Feedback-induced attitudinal changes in risk preferences

Domain: neuroscience
Published: 2026-01-14
Editorial outcome: minor_revision

Abstract
Decision-making under risk is often studied with fully described lotteries, where normative theory predicts that post-choice outcome disclosure (feedback) should not influence preferences. However, previous empirical work has generally shown that feedback does affect risk-taking, yet, without reaching a consensus on the consequences of feedback or the underlying cognitive mechanisms. Here, across seven behavioral experiments, we disentangle two competing accounts: the learning hypothesis, where feedback alters subjective values through experience, and the attitudinal hypothesis, where feedback changes preferences in anticipation of outcomes. We find that feedback does not improve maximization but consistently increases risk-taking. Fine-grained temporal analyses reveal that this effect emerges before any outcomes are experienced, ruling out learning as the primary driver. Moreover, the increase of risk-taking in partial feedback seems to be driven by curiosity, while incomplete feedback by anticipated regret. Our results indicate that feedback can bias decision-making primarily through attitudinal rather than learning mechanisms.

Introduction
Traditionally, empirical investigations of decision-making under risk have mostly been carried out in behavioral setups limited to one-shot description-based choice problems1,2: unique binary choices between mutually exclusive probabilistic options (lotteries), where relevant information (i.e., prospective outcomes and probabilities) is explicitly displayed, and considered known to the decision maker. This experimental setup matches the scope and limits of both normative and descriptive decision theories, which are generally silent about the effects of feedback and choice repetition3–5. Arguably, although both theoretically and empirically convenient, this one-shot description-based framework is not representative of the vast majority of decision situations that one faces every day. Most decision problems are recurrent, and, very often, one gets to know the outcome of one’s choice (partial feedback) – and sometimes also the outcome of the forgone option (complete feedback)6–9. To address those shortcomings, repetitions and feedback have been gradually incorporated into the study of human decision-making under risk over the last couple of decades10–13. This experimental innovation revealed that, in contrast to the normative dictate, human choices and risk preferences elicited in repeated decisions under risk do appear to change depending on the presence versus absence of feedback.

A widespread and intuitive hypothesis concerning the effect of feedback on risk preferences proposes that outcome information modifies the decision-maker’s subjective representation of probabilities. Indeed, from studies involving one-shot decisions, it appears clearly that individuals behave as if their subjective representation of probabilities is distorted (overweighting of rare events, underweighting of common events2,14). In the presence of feedback, the realized frequency of the outcomes received in the context of repeated decisions can be used to update (if not correct) the subjective beliefs concerning their probabilities, ultimately affecting one’s preferences and choices15. We shall refer to this category of accounts as the learning hypothesis. Because the integration of feedback in future choices is supposed to correct originally distorted subjective probabilities, the learning hypothesis often assumes that the presence of feedback should correct representational biases and, as a consequence, promote optimal (i.e., expected value maximizing) choices7,16. Admittedly, though, this simple prediction from the learning hypothesis can be challenged, e.g., by the presence of learning biases17,18, or when the probabilities of the outcomes are extreme, and the options are not sufficiently sampled: two conditions that lead the experienced and the actual frequency of the outcomes to diverge19.

However, despite the fact that learning does not always correct biases, the notion that feedback should enhance optimal decision-making remains dominant and goes beyond academic circles and has been widely proposed as a strategy to debias individuals and improve their decisions in significant applied contexts, such as finance and healthcare20–22. Feedback is, in fact, a fundamental element of “boosting”—an approach distinct from “nudging”—which aims to create a more enduring positive impact on decision-making performance by incorporating a learning component23–25.

A relatively recent instantiation of the learning hypothesis is the BEAST model (Best Estimate And Sampling Tool), which became particularly influential after emerging victorious from a choice prediction competition, notably featuring choices between fully described lotteries followed by complete feedback26. The model, rooted in the decision-by-sampling tradition27, postulates that as soon as feedback is available, the subjective estimations of decision variables (outcomes are probabilities) are based on samples drawn from the past experienced outcomes. The BEAST is currently considered a reference against which new (and old) descriptive models of decision-making under risk should be compared, as testified by numerous follow-up studies28–31.

An alternative category of accounts, which we shall refer to as the attitudinal hypothesis, conjectures that the mere presence of feedback changes the decision-maker’s preferences, independently of any learning process. We identify in the literature two main candidate cognitive processes for the attitudinal hypothesis: epistemic curiosity and anticipated regret.

Epistemic curiosity pertains to the idea of gaining utility from the resolution of uncertainty32–36. Indeed, when feedback is available, some options acquire different informational values with respect to the resolution of uncertainty. For instance, when only the outcome of the chosen option is revealed (partial feedback) and the decision features a riskier (high variance) versus a safer (low variance) lottery, choosing the safer lottery resolves less uncertainty about the final state of the world. In other words, there is an extra informational incentive to choose the riskier option if partial feedback is provided. This informational asymmetry explains how curiosity − or an uncertainty minimization drive − may shift choices in favor of the risky options if the participant anticipates that the decision will be followed by feedback37,38.

Regret can also cause attitudinal effects of feedback when it is expressed as an anticipated emotion during decision-making39. The rationale is that, when considering choosing a safe lottery over a risky one, one might forecast the regret elicited by observing a positive resolution from the best alternative outcome (the unchosen, riskier lottery)40, and therefore make more risk-seeking choices to avert this possibility. As opposed to epistemic curiosity, anticipated regret should notably emerge when the outcome of the unchosen option is also available (complete feedback). In support of the prominent role of counterfactual emotions in decision-making, regret has recently been invoked to explain certain aspects of choices elicited in paradigms that couple descriptions with feedback8,9,26,41.

Critically, in contrast to the learning hypothesis, which supposes that the effect of the feedback should emerge gradually, the attitudinal hypothesis allows the effect to emerge even before any feedback is experienced – i.e., by anticipation. Because the two hypotheses differ in the temporal relation with respect to the time of choice and outcomes, fine-grained temporal dynamics can dissociate the two accounts: attitudinal effects precede choices while learning effects follow outcomes. In addition, the two hypotheses are also different in their relation to choice optimality. Learning mechanisms are generally supposed to correct representational biases and, accordingly, should increase expected value maximization. Attitudinal ones are more silent in that respect.

