Risky effort ☆

Decision-making involves weighing up the outcome likelihood, potential rewards, and effort needed. Previous research has focused on the trade-offs between risk and reward or between effort and reward. Here we bridge this gap and examine how risk in effort levels influences choice. We focus on how two key properties of choice influence risk preferences for effort: changes in magnitude and probability. Two experiments assessed people ’ s risk attitudes for effort, and an additional experiment provided a control condition using monetary gambles. The extent to which people valued effort was related to their pattern of risk preferences. Unlike with monetary outcomes, however, there was substantial heterogeneity in effort-based risk preferences: People who responded to effort as costly exhibited a “ flipped ” interaction pattern of risk preferences. The direction of the pattern depended on whether people treated effort as a loss of resources. Most, but not all, people treat effort as a loss and are more willing to take risks to avoid potentially high levels of effort.

When making decisions, people often decide between courses of action that lead to the same outcome but vary in the possible levels of effort required.For example, should one take a known route or instead risk a potential shortcut that may be muddy and difficult to walk over?In such situations, people weigh up whether to put in a known amount of effort or choose a risky option where the effort exerted could be lower or higher.Prior research on decision-making under uncertainty has almost exclusively focussed on outcome uncertainty (Camerer & Weber, 1992;Rieskamp, 2008;Wulff, Mergenthaler-Canseco, & Hertwig, 2018).As a result, little is known about the fundamental question of how people treat uncertainty in the effort required to collect a reward, as depicted in Fig. 1.This paper addresses this question through three experiments and compares risk preferences in two effort-based tasks against risk preferences for numerically identical monetary gambles.
Risky choices can be classified along two core dimensions: probability and magnitude (Tversky & Fox, 1995).When dealing with uncertainty in monetary outcomes, people choose differently depending on whether the risky option includes common probabilities (e.g., p = .5)or rare events (e.g., p = .1).These differences in risk preferences can be attributed to overweighting of the rare outcomes by a probability weighting function, leading people to seek the rare win, but avoid the rare loss.Similarly, people choose differently depending on whether monetary gambles concern increases or decreases in magnitude.When risk preferences are compared across these four conditions, there is a perfect interaction between probability and changes in magnitude, often known as the fourfold pattern (see Fig. 4 Monetary Control group).These risk preferences are well summarised by Prospect Theory (Kahneman & Tversky, 1979), which has been influential in understanding decision-making in a variety of contexts including politics, consumer psychology, healthcare, risk management and beyond (Johnson & Goldstein, 2003;Treadwell & Lenert, 1999).Here, we use this fourfold risk pattern as the basis to examine people's risk preferences for effort.
Whilst behavioural economics primarily classifies decisions along the dimensions of risk and reward, the idea that effort operates alongside these two factors has gained traction (Westbrook, Lamichhane, & Braver, 2019).The role of effort in decision-making, however, has been primarily studied in terms of its relationship with reward.Unlike reward, effort can be perceived as either a loss or a gain, across different individuals, contexts, and tasks (Inzlicht, Shenhav, & Olivola, 2018).For example, people are willing to accept a lower reward to exert less effort, known as effort discounting, implying that effort is costly (e.g., Botvinick, Huffstetler, & McGuire, 2009;Hartmann, Hager, Tobler, & Kaiser, 2013).Building on the assumption that effort is costly, early research, such as Hull's Law of Least Effort, concluded that when different actions provide equal reward, the option with least effort will be chosen (Hull, 1943;Solomon, 1948).In labour markets, when wages are higher and therefore less effort (hours) are required to reach a target salary, taxi drivers and bike messengers do indeed exert less overall effort (Camerer, Babcock, Loewenstein, & Thaler, 1997;Fehr & Goette, 2007).Empirically, in lab tasks, people also generally choose lower effort tasks and avoid cognitive effort (Kool, McGuire, Rosen, & Botvinick, 2010;Schouppe, Demanet, Boehler, Ridderinkhof, & Notebaert, 2014;Westbrook, Kester, & Braver, 2013).
