample t-test against 0.2: t(61) = 9.4, p < .001; Fig. 2). This indicates that on average, participants are willing to use the hand dynamometer to bid on the non-instrumental information—the lottery outcomes—as predicted in our initial hypothesis.

Fig. 2.

Effort bid across risk and ambiguity in Experiment 1. Each black dot indicates the average normalized effort bid for each participant. The red dot represents the mean effort bid across all participants for each experiment. Error bars represent 95% confidence intervals. Y-axis represents normalized effort bid and is calculated as dividing baseline-corrected peak force during the effort bid phase by maximum 3-second effort measured in the calibration task. Note that bids may thus exceed 100%. Blue dashed line represents the cutoff for opt-out trials.

We then examined the factors influencing effort-based information-seeking behavior by entering both expected value and outcome uncertainty into the model to predict effort bid (see Supplemental result for analysis on opt-out trials). The data suggests that people’s effort bid is influenced by both expected value (β = 0.039, SE = 0.010, 95% CI [0.020, 0.059], p < .001; Table 1) and outcome uncertainty (β = 0.014, SE = 0.005, 95% CI [0.004, 0.025], p = .008; Fig. 3A). In other words, participants were willing to raise their bid as the likelihood of winning $10 or the uncertainty in outcome distribution went up. In contrast, the effort bid was not sensitive to ambiguity level (β = 0.003, SE = 0.011, 95% CI [-0.018, 0.024], p = .784; Fig. 3B), suggesting that the bid was consistent regardless of how ambiguous the lottery was. Additionally, we found that people were willing to exert more effort to receive information to resolve risk than ambiguity (β = 0.071, SE = 0.035, 95% CI [0.003, 0.139], p = .040).

Table 1.

Regression coefficients for expected value, outcome uncertainty, ambiguity, and gamble type when predicting willingness to exert effort in Experiment 1.

	Statistic
Model and effect	β ± SE	95% CI	t	p
Log(effort bid) ~ Expected Value + Outcome SD + (Expected Value + Outcome SD |ID)
Expected Value	0.039 ± 0.010	[0.020, 0.059]	3.942	<.001***
Outcome SD	0.014 ± 0.005	[0.004, 0.025]	2.672	.008**
Log(effort bid) ~ Ambiguity + (Ambiguity |ID)
Ambiguity	0.003 ± 0.011	[-0.018, 0.024]	0.275	.784
Log(effort bid) ~ Gamble Type + (Gamble Type |ID)
Gamble Type	0.071 ± 0.035	[0.003, 0.139]	2.054	.040*

All independent variables were standardized (z scored). The first model includes all trials with risky lotteries, and the second model includes all trials with ambiguous lotteries. The third model includes all trials with ambiguous lotteries and trials where the risky lottery has a winning probability of 50%. All models include trial number and age as covariates (regression results not shown). SD = standard deviation. SE = standard error. *p<.05; **p < .01; ***p < .001.

Fig. 3.

Normalized effort bid under risk (A) and ambiguity (B) in Experiment 1. Points indicate mean estimate and error bars indicate 95% confidence intervals. Expected value is computed as p(win)*10. Ambiguity level refers to the probability occluded by the gray bar. The ambiguity level for all risk lotteries is 0. Y-axis represents normalized effort bid and is calculated as dividing baseline-corrected peak force during the effort bid phase by maximum 3-second effort measured in the calibration task. Note that bids may thus exceed 100%.

Experiment 2

In Experiment 1, we found that people overall are willing to exert physical effort in exchange for non-instrumental information and that effort exertion positively correlates with EV under risk. It remains unclear whether people are sensitive to change in EV under ambiguity. Relatedly, in Experiment 1 EV perfectly correlates with winning probability since the winning amount is fixed ($10) for all lotteries. Therefore, Experiment 2 systematically varied the winning amount associated with each lottery with a goal of further testing the relationship between EV and effort-based information-seeking under risk and ambiguity. Experiment 2 was also designed to keep EV and outcome uncertainty orthogonalized while manipulating winning amount since they were entered into the same model to examine the impact of desirability- and uncertainty-based accounts on effort exertion. In addition, although we found that effort exertion does not correlate with ambiguity level, the raw behavioral data (Fig. 3B) seemed to hint at a quadratic relationship between ambiguity and effort, with a positive/negative linear trend when ambiguity approached the lower/upper bound of the parameter space. To further examine the effect of ambiguity on willingness to work, we sampled from a wider range of ambiguity levels in Experiment 2.