The goal of the present study is to evaluate the relative merit of these alternative hypotheses in seven newly conducted experiments (N=540) and a reanalysis of a previous dataset (N=446). The new experiments have been designed to systematically investigate the role of feedback in decision-making under risk across different experimental manipulations that allow discriminating competing accounts. Here, we show that the presence of feedback reliably increases risk-taking without improving expected value maximization. Temporal analyses reveal that this effect is attitudinal, emerging before any outcomes are experienced, and is therefore not driven by learning mechanisms. Moreover, the underlying psychological drivers differ across feedback regimens: curiosity appears to dominate under partial feedback, whereas anticipated regret plays a key role under complete feedback. Finally, we demonstrate that these behavioral patterns are not captured by the influential BEAST model, challenging its validity as a general account of decision-making under risk.

Results
Experimental design
To address our research questions, we ran a series of seven incentivized experiments (six online - N=100 for each experiment before the application of strict exclusion criteria ‒ and one in the laboratory - N=30; see “Methods”). The six online experiments were variants of the experimental paradigm that we will describe below.

Our experimental design allowed us to overcome several methodological shortcomings identified in previous literature, which overall delivered an unclear picture concerning the directionality of the effect of feedback in decision-making under risk (see Supplementary Note 1 for a quantitative survey of the literature). One specificity of our experimental design is using a factorial design with a within-subject manipulation of post-choice feedback (present or absent); feedback was treated as a between-subjects factor in most of the previous studies, with only one exception26 - our design improves over Erev et al., (2017) by equalizing the number of repetitions for the two conditions (their design featured five repetitions for no-feedback and twenty for feedback) and by counterbalancing the order of the conditions. Furthermore, unlike most of the previous experiments, we included the same number of trials (10) in both feedback conditions, to disentangle between the effect of mere repetition and the effect of feedback itself42. Trials featuring the same decision problem were clustered in blocks of 10 trials. Feedback and no-feedback blocks were randomly interspersed (Fig. 1A).

We used a binary choice task featuring a sure and a risky option in each trial. The risky option had the form of (m, p; 0, 1-p), namely giving m points with probability p and zero points otherwise. In addition to feedback (present or absent), we also factorially manipulated the option optimality, i.e., whether the risky or the sure option has a higher expected value (EV): in one condition, the risky option maximizes the EV; in the other condition, the sure option maximizes EV (Fig. 1B). This allowed us to orthogonalize risk preference and decision optimality ‒ two features that have often been confounded in the literature. Finally, we manipulated within-subject the probability of (positive) gain associated with the risky option (three levels, namely 10, 50, and 90%), and the magnitude of the risky option (two levels, 40 and 60 points), thus leading to a decision space of 12 unique decision problems. Together with our feedback/no feedback manipulation and the repetitions (×10 per decision context), our final factorial design comprised 240 choices per participant, which is larger than that commonly found in the literature.

The role of feedback and instructions on risk preferences
The first experiment (Exp. 1) featured partial feedback, i.e., we revealed only the outcome associated with the chosen option. Participants were not informed about the presence or absence of the feedback before starting a given block. Dependent variables, i.e., the propensity to choose the risky option (R-rate) or the optimal – EV maximizing – option (O-rate), were analyzed using a generalized linear mixed model (GLMM) with the task factors (including presence of feedback and option optimality) as independent variables (see “Methods” for more details).

Our analyses of the R-rate identified a significant main effect of feedback (logistic GLMM: z=5.13, P<0.001, OR=1.86, 95% CI [1.47, 2.35], see Table 1), which was characterized by an increased propensity to choose the risky option when trial-by-trial feedback was present (Figs. 2A, 1C, Exp 1). Interestingly, this increase was of the same size and direction both when the risky option was better and when the sure option was better (with respect to EV) (Bayesian paired t-test BF10 =8.0, Bayesian sign test BF10 =5.3, indicating moderate evidence in favor of the null; Fig. 1D, Exp 1), such that there was no effect of feedback on the optimal choice rate (logistic regression: P=0.78, see Table 1; Bayesian paired t test BF10 =8.0; Bayesian sign test BF10 =5.7; Figs. 1C, 2B). In other terms, there was a significant interaction between feedback and option optimality: feedback decreased the O-rate when the sure option was the EV-maximizing one (z=−6.45, P<0.001, OR=0.5, 95% CI [0.4, 0.62]), but increased it otherwise (z=5.01, P<0.001, OR=1.67, 95% CI [1.37, 2.05], see Table 1).

Finally, we examined the trial-by-trial unfolding of the main effect of feedback on R-rate. The learning hypothesis predicts that the effect of feedback should be absent at the first trial, then gradually emerge and increase after repeated experience with feedback. Our analyses revealed a slightly different pattern: while indeed no significant effect of feedback could be detected in the first trial, R-rate in feedback and no-feedback conditions abruptly diverged in the second trial and the difference remained significant until the end of the block (two-tailed Wilcoxon Signed-Rank Tests (Benjamini–Hochberg adjusted): Trial 1: z=1.54, P=0.124, rank-biserial r=0.23, 95% CI [–0.06, 0.51]; Trials 2–10: all pairwise tests are significant, with the most conservative comparison (Trial 10) yielding z=3.16, P=0.002, r=0.47, 95% CI [0.20, 0.70], n=80; Trial 1: BF10 ≈2–4; Fig. 2C).

Overall, the results of this first experiment appeared, at the macroscopic level, in line with most of the existing literature, generally showing an increase in R-rate in the presence of feedback. At a finer grain level, because the effects develop after the first feedback, they seem overall consistent with a learning effect. The fact that the effect is abrupt rather than gradual could be understood as one-shot learning. However, because participants in Exp. 1 started each block without knowing whether they would receive feedback or not, the first trial also implicitly but unambiguously informed them about the presence of feedback in the ongoing block (feedback or no-feedback), which may have altered their attitude toward risky options. Thus, although the separation of R-rates in the second trial can be a result of (one-shot) learning, it can also reflect the triggering of an attitudinal change. Of note, also against the learning hypothesis is the fact that the presence of feedback did not improve the optimal choice rate.