A considerable body of experimental work has investigated the relationship between effort and reward using the Effort-Expenditure for Rewards Task (EEfRT), which was adapted from a task developed to investigate effort-based decision making in rodents (Salamone, Cousins, & Bucher, 1994;Treadway, Buckholtz, Schwartzman, Lambert, & Zald, 2009).In the EEfRT task, people choose between an option that requires low effort to obtain a small reward and an option that requires higher effort for a larger reward.People's willingness to exert more effort to obtain more reward has been found to depend on many factors including motivation, personality traits, reward magnitude and the probability (risk) of obtaining the rewards (e.g., Lopez-Gamundi & Wardle, 2018;Ohmann, Kuper, & Wacker, 2022;Treadway et al., 2009).For example, people's willingness to exert more effort to obtain more reward generally decreases as the reward become less certain, but this tendency also interacts with trait anhedonia (Treadway et al., 2009).
Other research has found, however, that although effort can be costly, it can also be valued, as described by the effort paradox (Inzlicht et al., 2018).For example, when people exert effort to produce items (e. g., IKEA, Lego), they value these products more than their identical preassembled counterparts (Norton, Mochon, & Ariely, 2012).People may thus sometimes be motivated to choose high-effort options in anticipation of high rewards.
Although increased effort often yields higher rewards, in some situations, effort level is not related to (reward) outcome.For example, the outcome of determining the statistical significance of results should be the same, whether you laboriously compute the values by hand, or instead use statistical software.Less is known about decision making involving effort when the obtained reward does not vary with effort.Our research thus investigated people's risk preferences for effort irrespective of outcome and focused on the trade-off between effort and risk.Moreover, given the occasionally paradoxical nature of effort preferences, we also explored whether people show a similar heterogeneity in their risk preferences for effort.
With non-human animals, examining the effect of variability in response requirements (i.e., effort variability) on choice to obtain the same reward has a long history (e.g., Fantino, 1967).These studies have generally found a preference for actions associated with variable levels of effort.For example, when rats choose between a lever that can be pressed a fixed number of times and a lever that varies in the number of presses required to obtain the same amount of food, they prefer the variable (risky) option, even when the mean number of required presses is equal (e.g., Sherman & Thomas, 1968).
A handful of studies have studied people's preferences for safe or uncertain effort levels in tasks that require people to learn the probabilities and potential outcomes of their choices based on experience, as would be the case with non-human animals (Apps, Grima, Manohar, & Husain, 2015;Mason et al., 2022;Nagengast, Braun, & Wolpert, 2011).Those studies suggested that, when learned from experience, people's preferences for effort parallel their preferences for reward outcomes under uncertainty.To our knowledge, no studies have examined explicitly described risk in potential effort levels.Given that people show different risk preferences for described and learnt information about monetary rewards (Hertwig & Erev, 2009;Ludvig & Spetch, 2011;Madan, Ludvig and Spetch, 2017), it seemed likely that risk preferences for described effort may not follow those for learned information about effort.The experiments reported here directly tested how people respond to described gambles involving effort.
The three experiments examine risk preferences for common and rare problems and for either increases or decreases in effort using a task that we created to predominantly require physical effort (clicking task: Exp 1), or a task that we created to predominantly require mental effort (adding task: Exp 2).Experiment 3 used monetary gambles as a control condition.The set of tasks allows for comparison of risk preferences for effort and money, without assuming whether effort is treated as a loss or a gain.We hypothesize that people will exhibit the standard fourfold pattern for money (Exp 3).For the effort tasks (Exp 1 and 2), however, we predict that the direction of the pattern will depend on individual effort preferences.Specifically, we predict that individuals who show a preference for low effort will show a flipped fourfold pattern, whereas those who prefer the high-effort option may not.These hypothesized fourfold patterns would appear as significant interactions between probability (rare vs common) and changes in magnitude (increases vs decreases).

Methods
Data files, pre-registration documents and analysis code can be found on the Open Science Framework (https://osf.io/695js).The methods and analyses follow the pre-registered plan, except where explicitly indicated.Additional exploratory analyses were conducted to follow up on some results.