Method

Transparency and openness

The experiment design, sample size, exclusion criteria, and primary data analysis plan for Experiment 2 were preregistered at https://aspredicted.org/1T3_XQJ.

Participants

We intended to get a sample size comparable to that in Experiment 1 and recruited 67 participants (17 participants reported their genders as male, 49 as female, and 1 as nonbinary; 28 White, 2 Black, 31 Asian, 5 multiracial, 1 unreported; 6 Hispanic; age range: 18-32; M = 22.79, SD = 3.62) from the student pool and local area. All participants have given their informed consent before participating the experiment and the study was approved by Harvard University Committee on the Use of Human Subjects (IRB19–0789). All methods were performed in accordance with Harvard’s guidelines and regulations. The recruitment requirements, compensation, and exclusion criteria were the same as Experiment 1. The final sample includes 61 participants (15 participants reported their gender as male, 45 as female, and 1 as nonbinary; age M = 22.78, SD = 3.56; 25 White, 2 Black, 28 Asian, 5 multiracial, 1 Unreported; 6 Hispanic).

Experiment design

The experiment procedure is similar to Experiment 1 with the following modifications on the lottery set.

For risky lotteries, participants encounter 54 unique lotteries with winning amount varying between 10 to 15 and winning probability varying between 0.4 to 0.9 (see Supplemental Table 1 for a full list of the combination of winning amount and probability). This lottery set was selected not only because we wanted to introduce varying levels of the winning amount, but also because we wanted to orthogonalize EV and outcome uncertainty to reduce the collinearity when entered into the same regression model (r = .08; Supplemental Figure 1).

For ambiguous lotteries, the occluded probability spans from 4% to 96% with a step size of 4%. Ambiguous lotteries with occluded probability of 40% and 60% are reserved for practice and are excluded. Each ambiguous lottery is randomly paired with a winning amount of $10 or $15, resulting in 22 unique ambiguity trials.

Analytical plan

The analysis plan for Experiment 2 is similar to Experiment 1 with the following additions, which are made possible because the current lottery set had a varied winning amount. First, for risky lotteries, we construct a set of linear mixed-effects models predicting effort exertion using all possible additive combinations (including the subset) of three regressors: EV, winning amount, and winning probability. We then compare the model fit using Bayesian information criterion (BIC) to find the model that describes people’s willingness to work best. Second, we provide an alternative operationalization of outcome uncertainty using outcome entropy: -p(win)*log₂(p(win)) - (1-p(win))*log₂(1-p(win)). Compared to outcome SD, entropy is not affected by numerical values of the payout. It can be distinguished from outcome SD (though highly correlated, r = 0.6) in Experiment 2 due to the varying level of winning amount. Third, for ambiguity lotteries, we predict effort exertion using both ambiguity level and winning amount. Fourth, for all models involving ambiguous lotteries, we fit them with both the full ambiguity range (4%-96%) and the range comparable to Experiment 1 (20%-80%). Similar to Experiment 1, we focus on non-opt-out trials (n = 3520, 75.9% of all trials). We also excluded trials where the block baseline > 0.5 (n = 2), which implies technical difficulty in calibrating the hand dynamometer prior to the start of the block. This cutoff was also applied to Experiment 1. No block baseline exceeds 0.5 in Experiment 1, therefore no trial was excluded based on this criteria in that experiment. It may also be worth noting that the calculation of EV and outcome distribution standard deviation is p(win)*winning_amount and sqrt(p(win)*(1-p(win)))*winning_amount because the winning amount is not fixed at $10.

Results

Across all trials, we find that people are willing to exert effort in exchange for information about lottery outcomes (M = 0.518, SD = 0.198; one sample t-test against 0.2: t(60) = 12.6, p < .001; Supplemental Figure 2). This result replicates Experiment 1’s findings, suggesting that people are willing to expend effort to obtain non-instrumental information under risk and ambiguity.