To disentangle these two possibilities, we ran a second experiment (Exp. 2) in which, at the beginning of each block, participants received explicit instructions (hence block instructions) mentioning whether they would receive post-choice feedback in the upcoming block or not. Everything else was kept the same as in Exp. 1. At the aggregate level, Exp. 2 replicated Exp. 1 in all respects (logistic GLMM for R-rate: z=7.88, P<0.001, OR=2.06, 95% CI [1.72, 2.46], see Table 1; O-rate, F vs nF: Bayesian paired t test BF10 =7.1; sign test BF10 =7.2; Figs. 1C, D, 2D, E). Yet, the between-experiment manipulation of the block instructions produced a significant difference in the effect of feedback on the first-trial R-rates (two-tailed Mann–Whitney U test: U=2880.5, z=−2.77, P=0.0056, r=−0.24, 95% CI [−0.40, -0.07]; inset of Fig. 2F). Actually, the difference in R-rates between feedback and no-feedback blocks in Exp. 2 arose from the very first trial - and remained significant for the rest of the block (two-tailed WSRTs (BH-adjusted): Trials 1–10, most conservative at Trial 8: z=3.33, P<0.001, r=0.45, 95% CI [0.20, 0.67], n=95; Fig. 2F). Thus, it seems that the mere anticipation of feedback information induced by the block instructions was enough to change risk preferences before any feedback was actually experienced.

In summary, results from Exp. 1 and Exp. 2 clearly revealed that the presence of feedback about the outcome of the chosen lottery increased risk propensity but not choice optimality. Besides, while Exp. 1’s results only superficially supported the learning hypothesis, the results following the introduction of explicit block instructions in Exp. 2 favor the attitudinal hypothesis. Exp. 1 and Exp. 2 featured a partial feedback regimen, and since the result of the sure option is always known by definition and the result of the unchosen option is not disclosed, choosing the risky option provides the participant with more information about the current state of the world. Thus, this pattern of results is consistent with an attitudinal effect created by epistemic curiosity, where the demand for uncertainty resolution increases risk propensity because of the informational asymmetry between the risky and sure lotteries.

Regret as an additional determinant of the effect of feedback on risk preferences
If epistemic curiosity is the only driver of the observed effect, the informational asymmetry between the sure option (whose result can be inferred with certainty even when its outcome is not revealed) and the risky one (whose result cannot be inferred when its outcome is not revealed) causes the increased risk-taking propensity in the presence of feedback. Thus, according to the epistemic curiosity account, the effect should vanish (or, at least, decrease) under a complete (or ‘full’) feedback regimen, i.e., when the forgone outcome of the unchosen option is additionally revealed. To test this hypothesis, we ran Exp. 3 and Exp. 4, which were analogous to Exp. 1 (without block instructions) and Exp. 2 (with block instructions) except for the fact that they both featured complete feedback.

The complete-feedback experiments replicated the main effects observed in their partial feedback counterparts (Exp. 1 and Exp. 2). Most importantly, the presence of complete feedback still increased the R-rate (logistic GLMM: z=3.86, P<0.001, OR=1.42, 95% CI [1.19, 1.70] (Exp 3); z=6.34, P<0.001, OR=1.97, 95% CI [1.60, 2.43] (Exp 4), see Table 1; Fig. 1C, Exp. 3 and Exp. 4). Concerning the O-rate, in Exp. 3 we found evidence for no effect (Bayesian paired t-test BF10 =3.7; Bayesian sign test BF10 =6.8) while in Exp. 4 results were mixed, with the available evidence, if anything, pointing towards a slight decrease rather than an increase in performance (z=−1.49, P=0.136, OR=0.92, 95% CI [0.82, 1.03], see Table 1; two-tailed WSRT: z=−2.14, P=0.032, r=−0.27, 95% CI [−0.51, −0.02], n=85).

The pattern of results at the level of the trial-by-trial dynamic was also replicated. In Exp. 3 (without block instructions), the divergence induced by the presence versus absence of feedback was detectable from the third trial and remains significant for the rest of the block (two-tailed WSRTs (BH-adjusted): Trial 1: z=−1.69, P=0.101, r=−0.24, 95% CI [−0.53, 0.04]; Trial 2: z=1.25, P=0.210, r=0.16, 95% CI [−0.08, 0.41]; Trials 3–10: all pairwise tests are significant with the most conservative comparison (Trial 7) yielding z=2.69, P=0.009, r=0.36, 95% CI [0.11, 0.60], n=86; Fig. 3A). In Exp. 4, (the one with block instructions), contrary to the idea of epistemic curiosity being the sole determinant of the change in risk propensity between feedback and no feedback conditions, we found an effect from the first trial. The R-rates in the feedback blocks are significantly higher than the no-feedback ones starting from the first trial and throughout the block (two-tailed WSRTs (BH-adjusted): Trials 1–10, most conservative at Trial 4: z=2.62, P=0.009, r=0.35, 95% CI [0.10, 0.59]; n=85; Fig. 3B). As in Exp. 1 versus Exp. 2, the between-experiment manipulation of the block instructions produced a significant difference in the effect of feedback on first-trial R-rates in Exp. 3 versus Exp. 4 (two-tailed MWU test: U=2661, z=−3.11, P=0.0019, r=−0.27, 95% CI [−0.44, −0.11]; inset of Fig. 3B).

While these results are once again consistent with a feedback-induced attitudinal change in risk preference (the effect arose before any feedback was received), they are not easily accommodated by the epistemic curiosity account, because, under the complete feedback regimen, there is no uncertainty resolution utility bonus attributable to choosing the risky option. An alternative psychological mechanism for this effect that is compatible with the complete feedback scenario is the anticipated regret. To understand why anticipated regret could represent a possible explanation for this effect, it should be first noted that in many economic decision-making settings, regret is generally thought to be dependent on a comparison between the obtained and the forgone outcome and that this comparison is made explicit only in the complete feedback condition, where regret is experienced whenever the forgone outcome is higher than the obtained one. We propose that at the decision stage, the option that gives the best outcome most of the time gets a regret “premium”. Crucially, an option’s regret premium depends on the probability that its outcome is greater than that of the alternative. Note that, according to this definition and given the decision problems in our design, the regret premium of the risky option should be monotonically increasing with its probability of delivering the positive outcome.

Thus, to assess the anticipated regret hypothesis, we evaluated the effect of feedback on R-rates as a function of the probability of the best-risky outcome (10, 50 and 90%) and of the type of feedback (partial and complete). This analysis revealed a clear interaction (linear regression on the differences of participant-level average R-rates between F and nF conditions: significant interaction between probability and feedback type t(1034)=3.27, P=0.0011, β=0.048, 95% CI [0.019, 0.076]; Fig. 3E), which was driven by the effect of feedback increasing as a function of the probability of the best-risky outcome in the complete feedback experiments (t(1034)=5.63, P<0.001, β=0.058, 95% CI [0.038, 0.079]; see Table 1 for logistic regressions) but being stable in the partial feedback experiments (t(1034)=1.04, P=0.3, β=0.011, 95% CI [-0.009, 0.031], BF10 =13; see Table 1 for logistic regressions).