Participants
Participants were recruited on Prolific Academic.For all experiments, the target sample size after any exclusions was 128, which, with a frequentist approach, gives 95% power for a within-subjects ANOVA (magnitude change, probability) with a small-medium effect size (Cohen's d = 0.4) and an alpha of 0.01.As per the pre-registered sampling plan, we aimed to initially recruit 150 participants for each experiment to allow for exclusions, incomplete datasets and dropout during the experiment.In the effort experiments, we then continued to recruit in groups of 20 until we reached at least a sample size of 128 participants who were low-effort choosers (as defined by the valuepreference trials-see Trial Structure).All research was approved by the University of Warwick Research Ethics Board.All participants provided online informed consent.
In all three experiments, participants were paid a base payment for taking part (Experiments 1 and 2: £2.67; Experiment 3: £2).The expected study time was 20 min in Experiments 1 and 2 and 15 min in Experiment 3. In all experiments, one gamble was selected at the end of Fig. 1.Risk, reward, and effort are core dimensions along which people make decisions.Previous work has examined the relationship between reward (outcome) and risk and between effort and reward (solid arrows), but little is known about how effort and risk interact (dashed arrow).
A. Mason et al. the experiment and realized.In Experiments 1 and 2, the selected gamble related to effort during the clicking and adding tasks, and participants were given a fixed bonus of £4 once they completed the effort task.In Experiment 3, participants were endowed with an initial bonus of £4 because the gamble was monetary.The result of the gamble was added to or subtracted from the initial bonus resulting in a final bonus between £0.37 and £7.50 (mean bonus = £5.95± 0.59).

Procedure
In all three experiments, participants completed a set of 96 decisions (see below for a detailed description of the trial types).At the start of the experiments, participants were told that one decision would be selected at the end of the experiment and that the option selected would be played out.In Experiments 1 and 2, participants made decisions in one of two effort-based tasks: the clicking task and the adding task (see Fig. 2).The clicking task was based on prior work investigating experienced effort (Mason et al., 2022).Before making any choices, participants completed 40 rounds of the clicking task.On each round, a black response circle was presented at locations randomly selected (with replacement) from 9 evenly spaced locations on the computer screen.The cursor was not repositioned between clicks.A 500-ms delay preceded each presentation of a response circle, and the circle remained on the screen until it was clicked with the mouse.In the adding task, participants were presented with a grid of 9 numbers and asked to select the two numbers (to two decimal places) that summed to 10.If they answered incorrectly or if they chose to "skip", then a new grid appeared.Participants had to successfully complete 5 grids before they could proceed to the main task.In Experiment 3, participants made decisions about money.
Across all three experiments the options offered the chance for participants to increase or decrease either their effort expenditure (Exp 1 and 2) or monetary pay-out (Exp 3).Therefore, participants were given an initial endowment of money or baseline effort level (Experiment 1: 400 clicks; Experiment 2: 40 correct sums; Experiment 3: £4), which their subsequent choices could increase or decrease.
On each trial, participants were presented with two options on screen, one on the left and one on the right (see Fig. 3), and were instructed to pick the option they preferred.Each option was clearly labelled as an "INCREASE" or a "DECREASE" trial for Experiments 1 and 2 and "WIN" or "LOSE" for Experiment 3. The text appeared in different colours for each condition (blue or orange), which was counterbalanced across participants.The relevant word appeared in the centre of the screen in capital letters.Participants selected one option by clicking on the black box beneath that option.The selected box was then highlighted with a white border for 1.2 s as visual confirmation of which option was selected.Trials were self-paced, and after each choice a box appeared in the centre of the screen with the instructions "Click here to continue".

Trial structure
In all three experiments participants encountered a total of 96 choice problems which consisted of both risk-preference trials and valuepreference trials.Experiments 1 and 3 contained the exact same set of choice problems (see Supplementary Materials Table 1 for the full set of problems).For Experiment 2 (the adding task), the magnitude of the choice problems was reduced to keep the overall study time similar across experiments.In general, the numbers in each problem were divided by 10 but some had to be manually adjusted so that they all involved whole numbers (see Supplementary Materials Table 2).

Risk-preference trials
These trials provided a choice between options that had equal expected value (i.e., in effort levels or in monetary amounts) but that differed in risk.There were 40 risk-preference trials involving increases Once they submitted their answer, they were given feedback as to whether the answer was correct, and a new number grid was shown.Participants had the option to skip number grid, but to finish the experiment they still had to correctly complete the total number of grids required (40 +/− the outcome of the selected option).(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) A. Mason et al. in effort and 40 trials involving decreases in effort.The monetarygambles control experiment used increases and decreases in money which corresponded to gains and losses.For both increases and decreases, 20 of the problems involved a rare, risky option (p = .1)and 20 were common problems (both p = .5).These 80 problems were generated according to two criteria: changes in magnitude and probability.We used a similar process to Erev et al. (2010) to randomly generate a set of risk-preference problems.The exact process for generating the problems is explained in detail in the Supplementary Materials.