Next, we examine whether people’s decision to exert effort to resolve risk is sensitive to EV, winning amount, and winning probability. We ran separate models for these regressors and found that both EV and winning amount are positively associated with willingness to work (β_EV = 0.042, SE = 0.013, 95% CI [0.016, 0.068], p = .002; β_{winning amount} = 0.042, SE = 0.010, 95% CI [0.023, 0.062], p < .001; Fig. 4A and B). Model comparison suggests that the model with EV and winning amount predicts participants behavior the best (Supplemental Table 1), indicating that people are more motivated to seek information when facing a lottery with larger EV as well as with a larger possible winning amount. When it comes to outcome uncertainty, we entered both expected value and outcome uncertainty into the same model and the results also suggest that people are sensitive to outcome uncertainty (β = 0.035, SE = 0.014, 95% CI [0.008, 0.062], p = .001; see Supplemental Result for analysis on opt-out trials), consistent with Experiment 1. The results also hold if we operationalize outcome uncertainty using outcome entropy (β = 0.042, SE = 0.014, 95% CI [0.014, 0.069], p = .003; Table 2), controlling for the effect of expected value.

Fig. 4.

Normalized effort bid under risk (left and middle) and ambiguity (right) in Experiment 2. Points indicate mean estimate and error bars indicate 95% confidence intervals. Expected value is computed as p(win)*winning_amount. Ambiguity level refers to the probability occluded by the gray bar. The ambiguity level for all risk lotteries is 0. The blue vertical lines indicate the ambiguity range used in Experiment 1 (20%-80%). Y-axis represents normalized effort bid and is calculated as dividing baseline-corrected peak force during the effort bid phase by maximum 3-second effort measured in the calibration task. Note that bids may thus exceed 100%.

Table 2.

Regression coefficients for expected value, winning amount, winning probability, and outcome uncertainty when predicting willingness to exert effort in Experiment 2 under risk.

	Statistic
Model and effect	β ± SE	95% CI	t	p
Log(effort bid) ~ Expected Value + (Expected Value |ID)
Expected Value	0.042 ± 0.013	[0.016, 0.068]	3.149	.002**
Log(effort bid) ~ Winning Amount + (Winning Amount |ID)
Winning Amount	0.042 ± 0.010	[0.023, 0.062]	4.362	<.001***
Log(effort bid) ~ Winning Probability + (Winning Probability |ID)
Winning Probability	0.024 ± 0.014	[-0.003, 0.052]	1.729	.084
Log(effort bid) ~ Expected Value + Outcome SD + (Expected Value + Outcome SD |ID)
Expected Value	0.035 ± 0.014	[0.008, 0.062]	2.552	.001**
Outcome SD	0.037 ± 0.012	[0.014, 0.060]	3.106	.002**
Log(effort bid) ~ Expected Value + Outcome Entropy + (Expected Value + Outcome Entropy |ID)
Expected Value	0.059 ± 0.013	[0.34, 0.085]	4.498	<.001***
Outcome Entropy	0.042 ± 0.014	[0.014, 0.069]	3.007	.003**

All independent variables were standardized (z scored). All models include all trials with risky lotteries. All models include trial number and age as covariates (regression results not shown). SD = standard deviation. SE = standard error. *p<.05; **p < .01; ***p < .001.

When it comes to ambiguity, we find that people exert more effort when the ambiguous lottery has a higher EV (β = 0.050, SE = 0.013, 95% CI [0.025, 0.076], p < .001; Table 3). With a set of lotteries where ambiguity levels ranging from 4% to 96%, we also find a positive association between ambiguity level and effort exertion (β = 0.038, SE = 0.015, 95% CI [0.008, 0.068], p = .014; Fig. 4C). If we restrict the analysis to ambiguity level between 20% and 80% - similar to Experiment 1 – the coefficient of ambiguity level is no longer significant (β = 0.014, SE = 0.015, 95% CI [-0.015, 0.044], p = .331; Fig. 4C). This result implies that extreme ambiguity is important in detecting the linear upward trend between ambiguity level and willingness to work. Finally, when comparing effort bid for ambiguous lotteries and risky lotteries with winning probability of 50%, people exert less effort for information resolving risk than ambiguity (β = -0.060, SE = 0.028, 95% CI [-0.115, -0.006], p = .030;), which is in contrast to Experiment 1. This effort exertion difference disappears (β = -0.019, SE = 0.032, 95% CI [-0.082, 0.044], p = .554) when comparing risky lotteries to ambiguous lotteries with moderate ambiguity level (20%-80%) Table 4.