Extending the results to moderate risk options and losses
Next, we attempted to further clarify the psychological mechanisms involved in this effect. The fact that, in all experiments, the sure option is systematically a certain prospect leaves open the possibility that the effect of feedback is idiosyncratic to this framing. Indeed, certainty effects are known to heavily weigh decisions and to create robust paradoxes43. In the next two experiments, we therefore assessed the robustness of our results to variation in outcome probabilities, specifically in contexts where the non-risky option is not certain. To do so, we designed Exp. 5 and Exp. 6, where we substituted the sure option (which gives a specific amount with certainty) with a 50%-50% low variance lottery with EV equal to the EV of the sure option (Fig. 1B). This new option remains relatively safe (given its low variance), yet now features an uncertain outcome. We shall refer to this option as the safe option, to differentiate it from both the sure and the risky. All other things considered (i.e., except for the sure options being substituted with the corresponding safe ones), Exp. 5 and Exp. 6 were respectively indistinguishable from Exp. 2 (partial feedback) and Exp. 4 (complete feedback) (Fig. 1A). Consolidating our conclusions, all the main results identified in Exp. 1-4 were replicated in this modified setup (Supplementary Fig. S1). Notably, the presence of feedback significantly increased risk-taking from the first trial in the partial feedback Exp. 5 and from trial 2 in the complete feedback Exp. 6 (two-tailed WSRTs (BH-adjusted within-experiment): Exp. 5: Trials 1–10, all pairwise tests significant, with the most conservative comparison at Trial 10 yielding z=3.65, P<0.001, r=0.52, 95% CI [0.28, 0.72], n=80; Exp. 6: Trial 1, z=1.22, P=0.221, r=0.17, 95% CI [–0.11, 0.44]; Trials 2–10, all pairwise tests significant, with the most conservative comparison at Trial 4 yielding z=2.82, P=0.005, r=0.39, 95% CI [0.14, 0.62], n=84).

This attitudinal effect interacted with the probability of the risky option in the complete feedback condition but not in the partial one. To statistically substantiate this we run a linear regression on the differences of participant-level average R-rates between F and nF conditions (significant interaction between probability and feedback type: t(482)=2.47, P=0.014, β=0.052, 95% CI [0.011, 0.093]; slope in the complete condition: t(482)=4.73, P<0.001, β=0.070, 95% CI [0.041, 0.099]; slope in the partial condition: t(482)=1.19, P=0.23, β=0.018, 95% CI [−0.012, 0.047], BF10 =6.8; see also Table 1). This result illustrates that our key findings are not idiosyncratic to some design choices and might therefore reflect a generalizable psychological effect.

Leveraging this robustness, we completed our demonstration by a comprehensive assessment of our main claims, evaluated over our six experiments. This analysis indicated that the attitudinal effect induced at the first trial was robustly elicited in the experiments featuring block instructions (two-tailed WSRT: z=6.42, P<0.001, r=0.45, 95% CI [0.32, 0.56], n=344; Experiments 2, 4, 5, 6; Fig. 4B), vanished in the absence of the said instructions (Bayesian paired t-test BF10 =11.4; Bayesian sign test BF10 =8.4, n=166; Experiments 1, 3; Fig. 4A) and was significantly different in the two conditions (two-tailed MWU test: U=22108, z=−4.08, P<0.001, r=−0.22, 95% CI [−0.32, −0.12]). Consistent with different psychological mechanisms operating under partial or complete feedback regimens, the effect of feedback was identical across all levels of the probability of the risky option in the partial feedback experiments, while significantly modulated by this factor in the complete feedback experiments (significant interaction between probability and feedback type: t(1520)=4.11, P<0.001, β=0.049, 95% CI [0.026, 0.073]; slope in the complete condition (t(1520)=7.32, P<0.001, β=0.062, 95% CI [0.045, 0.079]); slope in the partial condition (t(1520)=1.53, p=0.127, β=0.013, 95% CI [–0.004, 0.029], BF10 =7.85); Fig. 4C–E).

Concerning O-rates, the partial-feedback experiments exhibited strong evidence for a null effect (Bayesian t-test: BF10 =14.13, Bayesian sign test: BF10 =12.45, n=255), whereas aggregating the complete-feedback experiments indicated a small decrease in O-rate in the presence of feedback (two-tailed WSRT: z=−2.85, P=0.004, r=−0.21, 95% CI [−0.36, −0.07], n=255; mean Δ±std= −0.020±0.007).

Finally, in a last experiment performed in the lab, we also showed that our main findings hold when incentives are increased, and monetary losses are introduced (see Fig. 1C, Exp 7 and Supplementary Note 2).

Trial-by-trial analysis
A follow-up question is whether the abrupt emergence of the feedback effect on the second trial in the experiments without block instructions was dependent on the choice made on the first trial. We observe that the main effect of feedback is observed regardless of the previous choice type (sure/safe versus risky), and additively to the main effect of the previous choice type on R-rates (two-tailed WSRTs F vs. nF: Choice t=1 safe: z=3.83, P<0.001, r=0.39, 95% CI [0.20, 0.57], Choice t=1 risky: z=2.83, P=0.005, r=0.32, 95% CI [0.11, 0.52], n=166; Fig. 5A). Moreover, the magnitude of the feedback effect did not differ between the two cases (Bayesian paired t-test BF10 =10.9, Bayesian sign test BF10 =8.1; Fig. 5C). The fact that, in experiments without block instructions, the second-trial effect is present regardless of the choice made on the first trial is again consistent with the idea that the discovery of the presence of feedback — and the consequent attitudinal change — explains the effect.