Value-preference trials
These trials provided a choice between options with different expected values.There were 16 value-preference trials: 8 for increases and 8 for decreases.In these trials, there was always a strictly dominant option, whereby the fixed option was better (or worse) than both possible outcomes for the risky option.For the effort-based experiments, we cannot assume that people prefer the higher or the lower effort options.Instead, we use these value-preference trials to calculate the proportion of times a person chooses the high-magnitude option and classify them as high-or low-effort choosers.

Data Analysis
For each statistical test reported, we report both frequentist (including effect sizes) and Bayesian statistics.The value of the Bayes factors quantifies the strength of evidence in favour of the model of interest with respect to the null model, given the data obtained.We used R to run the analysis (v 4.1.3;R Core Team, 2020) and the BayesFactor package, with the default priors, was used to estimate Bayes Factors (v0.9.12-4.3;Morey & Rouder, 2022).
Our pre-registered analysis plan was to examine risk preferences for participants who chose the low effort (Experiments 1 and 2) or high monetary amounts (Experiment 3) on at least 60% of the value preference trials.The 60% threshold has been used in many previous studies using monetary rewards and was designed to exclude participants who did not learn or were not motivated to maximize reward.In Experiment 2, we further pre-registered a plan to conduct parallel analyses on participants who selected the high-effort options on 60% or more of the value-preference trials, and this analysis was therefore conducted for both experiments.This subdivision resulted in the exclusion of participants who showed no consistent preference for either high or low effort.This additional analysis was not pre-registered for the monetary reward task because past research suggested that very few people would show preference for lower reward amounts (as indeed was the case; see Fig. 6 below).To ensure, however, that our pre-registered 60% thresholds did not bias the conclusions, we conducted two sets of additional follow-up analyses.
First, we conducted correlational analyses with all participants (including those who did not meet either threshold) to assess the relationship between patterns of risky choice and value preference across the full sample.To this end, we calculated a Fourfold Score for each participant.This score indicates the direction of the interaction in their risk preferences.The score was calculated as follows: [P(Risky) Rare Increase -P(Risky) Rare Decrease] + [P(Risky) Common Decrease -P (Risky) Common Increase].A positive score indicates the classic fourfold pattern, and a negative score indicates a flipped fourfold pattern.For each participant we also calculated the proportion of times they choose the higher magnitude (in effort or money) option in the value-preference choice to provide a measure of the degree of preference for higher magnitudes of effort or money, based on a preference threshold of 60%.We additionally tested the robustness of our results using thresholds of 55%, 65% and 70% and found similar conclusions (see Fig. S1 Supplementary Materials).

Results
Fig. 4 plots the proportion of times participants chose the risky option in the effort-clicking task (Exp 1), the effort-adding task (Exp 2), and the monetary-control condition (Exp 3).For the effort tasks, we first report the results for all participants and then we report the preregistered analysis for high-and low-effort choosers.For the monetary control condition, we report the pre-registered analysis which excludes 3 people who chose the high-value option in fewer than 60% of the Fig. 3. Experimental paradigm.In each experiment participants were shown trials that involved increases or decreases in amounts of effort or money.In this task (Experiment 1), the options referred to how many clicks the participant would have to make in the clicking task.For each choice problem, participants were presented with a choice screen with two options.Each choice problem gave the opportunity to either INCREASE or DECREASE the number of clicks required to complete the experiment.To select an option, they clicked on one of the two corresponding black boxes.The next choice then appeared on screen.Participants were shown both increase and decrease choice problems for the value-preference and risk-preference trials.For the adding task (Experiment 2), instead of referring to clicks, each option was either the chance to INCREASE or DECREASE the number of grids that needed to be completed.In Experiment 3, participants chose between options for different amounts of money (in pence).Each trial was clearly labelled as a WIN or LOSE option to indicate increases and decreases.
value-preference trials.For all tasks, there was a clear interaction between probability and direction of magnitude change, consistent with our hypotheses.
In the effort-based tasks, when all participants were included, people were substantially more risk-averse for rare increases than for rare decreases, and they were slightly more risk averse for increases with  A. Mason et al. common gambles (more notably in the adding task).For the monetary control condition, the pattern of preferences was consistent with the typical fourfold pattern (Kahneman & Tversky, 1979), with more risk seeking for rare increases (gains) than decreases (losses) and less risk seeking for common increases (gains) than decreases (losses).
We ran a 2 × 2 (probability [rare, common] x change in magnitude [increase, decrease]) within-subjects ANOVA.The hypothesized fourfold patterns would appear as a significant interaction, but we did not have specific predictions regarding the main effects.In all three experiments, there was a significant interaction between probability and