Table 3.

Regression coefficients for ambiguity level and expected value when predicting willingness to exert effort in Experiment 2 over full range of ambiguity and middle-range ambiguity.

	Statistic
Model and effect	β ± SE	95% CI	t	p
Log(effort bid) ~ Ambiguity + Expected Value+ (Ambiguity + Expected Value |ID)
Full range of ambiguity (4%-96%)
Ambiguity	0.038 ± 0.015	[0.008, 0.068]	2.452	.014*
Expected Value	0.050 ± 0.013	[0.025, 0.076]	3.824	<.001***
Middle range of ambiguity (20%-80%)
Ambiguity	0.014 ± 0.015	[-0.015, 0.044]	0.973	.331
Expected Value	0.063 ± 0.014	[0.035, 0.091]	4.438	<.001***

All independent variables were standardized (z scored). The first model includes all trials with ambiguous lotteries, and the second model includes trials where the ambiguous level of the lottery falls between 20% and 80%. All models include trial number and age as covariates (regression results not shown). SE = standard error. *p<.05; ***p < .001.

Table 4.

Regression coefficients for gamble type and expected value when predicting willingness to exert effort in Experiment 2 over full range of ambiguity and middle-range ambiguity.

	Statistic
Model and effect	β ± SE	95% CI	t	p
Log(effort bid) ~ Gamble Type + Expected Value + (Gamble Type + Expected Value |ID)
Full range of ambiguity (4%-96%)
Gamble Type	-0.060 ± 0.028	[-0.115, -0.006]	-2.168	.030*
Expected Value	0.043 ± 0.010	[0.024, 0.063]	4.392	<.001***
Middle range of ambiguity (20%-80%)
Gamble Type	-0.019 ± 0.032	[-0.082, 0.044]	-0.592	.554
Expected Value	0.064 ± 0.015	[0.036, 0.093]	4.404	<.001***

All independent variables were standardized (z scored). The first model includes trials where either the lottery is ambiguous or the lottery is risky and has a winning probability of 50%. The second model includes trials where either the ambiguous level of the lottery falls between 20% and 80% or the lottery is risky and has a winning probability of 50%. All models include trial number and age as covariates (regression results not shown). SE = standard error. *p<.05; ***p < .001.

Discussion

Despite the ubiquity of effort exertion in information-seeking, the cognitive mechanisms behind deciding how much effort to exert remains unclear. The current study aimed to examine whether people are willing to exert effort in exchange of non-instrumental information, and if so, determine how the effort exertion differs under risk and ambiguity. Our analysis revealed a strong overall tendency to expend effort for information that does not impact the lottery outcome. This preference for information is positively associated with outcome desirability, which in the current experiment is operationalized as the expected value of the lottery outcome. In addition, people’s willingness to work is modulated by uncertainty differently depending on the type of uncertainty: while people exert more effort when outcome distribution uncertainty is high, they are not sensitive to ambiguity unless ambiguity is extremely low/high.

Our study is consistent with previous studies on information-seeking showing that people treat information as valuable even if it is of no use for future decisions¹⁰. In our study, we created the non-instrumentality by endowing participants with a unique lottery on each trial and letting them decide whether to see the outcome. In other words, participants do not choose whether to play the lottery. In addition, the independence of trials prevents people from using the information to learn about the task structure. Despite this, participants still choose to exert effort - on average more than half of their maximum effort - in exchange for information about the lottery outcome. Since people usually find effort aversive and tend to avoid it^{18,34,59–61}, this finding demonstrating people’s preference for non-instrumental information. Though it has also been suggested that people might seek information and/or exert effort to avoid boredom^62,63, we think it is unlikely in our case. If it is true, we would expect to find a relationship between previous auction outcome and current effort bid i.e., observing the outcome should temporarily reduce boredom and lead to a reduced subsequent desire to exert effort. Our data is not consistent with this prediction (see Supplemental Result). Additionally, it cannot explain the result that people’s effort bid varies as a function of desirability- and uncertainty- related variables (see below).