The existence of feedback-induced attitudinal effects on risk preferences does not rule out that additional feedback-induced learning processes co-exist. However, feedback-induced learning processes may not be apparent when looking at the average risky choice rate, because their effect depends on the previous trial choice and outcome. To investigate possible learning effects in trial-by-trial dynamics, we analyzed the probability of repeating a risky choice as a function of the outcome received in the previous trial. The logic of this analysis is that virtually any instantiation of a learning process would induce a “positive recency” effect, meaning that the probability of repeating a risky choice should increase after receiving the best possible (positive) outcome, compared to receiving the worst possible (zero) outcome (Fig. 5E, left). We tested this hypothesis by analyzing this behavioral variable (probability of repeating a risky choice, p(R|Rt-1)) in the feedback condition across all datasets. The results are in sharp contrast with the predictions of the learning hypothesis (Fig. 5F). In fact, the probability of repeating a risky choice was lower after receiving positive (i.e., the “max”) feedback as opposed to zero (i.e., the “min”) (logistic GLMM: z=−11.67, P<0.001, OR=0.38, 95% CI [0.32, 0.45], see Table 1). The analysis of trial-by-trial dynamics thus shows no support for any form of feedback-induced learning process, and rather falsifies it. The observed behavioral pattern exhibits in fact “negative recency”, which is better understood as a manifestation of the gambler’s fallacy (in the laboratory44–46 and in an ecological (real-life) setting47), according to which participants would move away from a recently rewarded risky choice because they (wrongly) assume that the subsequent likelihood of positive feedback will be lower (Fig. 5F, G). This gambler’s fallacy interpretation is further supported by conditioning this analysis on the probability of the risky outcome (recall, in our task, we featured three probability levels: 10, 50, and 90%). This actually reveals that the effect is modulated by the underlying outcome probability and is maximal when outcomes are rare (difference between p=10% and p=50%: z=6.35, P<0.001, OR=2.19, 95% CI [1.72, 2.79]; difference between p=10% and p=90%: z=11.11, P<0.001, OR=5.31, 95% CI [3.96, 7.13]) and absent when the outcomes are common (effect of previous risky outcome in p=90% condition: z=–0.64, P=0.52).

Next, we wanted to check whether the abrupt effect of feedback between the first and the second trial in experiments without block instructions was influenced by the outcome received on the first trial. The results also show that the effect of feedback is detectable, regardless of the nature of the outcome (zero or positive) received on the first trial (two-tailed WSRTs F vs. nF: Out t=1 = 0: z=2.28, P=0.022, r=0.32, 95% CI [0.05, 0.57], Out t=1 > 0: z=4.54, P<0.001, r=0.43, 95% CI [0.26, 0.58], n=166; Fig. 5B) and notably the effect did not differ across conditions (Bayesian paired t-test BF10 =9.8, Bayesian sign test BF10 =8; Fig. 5D). This result further supports the idea of an outcome-independent attitudinal change in risk preferences. To sum up, not only do we demonstrate that the effect of feedback on risk preference precedes the reception of any feedback (and is, therefore, better understood as a change in attitude), but we also disprove any residual role for feedback-induced learning processes in the trial-by-trial dynamics by evidencing biased reactions to probabilistic and stochastic events akin to the gambler’s fallacy44–47.

Verifying our findings in a previous dataset
We started our investigation by noting some discrepancies in the literature concerning the directionality of the effect of feedback in decision-making under risk, which was generally understood as stemming from a learning process (Table S2, S3). Over 7 experiments, we found that the presence of feedback increases the propensity of taking risks, with no detectable consequence on the optimal choice rate. By manipulating block-wise instructions (present vs absent), we also found that the effects were mediated by a change of attitude of a different nature in the partial (curiosity) and complete (regret) feedback condition; trial-by-trial dynamics analysis further ruled out that outcome-based learning plays a role in these processes.

We re-analyze a previously published dataset26 that stands out as containing the largest sample size among the relevant studies (N=446) and proposing an influential cognitive model of decision-making (see next paragraph)26,28,31, despite featuring some limitations (it involved only complete feedback, the feedback and no-feedback conditions featured different number of trials and always appeared in the same order, there was no clear manipulation of the instructions).

To replicate our analyses as comprehensively as possible, we restricted this re-analysis to the decision problems that feature identical or similar properties to ours, namely decisions opposing a sure to a risky option (to quantify the risky choice rate), decisions involving options with different expected values (to quantify the optimal choice rate) and decisions featuring non-extreme probabilities (excluding 1% or 99%) for the risky option. We also excluded trivial decision problems in which one option dominates the other (see Methods for more details about the study and the decision problem selection).

This re-analysis of Erev et al. (2017)26 data was consistent with our own results on the absence of a positive effect of feedback on the optimal choice rate (without feedback 0.66±0.21, with feedback: 0.65±0.17; Bayesian paired t-test: BF10 =17.1, Bayesian sign test: BF10 =14.1, n=446; Fig. 6A), as well as on the increase in risk choice rate (without feedback 0.38±0.22, with feedback: 0.42±0.18; two-tailed WSRT: z=−6.34, P<0.001, r=−0.36, 95% CI [−0.46, −0.25; Fig. 6B – see Table 1 for logistic regressions). Having in mind the fact that Erev et al. (2017) featured complete feedback, we looked at the effect of feedback specifically for different probability levels (low: prob≤25%, medium: 25%<prob<75%, high: prob≥75%) of the risky high-value outcome. As expected by the regret hypothesis, and consistent with our own findings, the effect of feedback monotonically scaled with the risky best-outcome probability (linear regression on the differences of participant-level average R-rates between F and nF conditions: t(1095)=8.31, P<0.001, β=0.093, 95% CI [0.071, 0.114]; Fig. 6C). Moreover, we looked at the trial-by-trial dynamics and found a negative recency pattern, consistent with a gambler’s fallacy bias (logistic GLMM: z=−8.86, P<0.001, OR=0.49, 95% CI [0.42, 0.58], see Table 1; Fig. 6D). Finally, while the manipulation of instructions was not present as such in Erev et al. (2017), the different orders of presentation of decision problems allowed us to perform an analogous analysis, which further supports a first-trial/attitudinal effect (for the details, see Supplementary Note 3 and Supplementary Fig. S2). Overall, all the behavioral analyses that could be replicated in Erev et al. (2017) lead to similar results and conclusions as the ones performed on our own new data.

BEAST model and key behavioral results
Having verified that all the results that we could test in Erev et al. (2017) are replicated, we turned to test whether or not the model originally stemming from this dataset and later picked up by many other influential studies of human decision–making28,30,31,48 is able to capture the main behavioral patterns we observed.

The main idea of the Best Estimate and Sampling Tools (BEAST) model is that the attractiveness of one option is the sum of its Expected Value (assuming, for simplicity that no ambiguity is involved, which is the case here) and an average Sampling Value, which is generated by the use of four sampling tools (which correspond to four behavioral tendencies)26. Three of the sampling tools are “biased” in the sense that they comprise mental draws from distributions that differ (in a specific, biased manner each) from the objective distributions of the prospects; they are not related to our discussion, so we omit the details here. The unbiased tool consists of mental draws either from the objective described distribution of the prospects, in case of no feedback, or from the realized one, in case of feedback. Crucially, the reliance on the observed history of outcomes when feedback is present makes the BEAST model a learning model. The unbiased tool captures the tendency to minimize immediate regret - or, to put it another way, it captures the tendency to prefer the option that gives the best outcome most of the time. The reliance on the unbiased tool increases as the participant receives more feedback, thereby making the impact of regret stronger.