Low-Effort Choosers
Our pre-registered analysis plan was to examine risk preferences for high-and low-effort choosers separately.In Experiment 1, there were 132 participants who chose the low-effort option in at least 60% of the value-preference trials.In Experiment 2, 146 participants chose the loweffort option in at least 60% of the value-preference trials.
Fig. 5 plots the proportion of times that the low-and high-effort participants chose the risky option in the effort-clicking task (Exp 1) and the effort-adding task (Exp 2).For all tasks, there was a clear interaction between probability and change in magnitude.In the effortbased tasks, with rare gambles, people were more risk-averse for increases than for decreases.In contrast, with common gambles they were more risk-averse for decreases than for increases.Thus, as hypothesized, low-effort choosers showed a flipped fourfold pattern.
As pre-registered, for each experiment we ran a 2 × 2 (probability [rare, common] x change in magnitude [increase, decrease]) withinsubjects ANOVA.The hypothesized fourfold patterns should appear as a significant interaction.For low-effort choosers in both experiments, there was a significant interaction between probability and magnitude To compare the specific patterns of risk preferences in each experiment, we ran a set of four pairwise t-tests (Bonferroni corrected) to examine whether people's risk preferences aligned with the key features of the fourfold risk pattern.For the effort-based problems, in line with the pre-registered hypothesis, low-effort choosers exhibited a flipped fourfold pattern of risk preferences in magnitude space: 1) In the clicking task in Experiment 1, they chose the risky option 29.1 ± 2.7% less often for rare increases compared to common increases [t( 131 In Experiment 2, with the adding task, low-effort choosers also exhibited a reversed fourfold pattern: 1) They chose the risky option 29.6 ± 2.2% less often for rare increases compared to common increases [t(145) = 13.5, p < .001,d = 0.93, BF = 3.27e+20].2) They chose the risky option 24.7 ± 2.1% more often for rare decreases compared to common decreases [t(145) = 11.62,p < .001,d = 0.96, BF = 3.42e+13].
We also conducted this analysis for the monetary choices in the control condition (Exp 3), people's risk preferences exactly aligned with the typical fourfold risk pattern: 1) People chose the rare option 16.5 ± 2.4 percentage points more for the rare monetary increases compared to the common monetary increases [t( 146

High-Effort Choosers
In Experiment 1 (the clicking task), 77 participants consistently chose the high-effort option on the value-preference trials >60% of the time. 1 In Experiment 2, with the adding task, there were only 20 higheffort choosers, making that analysis substantially underpowered.
Fig. 5 plots the risk preferences for these high-effort choosers for the clicking and adding tasks.For the clicking task, in contrast to the loweffort choosers, these people's risk preferences align with the fourfold pattern shown for monetary gambles (see Fig. 4).For the adding task, these high-effort choosers trended toward the same pattern as the clicking task with rare outcomes, but they were mostly indifferent with common problems.We conducted the same 2 × 2 (probability [rare, common] x change in magnitude [increase, decrease]) within-subjects ANOVA on this subset of participants to confirm the reliability of this pattern of risk preferences.There was a significant interaction between probability and change in magnitude in Exp 1[F(1,76) = 26.43,p < .001,η 2 p = 0.26, BF = 28,798] but not in Exp 2, [F(1,19) = 2.71, p =. 12, η 2 p = 0.13, BF = 0.41], likely due to the low sample size in this subset.There was no main effect of change in magnitude [Exp 1: F(1,76) = 0.02, p =. Following up on the significant interaction, we conducted the followup t-tests for the high-effort choosers in the clicking task.In contrast to the low-effort choosers (see Fig. 5), the risk preferences for effort for this subset of participants followed the classic fourfold pattern observed with monetary gambles: 1) The high-effort choosers chose the risky option 8.7 ± 3.2 percentage points more for the rare increases compared to the common increases [t(76) = 2.71, p = .04,d = 0.31, BF = 1.79].2) They chose the risky option 19.4 ± 3.4% less often for rare decreases compared to common decreases [t(76) = − 5.75, p < .001,d = 0.66, BF = 12,134].3) They were 14.4 ± 5.2% more risk seeking for rare increases than rare decreases [t(76) = 2.75, p = .037,d = 0.31, BF = 12.6].4) They were 13.7 ± 2.3% more risk seeking for common decreases 1 The analysis for high-effort choosers was not pre-registered for Experiment 1, but was pre-registered for Experiment 2.
A. Mason et al. compared to common increases [t(76) = − 5.98, p < .001,d = 0.69, BF = 9420].The high-effort choosers thus displayed the same fourfold pattern as observed with increases or decreases of money in the monetary control condition.