This effort-based preference for non-instrumental information is not a mere constant. Instead, it is context dependent, fluctuating based on features related to the information sought. One prominent feature is the desirability of the outcome, which we quantified as the expected value of the lottery outcome. Experiment 1 suggested that under risky situations, if the information is more likely to reveal a positive outcome, people are more willing to exert effort to achieve it. Experiment 2 extended this finding in two important ways. First, we confirmed that the willingness to work is sensitive to the expected value of the outcome under different levels of winning amounts. Second, we validated the relationship between effort exertion and expected value in ambiguous scenarios, showing that people exert more effort for ambiguous lotteries associated with higher possible payoff. These findings are consistent with previous work quantifying information value using willingness to pay and subjective rating⁶, supporting a desirability-based account for non-instrumental information seeking. The relationship between effort and payoff magnitude is also in line with existing work on effort showing that the exertion of effort is influenced by expected reward^64,65. Compared to existing work showing null relationship between information-seeking and outcome magnitude in non-effort domain^26,27, our results suggest a distinction between information-seeking in effort vs. non-effort domain. One alternative explanation could be that people anticipate a positive relationship between required effort and reward even in situations where effort and reward are non-contingent⁶⁶. However, we deem this account unlikely because participants exert effort in exchange for non-instrumental information instead of for a real payoff. Our study also focused on people’s willingness to exert effort (i.e., effort bid) instead of the real effort exertion during the execution phase. Even if people mistakenly equate the information with reward and treat the effort bid as an effort realization, we would expect to see more opt-out trials when expected value is high since people should be more likely to avoid exerting effort if they anticipate a high effort cost⁵⁹. We did not find a positive association between expected value and decision to opt out (Supplemental Results), a result that appears to contradict the effort-reward correlation hypothesis. On the other hand, it may be worth noting that the current study tested the desirability-effort relationship in the gain domain - all the lotteries used in the experiment have non-negative outcomes. Though we would expect the overall positive association between expected value and effort applies to the loss domain, it is possible that the effort-based information-seeking pattern differs between gain and loss as previous work on information-seeking has suggested^6,67. In addition, there exists evidence showing that people actively seek information about negative outcomes^23,25,96. Therefore, future work should examine the desirability-effort relationship when the outcome has non-positive or mixed outcomes.

Besides desirability, uncertainty plays an important role in determining the willingness to work in exchange for non-instrumental information. The relationship between uncertainty and willingness to exert effort is further modulated by uncertainty type. Under risk, people are willing to exert more effort when they are more uncertain about the exact outcome. In other words, people are more motivated to exert effort in exchange of information when it reduces more uncertainty in their belief about the outcome. Future studies could employ more complicated lotteries (e.g., lotteries with more than two possible outcome) to independently set the winning probability and outcome uncertainty. When interpreting results from the current study, it is important to note that this uncertainty-effort relationship holds when expected value and outcome uncertainty are orthogonalized (both Experiments; Supplemental Figure 1), suggesting that desirability- and uncertainty-based accounts are dissociable and jointly influence people’s decision to seek information under risk.

When it comes to ambiguity, the effect of uncertainty on willingness to work is more nuanced. When examining people’s behavior in the moderate ambiguity range (i.e., 20%-80% of the lottery outcome is occluded, Experiments 1 & 2), we do not find a relationship between effort exertion and ambiguity level, while we observe a positive linear relationship when considering the full range of ambiguity (4%-96% of occluded probability, Experiment 2). In other words, our predicted positive uncertainty-effort relationship under ambiguity is only partially confirmed under extreme ambiguity situations. There are a few possible reasons to explain the differential effort-based information-seeking pattern under moderate and extreme ambiguity level. First, people may treat the group of low ambiguity lottery (e.g., < 20% occluded probability) the same as their risky counterpart (i.e., the risk lottery with 50% winning probability), thus demonstrating a distinct behavior pattern compared to other ambiguous lotteries. People’s behavior when facing low ambiguity is generally understudied, as the lowest ambiguity level used in previous decision-making work (e.g.^41,68,69) is usually bounded around 24% (e.g.,). Second, it is possible that people are less accurate in representing middle range ambiguity levels than more extreme levels, which could result in a step-wise response and only shows differential response when extreme ambiguity levels are included in the analysis. Future work could directly examine the similarity in the representations of different lotteries using techniques such as neuroimaging to test the above mentioned hypotheses.