We fitted the participants’ data from our experiments 1-6 to the BEAST model, and then we ran simulations with the fitted parameters to compute predicted choice probabilities for each participant. The model predictions replicate the main effect of feedback in increasing R-rates, but fail to capture the effect induced by the manipulation of block instructions - the effect of feedback is absent in the first trial, independently of the presence or absence of the block instructions (Fig. 7A, B). This is an expected result since, in the BEAST, attitudinal changes occurring before any feedback is experienced are not contemplated. When it comes to the interaction of feedback with probability, model predictions capture very accurately the complete feedback case, but fail to capture the partial feedback case (Figs. 7C–E). This is also an expected result, given that the regret component of the BEAST model does not depend on the feedback regimen and is equally deployed in partial and complete feedback conditions. Finally, in contrast to our robust behavioral finding, BEAST predicts a positive recency pattern resulting from its learning nature (Fig. 7F, G).

Consequently, the BEAST model is effective in capturing some of the behavioral patterns emerging in the setup of Erev et al. (2017) (a role for regret), while missing the negative recency effect also present in the original dataset. Furthermore, we provide conclusive evidence that the model’s predictions miss key behavioral findings, as soon as changes of the experimental setup are implemented, such as the presence of explicit block-wise instructions (attitudinal change) and partial feedback (role for curiosity).

Methods
Participants
The INSERM Ethical Review Committee approved the study, and participants were provided written informed consent before their inclusion. The research was carried out following the principles and guidelines for experiments including human participants provided in the Declaration of Helsinki (1964, revised in 2013). For the six online experiments, we recruited a total of 620 participants (4×100 for Exp 1-4, 104 for Exp 5, and 116 for Exp 6 | 300 females, 300 males, 20 gender not available | aged 29.29 ± 9.24 years) from an online platform (www.prolific.com).

For the laboratory experiment, 30 healthy participants completed the experiment (18 females | aged 28 ± 7.22). Given that Bellemare et al.69 assert that 20 participants are needed in a within-subject analysis to achieve a power of 80%; a sample size of 30 is expected to have enough power to detect any effect. The choice of model to analyze the dataset, the generalized mixed effect model, also requires a smaller sample size than traditional ANOVA. Participants were contacted via the “Relais d’information en sciences de la cognition” (RISC), part of the French “Center national de la recherche scientifique”. Participants enroll on the platform and, as such, voluntarily accept to be contacted for scientific studies. Participants were recruited on the basis of their good understanding of French. They received an email in their mailing list containing a link to a questionnaire asking them for general information. After completion, they are contacted by the experimenter to agree on the day of the experiment. Participants, which, on average, lasted 45 minutes.

We note that gender information was determined based on self-reports. No statistical method was used to predetermine sample size, other than aligning with current practices in the literature for similar studies. The assignment of participants to a given experiment was not randomized, but the researchers played no role in it because it depended on Prolific’s matching procedure. Nonetheless, we ensured that no participant took part in more than one experiment.

Exclusion criteria
To ensure the high quality of the data of the online experiments, we applied the following exclusion criteria (which were explicitly mentioned in the master thesis pre-planning document produced by the first author):
(cid:129) participants with a missing trial or with a repetition of a trial in the test phase
(cid:129) participants with two or more submissions of more than 100 out of 270 trials (the total number of trials, 270, includes training trials. So, we kept the complete submission of participants that had, for example, two submissions one with only a few trials and a complete one)
(cid:129) participants with less than 9 (out of 10) correct answers in the catch block (see below for more information on the catch block)
(cid:129) excessively long completion time [two standard deviations more than the average]
(cid:129) right or left option >95% of the time [low quality data] - note that the position of the options was counterbalanced, so this behavior is aberrant

After applying the above exclusion criteria, we were left with a total of 510 participants for the main analyses (80, 95, 86, 85, 80, 84 for experiments 1-6, respectively). It is worth noting that all our main results replicate when we drastically lower our exclusion criteria (keeping participants with less than ten missing trials and with an accuracy in the catch block of at least 6/10), thereby including 609/620 participants in the analysis.

No participants were excluded from the analysis of the laboratory experiment.

Incentives
For the online experiments, participants received a fixed compensation of £3 for about half an hour of engagement (average completion time in minutes: 28.47 ± 8.68). In addition, we incentivized participants to reveal their true preferences by offering a monetary bonus determined by the outcome of a randomly selected trial of the testing phase (average bonus won in British pounds: 2.68 ± 2.21).

For the laboratory experiment, participants received a show-up fee of 10€ for an average engagement of 45 min. To motivate the revelation of true preferences, an incentive system was settled on the basis of hypothetical gains or losses. Each decision gave a payoff in points — a draw from the selected option payoff distribution. They were told that their goal was to maximize their number of points in the gain domain and to minimize the number of losses. The total of points would determine their final payoff. The conversion rate between experimental units (EU) and euros was set according to the maximum and minimum possible payoffs at 0.02€/EU. The payoff structure was determined such that no participant would incur a loss. On average, they received 15€. At the end of the experiment, participants received and signed the receipt for their payments.

Experimental design
The online experiments started with participants giving their consent to participate, followed by detailed instructions on the behavioral task, the structure of the experiment, and the compensation. Afterward, participants went through training, which was a mini version (four blocks of five trials each) of the actual experiment featuring similar yet not identical decision problems to those of the actual experiment.

Then, participants started the actual experiment, which consisted of 24 blocks (12 decision problems with and without feedback, as described in the main text) and a catch block (see below) in the middle of the actual experiment. The 24 blocks were comprised of 10 trials each and were randomized within and across participants. The actual experiment was divided into three sessions, between which the participants were allowed to take a self-paced break.