Value preference and Risk preference
To further examine heterogeneity in risk preferences, we conducted a follow-up analysis to examine how well people's preferences for money and effort correlated with their risk preferences as measured by the Fourfold score.This analysis includes all participants.Fig. 6 shows the relationship between risk preference and value preference.In both effort tasks, people who choose the higher magnitude effort options in effort-preference trials have a higher Fourfold Score, more in line with the classic fourfold pattern.In contrast, people who choose the lower magnitude effort option have a lower Fourfold score (a flipped fourfold pattern).In both the effort tasks, this positive correlation was significant (Clicking Task: r(245) = 0.63, p < .001;Adding Task: r(187) = 0.52, p < .001),and there was a mild, but not significant, positive correlation in the Monetary Control task (r(148) = 0.12, p = .14).

General Discussion
Risk, reward, and effort are three key determinants of human choices.Although the relationships between risk and reward, and between effort and reward, have been studied extensively, the relationship between risk and effort has been largely ignored (but see Apps et al., 2015;Mason et al., 2022;Nagengast et al., 2011).This set of three experiments establishes how people choose with risky effort.To answer this fundamental question, we explicitly varied both the probabilities and the magnitudes of the effort levels required to obtain a fixed reward outcome.Across two effort-based experiments, one more physical and one more cognitive, we demonstrated an interaction between probability and magnitude in people's risk preferences.This interaction parallels the fourfold pattern that has been observed with monetary gambles (see Exp 3 and Tversky & Kahneman, 1992).Notably, however, there was substantial heterogeneity in the direction of people's effort preferences suggesting that people differ in how they value effort, which impacts their risk preferences.
The effort paradox highlights how effort can be both costly and valued (Inzlicht et al., 2018), and the current work examines the impact of effort preferences on risk preferences.Most people's risk preferences for effort show a "flipped" fourfold pattern.For risky choices, the prospect of exerting more effort ("increase" in the effort tasks) is viewed differently to the prospect of gaining a financial reward ("increase" in the monetary-control task).For gambles involving rare probabilities, most people were more risk averse for increases in effort and more risk seeking for decreases in effort.This pattern was reversed, but less pronounced, for common gambles, where people were equally or more risk seeking for increases in effort than for decreases in effort.This pattern highlights how effort is usually viewed as costly and that people and other animals typically choose to avoid both physical and cognitive effort (Kool et al., 2010;Schouppe et al., 2014;Westbrook et al., 2013).
In the effort-discounting literature, the monetary value of a reward decreases in relation to the effort taken to obtain it (Botvinick et al., 2009;Hartmann et al., 2013;Westbrook et al., 2013).People's willingness to exert more effort to obtain more reward varies with trait anhedonia, reward magnitude, and reward probability as shown in the EEfRT task (Treadway et al., 2009).How the interaction between risk and effort depends on these parameters is an open question.Furthermore, the reward regions of the brain have been shown to respond to effort as a disutility (Sayalı & Badre, 2019;Botvinick et al., 2009; but see Schouppe et al., 2014).Recent work has shown that people will exert more effort to avoid losses than to obtain gains (Farinha & Maia, 2021).In the current experiments, the parallel between effort increases and monetary decreases (losses) when faced with risk further ensconces this view of effort as disutility for most people.
Our results, however, indicate that the direction of people's risk preference patterns depends on their effort preference.This heterogeneity highlights that the utility of effort cannot be assumed across individuals and tasks.In Experiment 1, there was a large spread in people's effort preferences (see lower panels in Fig. 6).The people who preferred higher effort showed a pattern of risk preference consistent with effort being valued.This result is consistent with work demonstrating that higher levels of effort can be a desirable state used to motivate behaviour (Csikszentmihalyi & Larson, 2014).People will contribute more to a charitable cause when there is increased effort or pain associated with a sponsored activity (e.g., a picnic vs a 5-mile run).Similarly, in public-goods games, willingness to contribute to a public cause is greater when the process is expected to be painful and effortful rather than easy and enjoyable (Olivola & Shafir, 2018).In animal learning, increased effort has been found to increase the subjective value of the outcome obtained leading the animal to show a preference for the option requiring more effort (Kacelnik & Marsh, 2002;Lydall, Gilmour, & Dwyer, 2010;Zentall, 2010).Under some conditions, effort clearly adds value (Inzlicht et al., 2018).Fig. 6.The relationship between Fourfold Score (a measure of the pattern of risk preferences) and preference for high-magnitude options (increases in effort or money).There was a strong positive correlation between Fourfold Score and value-preference for both the effort tasks and a mild positive relationship for the Monetary-Control task.
A. Mason et al.Interestingly, however, this effort-seeking pattern was only present for a much smaller proportion of participants in the adding task, which presumably predominantly involved mental effort (Experiment 2).These results add to existing findings that, in experimental mental-effort tasks, effort seeking is rare (Embrey, Donkin, & Newell, 2022;Westbrook & Braver, 2015).The clicking task (Experiment 1) required participants to click a black circle that moved across the screen, which presumably required less mental effort.A high clicking speed is desirable for gaming, and the task may have been seen as a positive challenge by some.In Experiment 2, the adding task required participants to find numbers that added up to 10, and this task presumably required mental effort.Other differences between the two experiments, however, may have also contributed to the difference in effort seeking.For example, there were some demographic differences between the experiments.Alternatively, the adding task may have been perceived as generally more effortful than the clicking task, and it included verbal feedback (correct or incorrect) that was not present in the clicking task.For both experiments participants completed practise trials.In the clicking task they simply had to click the circle to proceed to the next trial.In the adding task they had to complete 5 correct trials.An analysis of baseline performance in the adding task showed no difference in performance between high-and low-effort choosers (see Supplementary Materials).