Given existing work in economics that consistently shows people are more averse to ambiguity than risk⁴⁴, we also predicted that people are more motivated to exert effort to resolve ambiguity than risk. However, our data is inconsistent with this intuition and we did not find a systematic relationship between uncertainty type and effort exertion. These findings did not support earlier theoretical work linking information seeking with ambiguity aversion⁷⁰ but are in line with the recent paper where it shows that people’s risk attitude is independent of their preference for non-instrumental information resolving risk^65,71. We speculate that willingness to work can be influenced by perceived efficacy i.e., how likely people can achieve their goal through their own actions. Previous work has shown that the amount of effort people exert is sensitive to efficacy^65,97. It is possible that some people think that knowing the outcome of one ambiguous lottery does not meaningfully reduce ambiguity since the trial-wise lottery outcome is a single data point and is far from providing information about the overall distribution. Relatedly, people’s willingness to exert effort could also be influenced by the perceived instrumentality of the information, which is sensitive to the decision context⁷². In Experiment 1, since the winning amount is fixed and the risk level space is densely sampled (step size = 2%), people may think that knowing the risky outcomes help calibrate their subjective perception of probabilities, similar to the idea of learning from experience^73,74. Although we have made it clear that all lotteries are unique, people may have the illusion that learning about a specific risky gamble outcome (e.g., 30%) could inform them the outcome of other lotteries with similar probability (e.g., 32%) while still treating lotteries with different ambiguity levels independent from each other. Together, this may result in a higher valuation of information that resolves risk than ambiguity in Experiment 1. The varied winning amount in Experiment 2 may reduce the perceived instrumentality across risky lotteries, which could lead to an indifferent willingness to pay under risk and ambiguity. This hypothesis of the utility of learning the world - similar to the concept of cognitive utility in previous literature^10,75 - can be empirically tested by manipulating the possibility of encountering the exact same lottery again in the future, with one extreme case being participants always face the same lottery and the other extreme being they only interact with each lottery once i.e., the current experiment design. Zooming out, it is possible that motives other than desirability- and uncertainty-based accounts play a role in influencing people’s willingness to exert effort in exchange of non-instrumental information under both risk and ambiguity. For instance, similar to the utility of learning the world, the utility of predicting final payout could influence people’s effort exertion. Because the random lottery incentive system samples one lottery that the participant has encountered and realize its monetary outcome, the participant can obtain a more accurate estimation of the overall outcome distribution by seeking more information. In other words, although non-instrumental information is not useful for improving task performance, it can be useful for prediction, which is strongly associated with engagement⁷⁶. Future studies should also try to move beyond properties related to the lottery itself and investigate whether people’s willingness to exert effort is influenced by other factors, such as delay length³¹, temporal predictability⁷⁷, perceived importance⁷⁸ and the relevance of the information to oneself^79,80.

We were especially interested in studying effort-based information-seeking because it is closely related to information search behavior in naturalistic settings where information is not readily available upon request. Effort could reflect people’s motivation to engage in an activity, with previous work showing that people expend more physical and cognitive effort in exchange for larger monetary and social rewards^{17,57,81–85}, and better-quality advice⁸⁶. In our task, though participants do not need to search for information, they do need to exert a nontrivial amount of effort for a sustained period of time before they get access to the information. To ensure that our measure reflects participants true desire to exert effort, we incorporated a standard economic auction paradigm - BDM auction - in our task. BDM auction is a mechanism designed to elicit the subjective value of the good for the bidder and have been widely used in decision-making literature to measure valuation of both concrete and abstract constructs such as reward, effort, craving, and self-control^87–91. To our knowledge, this is the first time that a BDM auction has been applied to the effort domain, which shows a promising venue for future studies to measure the subjective value in the unit of effort. Specifically, it would be interesting to apply the current paradigm to measure the value of non-instrumental information in units of cognitive effort, which is admittedly harder to measure given its covert nature^61,92. We presume that our findings in physical effort would apply to the domain of cognitive effort, given that physical and cognitive effort shares overlapping neural underpinnings³⁴ and the willingness to exert physical and cognitive effort are correlated³⁵. However, physical and cognitive effort arises under very different circumstances, and there also exists evidence showing that physical and cognitive effort have dissociable neural influences on reward after-effects (i.e., previous effort exertion changes reward evaluation⁹³) and a differential relationship with anxiety and depression^35,94. Therefore, it is possible that people may demonstrate different effort-information relationships depending on the type of effort required and the task structure.