Each block started with a screen providing block instructions about the presence or absence of feedback in the upcoming block (Experiments 2, 4, 5, 6) or just prompting the participants to start the block by clicking on the “Start Block” button (Experiments 1 & 3). This step was self-paced. Then, the two options (their magnitude and probability) were presented side-by-side, with a clickable white square below each option. The position of the options (left or right) was randomized. Also, the relative vertical position of the magnitude and the probability (magnitude above and probability below or vice versa) was randomized across participants (but was constant within participants). Participants could make their choice at their own pace by clicking the white square below their preferred option. The outcome of the risky (or the safe) option was determined by an independent random draw – by definition, the outcome of the sure option was fixed.

After the choice was made and the outcomes were determined, the outline of the selected square/option was highlighted, and inside the white square, the outcome of the chosen option was revealed (showing the obtained points) or hidden (showing a question mark) for 1500ms. In experiments where complete feedback was used, the forgone outcome was revealed as well (showing the points of the unchosen option) or hidden (showing a question mark) in a light gray font (in contrast to the standard black font for the obtained outcome). Note that partial feedback means that the outcome of only the chosen option is revealed; complete feedback means that the outcome of both the chosen and the unchosen option is revealed. Then, the next trial started showing the same options (potentially in a different position).

At the end of the block, a screen marking the end of the block was presented for 1500ms.

In the middle of the actual experiment, a catch block featuring the trivial choice between a sure option (probability=100%) giving 5 points and a sure option giving 30 points was presented. The catch block was identical to all the rest blocks of the actual experiment. The related exclusion criterion (participants who scored below 9/10 correct answers in the catch block were excluded from the analysis) enabled us to ensure that participants understood and paid attention to the task.

At the end of the online experiments, participants were informed about the randomly selected trial and the associated monetary bonus, about their total compensation, and they were redirected to the recruiting platform (Prolific) to formally complete their participation.

The laboratory experiment was conducted at the laboratory of the Département des Etudes Cognitives at École Normale Supérieure, Paris. Participants were told their rights and gave their consent. They completed a mathematical questionnaire assessing their ability to perform multiplication. The experimenter explained the task using a visual support and read an example of a gamble that might be encountered by the decision maker to ensure that they understand the possible outcomes of the gamble. Participants were told to maximize their gains and minimize their losses.

On the computer, participants were presented with an instruction screen indicating the type of information that they would be facing in the block. Individuals read “réalisation révélée essai par essai - feedback provided after each trial” or “réalisation cachée - feedback not provided” and were informed that, at the end of the block, they would be told the number of points gained or lost at that block. After reading the instructions, participants were presented with two options side by side on the screen. Each was associated with a geometrical shape and two labels: one gave information on the probability of occurrence of the outcome, and the other, on the magnitude of the outcome. The shapes and their color varied randomly throughout the experiment and across participants. Colors and the brightness of the screen were adjusted to prevent eye fatigue and for easy reading. Labels describing the magnitude and the probability of each lottery figure were above and below the shapes. For half of the participants, the probabilities are always above and the magnitude below. For the other half of the sample, the labels are reversed. The position of the risky and the sure lotteries was randomized within and across blocks. Participants could not anticipate their position and therefore had to stay attentive during the sequential choices. Choices were made using a mouse. After each one, an arrow indicated the localization of the choice, disappeared after 500ms to be replaced by a text at the place of the label of the magnitude of the chosen lottery. The text indicated either the number of points gained or lost (e.g -32 pts) or hid them (XX pts) – as in the online experiments, the outcome of the risky lottery was determined by an independent random draw. The disclosure of the points depended on the type of information provided at the beginning of the block. 1.5s after, another screen appeared with the second round of choice, providing the same gamble as before. At the end of the sequence of 10 choices, the accumulated points were shown on the screen.

Most steps of the task were self-paced, such that the participant could read and take as much time as needed for the instruction, the choice, and the bonus screens. The experiment was divided into three sessions to avoid fatigue. Participants were given feedback on their total points accumulated at the end of each session. At the end of the experiment, their payoff was computed on the basis of their total points.

Decision Problems
By experimental design, the magnitude and the probability of the risky option were determined, and by definition, the probability of the sure option was determined too. Given these, we computed the magnitude of the sure options for Experiments 1-4, so that the EV difference between the risky and the sure option was at 5%. Namely,

mag_sure = (1 + (1-2*riskyBetter)0.05) * mag_risky * prob_risky

In the end, we rounded the mag_sure toward the direction that agrees with the riskyBetter factor (if riskyBetter=1, we rounded mag_sure with the floor and if riskyBetter=0 with the ceiling function).

Safe options (Experiments 5 & 6) had also defined probabilities (50/50) and were set such that EV_safe = EV_sure. In addition, one of the two magnitudes was set equal to the EV_risky, so that both outcomes of the safe option were above (below) EV_risky when riskyBetter=0 (=1).

So, the two outcomes for the safe options satisfied the following:

mag_safe1 = EV_risky & mag_safe2 = 2*EV_sure - mag_safe1

In the laboratory experiment (Experiment 7), the EV of the two options was set to be equal. Hence, the magnitude of the sure option was determined given the magnitude and the probability of the risky one. Rounding to the closest integer was used in this experiment.

Statistical analysis
The main analyses included two dependent variables: risky choice (1 if one chooses the risky option and 0 if one chooses the sure/safe one) and optimal choice (1 if one chooses the Expected Value-maximizing choice; 0 otherwise). We ran a regression analysis using a Generalized Linear Mixed-Effects model (GLMM). We used the canonical link function for response variables with the binomial distribution, namely the logit function. The method for estimating model parameters was maximum likelihood, and the analysis was run with R. The predictors were feedback (categorical: absent/present), riskyBetter (categorical: no/yes), the probability of the risky option (categorical: low, medium, high for 10%, 50%, 90% respectively), the magnitude of the risky option (categorical: low and high for 40 and 60 respectively) and trial (continuous: from 1 to 10). In the basic model, we included the main effects. Specific pairwise interactions were also added when they were relevant. To account for individual differences, we incorporated a random effects structure with random intercepts and random slopes at the participant level. The main effects of all predictors were included as random slopes (the only exception being the predictor trial in the optimal choice case, which had a very small variance and led to singular fitting; therefore, it was excluded). The magnitude of the risky option was not relevant for the Erev dataset, as the lotteries were not necessarily of the form (m, p; 0); therefore, this predictor was excluded from the analysis of this dataset. In addition, in the Erev dataset, the trial was centered and scaled within each feedback condition to remove the dependency between feedback and trial (since trials 1–5 occurred without feedback and trials 6–25 with feedback) and to improve model interpretability and convergence.