Although a substantial proportion of high-effort choosers was observed only in Experiment 1, even in Experiment 2 there was more heterogeneity in effort preference than for monetary preference in Experiment 3 (see Fig. 6).Moreover, preference for effort correlated significantly with the fourfold pattern of risk preference in both effort experiments, suggesting considerable generality given the differences between the two tasks.Thus, consistent with the effort paradox literature, effort is not always treated as a disutility.The novel result we report here is that the extent to which people treat effort as a disutility determines their response to risk in effort.
Our findings, and the addition of risk, provide a new angle for several models of effort that formalise the costly nature of effort (Shenhav et al., 2017).This cost is either quantified as a loss of physical resources (Muraven & Baumeister, 2000) or as an opportunity cost (Kurzban, Duckworth, Kable, & Myers, 2013;Otto & Daw, 2019).These models often focus on the trade-off between effort and reward outcome and suggest that people's decision to expend effort on a given task depends on a cost-benefit analysis (Botvinick & Braver, 2015;Gratton, Coles, & Donchin, 1992;Sandra & Otto, 2018).More recently, the cost of expending effort has been linked to the "sense of effort" associated with completing a task (Embrey et al., 2022;Otto & Daw, 2019).The current results establish how uncertainty in these effort-cost functions gets translated into choice.
The time taken to solve a task and the difficulty of the task are potential confounds when looking at effort-based decisions.In many everyday decisions, however, effort and time are highly correlated.It takes longer to solve a hard crossword clue compared to an easy one.In these experiments, the decision tasks all used a set of described choice problems where one choice was played out at the end of the task.Arguably, this set-up makes time less of an issue, but participants could still have been making their decisions in order to minimise their time spent participating in the experiment.A recent experience-based effort task controlled for time and found that risk preferences were stable irrespective of time (Mason et al., 2022).
The fourfold risk pattern succinctly summarises how changes in probability and magnitude influence people's risk preferences for (monetary) outcomes.In both effort experiments here, people who preferred lower-effort options also showed a fourfold pattern in their risk preferences, but in the opposite direction compared to monetary gambles.In Experiment 3 we replicated the direction of the classic fourfold risk pattern in the decisions-from-description literature (Kahneman & Tversky, 1979), using the same numerical outcomes and probabilities as were used in the first effort task.Although the general pattern is well established, the specific conditions and associated patterns (e.g., that people are risk-averse for rare losses) have typically been examined across rather than within experiments.Each experiment here used a full set of gambles that included both rare and common probabilities and increases and decreases in magnitude.The monetary control condition (Exp 3) thus provides a clear empirical example of the fourfold pattern when all four conditions are included in a single experiment.
The current study details how people trade off risk and effort, in the absence of changes in extrinsic reward.The study extends the previous research which has examined uncertainty in effort during experiencebased decision-making, where the probabilities and outcomes were learned through repeated experience with feedback (e.g., Apps et al., 2015;Mason et al., 2022).For example, in a physical-effort task, Nagengast et al. (2011) found that people were risk seeking to avoid effort; another recent paper, using a similar clicking paradigm to the current paper, found that people were overall risk averse for effort, but were more risk seeking for easy-effort problems compared to hardereffort problems (Mason et al., 2022).These studies, however, did not study the impact of rare outcomes on effort risk preference and only included common risk probabilities.In our study, for the common described problems, participants were more risk seeking for the harder problems (i.e., increases in effort) compared to the easier problems (i.e., decreases in effort).This pattern is opposite to the one in Mason et al. (2022) in their experience-based task.With monetary outcomes, risk preferences often differ depending on whether decisions are based on description or experience, known as the "description-experience gap" (see Hertwig & Erev, 2009;Ludvig & Spetch, 2011;Olschewski, Luckman, Mason, Ludvig, & Konstantinidis, 2023).These differences in risk preferences based on the information format indicate that this description-experience gap extends beyond rewarding outcomes to effort-based choices as well.
Despite this evidence of a potential decision-experience gap in effortbased risk preferences, there are still some further inconsistences in the literature.Another experience-based study found that people were risk averse for cognitive effort (number of attention shifts required within a time period) (Apps et al., 2015).A possible explanation for this inconsistency is the different types of effort tasks used.Previous work has suggested that physical and mental effort might be underpinned by different structures (Apps et al., 2015).The two effort tasks used in the current study aimed to measure different types of effort, but there is likely to be considerable overlap (Thomson & Oppenheimer, 2022).It is not yet clear whether these patterns would hold across purely physical or cognitive effort-based tasks or if such a distinction between cognitive and physical effort truly exists.
This paper extends the study of risk preferences to effort-based decisions and demonstrates a clear fourfold pattern of risk preferences in effort, but one which varies across individuals.These individual patterns of choice in the current study reveal the heterogenous nature of risk preferences for effort and have important implications for real-world effort problems.The systematic differences in risk preferences for effort may help us understand individual differences in motivation and its associated disorders and why some people choose to avoid effortful options such as walking the longer route home, while others will take that risk, even if it involves potentially trudging through the mud. A. Mason et al.