Given the ecological validity of effort-based decision-making, a question naturally arises: are findings from studies quantifying information value as willingness-to-pay generalizable to situations involving effort? Our results suggest that the desirability of the outcome, which covaries with the expected value of the lottery, is a strong predictor of people’s information preference across effort and non-effort domains. The effect of uncertainty on effort-based information-seeking is partially consistent with previous literature. Under risk, our findings converge with existing work, suggesting a positive relationship between information valuation and outcome distribution variability. In contrast, we did not find people value information resolving ambiguity more than its counterpart resolving risk, and we find limited evidence suggesting that people are willing to exert more effort to reduce ambiguity only when taking extreme ambiguous scenarios into account. These two findings went against our predictions, which we derived from existing literature on decision-making under uncertainty in neuroeconomics. This inconsistency implies that people’s uncertainty attitude is multidimensional and is sensitive to the specific context under which the decision is executed. Since few studies have directly investigated information-seeking under ambiguity - let alone comparing the behavioral pattern under risk and ambiguity - it is hard to tell whether the discrepancy between our finding and the past literature is due to using effort as measurement or different decision tasks (i.e., choosing between lotteries vs. choosing between receiving information or remaining ignorant), or both. Our results suggest that principles emerging from monetary decision-making under uncertainty do not necessarily apply to effort-based information-seeking, which calls for more studies that systematically vary the task demand, uncertainty type, and measurements to elucidate the mechanisms underlying people’s information-seeking behavior.

Constraints on generality

This study took place within the laboratory and thus we recruited from the general Harvard community and the Cambridge, MA local area. As such, the sample may not reflect broader demographic, cultural, or socioeconomic diversity, which may limit the generalizability of our findings to other populations or contexts. In addition, we have restricted our sample to young adults aging between 18 to 35. Considering the impact of aging on effort exertion as well as cognitive processes such as information-seeking and risk identification^46–49, our results may not generalize to other age groups and future studies should systematically investigate effort-based information-seeking under uncertainty across multiple age groups.

Author contributions

Haoxue Fan played a lead role in data curation, formal analysis, methodology, project administration, software, visualization, writing of original draft, and writing of review and editing, and an equal role in conceptualization. Bryan J.W. Dong played an equal role in investigation, and a supporting role in data curation, software, and writing of review and editing. Dorothy Grace Benkelman played an equal role in investigation, and a supporting role in data curation. Alexandra M. Rodman played a supporting role in conceptualization, formal analysis, methodology, and writing of review and editing. Hayley M. Dorfman played a supporting role in conceptualization, formal analysis, project administration, and writing of review and editing. Paul W. Glimcher played an equal role in conceptualization, and a supporting role in formal analysis, methodology, supervision, and writing of review and editing. Elizabeth A. Phelps played a lead role in funding acquisition, resources, supervision, and writing of review and editing, an equal role in conceptualization, and a supporting role in formal analysis and methodology.

Funding

This work was supported by the National Institute on Drug Abuse (R01 DA042855 to EAP), the National Institute on Mental Health (R00MH126163 to AMR), the National Science Foundation SBE Postdoctoral Research Fellowship (2105147 to HMD), the Oak Ridge Institute for Science and Education (ORISE), the U.S. Department of Energy, and the Office of the Director of National Intelligence (ODNI) (Intelligence Community Postdoctoral Research Fellowship awarded to HMD). The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors declare no conflicts of interest.

Data availability

De-identified behavioral and self-report data as well as analysis code have been made publicly available via the Open Science Framework and can be assessed at https://osf.io/2mze4. The preregistration form for Experiment 2 is available at https://aspredicted.org/1T3_XQJ. Some of the data and ideas were presented at the 2023 Society of Neuroeconomics Annual Meeting and a research seminar at University of Birmingham. A preprint of this article was made available on PsyArXiv (https://osf.io/tz9jr/).

Declarations

Competing interests

The authors declare no competing interests.