Fig. 2 .
Fig. 2. Effort tasks.A) Example of the clicking effort task.Participants had to move their mouse to click on a black circle that appeared at random locations on the screen.B) Example of the number grid used in the adding task.Participants had to select two numbers that summed to 10.When they clicked a number, it turned red.Once they submitted their answer, they were given feedback as to whether the answer was correct, and a new number grid was shown.Participants had the option to skip number grid, but to finish the experiment they still had to correctly complete the total number of grids required (40 +/− the outcome of the selected option).(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4 .
Fig. 4. Risk preferences for choices involving effort (left two panels) and for the monetary control condition (right panel) for all participants (no exclusions).Across all three experiments, there was an interaction between probability (rare or common) and change in magnitude (increase or decrease).For the two effort tasks, the pattern of risk preferences was different from the classic fourfold pattern observed for the gambles involving money.Error bars indicate the standard errors of the mean.The dashed line indicates risk neutrality.Each grey dot represents an individual participant.

Fig. 5 .
Fig. 5. Risk preferences for low-and high-effort choosers.These are the subsets of participants who chose the low-effort option [Clicking task (n = 132/222); Adding task (n = 146/166)] or high-effort option [Clicking task (n = 77/222); Adding task (n = 20/166)] at least 60% of the time in the value-preference trials.For both tasks, the direction of the interaction between probability (rare or common) and change magnitude (increase or decrease) was opposite the low-and high-effort choosers.Error bars indicate the standard errors of the mean.The dashed line indicates risk neutrality.Each grey dot represents an individual participant.