We also ran similar regressions for the dependent variable repeatRisky (1 if one chooses the risky option and 0 if one chooses the sure/safe one at time t, conditional on having chosen the risky option at time t-1). The predictors were the probability of the risky option (specified as above) and whether the previous (at time t-1) risky outcome was the minimum or the maximum among the possible outcomes of the risky option (categorical: 0/1). As fixed effects, we included a basic model with the main effects only and a full model with the interaction too. The main effects of the predictors were used as random slopes. Note that the analysis was run only on feedback blocks.

Because participants’ choice frequencies and experienced outcomes were not experimentally controlled, not all participants contributed data to every combination of previous-outcome and probability conditions. Consequently, the dataset is unbalanced across participants and conditions. This does not pose a problem for the statistical analysis, as generalized linear mixed-effects models (GLMMs) are robust to unbalanced designs and appropriately accommodate unequal numbers of observations per participant. Accordingly, the related figures display variable sample sizes across conditions, with exact values reported in the legend of Fig. 5.

To further examine whether the effect of feedback on risky choice rates depended on the probability of the risky option, we conducted a focused analysis testing the interaction between the probability of the risky option and the type of feedback (partial vs. complete). For each participant, we computed the difference in risky-choice rates between feedback and no-feedback conditions (R(F) – R(nF)), yielding a dependent variable (“Value”) representing the feedback effect on risk-taking. This variable was analyzed using a linear model with the continuous probability of the risky option (pRisky) and feedback type (TypeOfFeedback, coded as 0=partial, 1=complete) as predictors, including their interaction term (pRisky×TypeOfFeedback). The model was estimated using ordinary least squares in MATLAB’s fitlm function. To decompose the interaction, we conducted simple-slope analyses estimating the effect of pRisky separately for each feedback type. When simple slopes were nonsignificant, we quantified the evidence for the null hypothesis using BIC-based Bayes factors comparing full and intercept-only models (BF01), with values greater than 1 indicating evidence for the absence of an effect, and larger values reflecting stronger evidence.

To assess the difference between the feedback and no-feedback conditions at the participant level, we conducted a comprehensive paired-condition analysis. We first computed Bayesian paired t-tests and Bayesian sign tests (following JZS and Beta priors, respectively) to quantify the relative evidence for or against a difference between conditions. Sensitivity analyses were performed across a range of prior scales for the t test (r=0.35, 0.71, 1.0) and Beta priors for the sign test (Beta(0.5, 0.5), Beta(1, 1), Beta(2, 2)); all yielded confirmatory evidence consistent with the main analysis, which is reported in the Results. Additional robustness checks, including a Wilcoxon signed-rank test, nonparametric bootstrap confidence intervals for the mean and trimmed mean (20%), and a permutation test on the mean difference, were also conducted and provided convergent confirmatory results.

Erev et al. (2017) re-analysis
This is one of the most extensive studies that includes description-only and description+experience choices, consisting of 150 decision problems and 446 participants. However, the main goal of the Erev et al. 2017 paper was not to compare these two paradigms. In an attempt to facilitate this comparison, we processed the raw data of the aforementioned paper and examined whether we could replicate with their data our main results. In doing so, we focused on a subset of their decision problems that enables us to answer the most important questions of our investigation.

First of all, we excluded from our analysis problems that involve ambiguity, more than two outcomes for one option, a correlation between the outcomes of the two lotteries, and decisions without lotteries (e.g., coin-toss). In addition, to be able to assess the effect of feedback on EV-maximization and on risk propensity, we further excluded decision problems in which the two options had equal EVs, problems that did not have the form of a sure vs a risky lottery, trivial problems (problems in which one option dominates the other) and problems with extreme probabilities for the risky option (1% or 99%); this left us with 31 decision problems, which constitute the pool for the related analysis.

Cognitive modeling
The Best Estimation And Sampling Tools (BEAST) model contains six free parameters, with one capturing attitudes towards ambiguity, so it is irrelevant to us. The key idea behind the BEAST model is that it assumes decisions to be determined by a combination of the best estimation of the expected value of an option and its subjective value determined by different sampling tools27. Four parameters in the model are dedicated to quantifying the weight of different sampling tools (i.e., rules for drawing and comparing hypothetical outcomes) as well as parameters governing the probability of using one of these tools. In the original publication, the authors estimated the best-fit parameters on a population level, allowing parameters of individual agents to be drawn from U(0, param_best-fit) or {1,…, param_best-fit) (depending on whether the parameter is continuous or discrete). Mean squared deviation and some additional constraints to capture various fundamental behavioral phenomena were used for estimating these population parameters. For all the details of the model and its optimization, we refer to the original publication26.

We used a different approach. We fixed a search space on the population level which was quite wider than the one resulting from the original optimization (the best fits for the parameters (σ, β, γ, θ, κ) was (7, 2.6, .5, 1, 3) in Erev, et al. (2017) while we used (10, 10, 1, 5, 6) as the search space). We computed the best-fit parameters on the participant level using maximum likelihood estimation (note that we fixed the individual parameters on the participant level and simulated each decision problem one hundred times to obtain the predicted R-rates for each participant). Then we ran simulations using the fitted parameters of each participant to obtain the predictions of the BEAST model and compare them with the behavioral data (but note that we also produced simulations using the originally proposed best-fitting parameters, which led to the very same conclusions).

We also submitted our data to a modeling analysis, which involved a standard descriptive behavioral model ‒ a variant of cumulative prospect theory70. Details about the model, the fitting procedures following standard guidelines71,72, and the resulting statistical analyses can be found in the Supplementary Note 4.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study shows that the presence of feedback increases the frequency of risky choice. This effect appears on trial one,\nwhen it is known whether feedback would be received. Moreover, feedback does not make choices more optimal. Thus, this\nsuggests the impact of feedback is not via learning (that is - subjects are not learning to select more risk when it is optimal).\nUnderlying mechanism is suggested to be regret minimization and uncertainty reduction.\nThe study is well executed, the data supports the conclusions, the analysis appropriate, the paper easy to read.\nI am not sure if the paper addresses a ‘general interest’ problem, or a specific problem of interest mostly to people in a\ncertain field. The paper does not necessarily attempt to identify (or convince us of) the ‘big picture’ implications in terms of\ntheory and/or practice. Though, the final part of the discussion does go some way towards that end. Such attempts should be\nmade stronger and be placed already in the introduction (and abstract if possible). Though, as written I think the authors are\nhonest about the implications of their study.\n1. Figure 3E right panel – would a regret account not predict that 0.1 probability will lead to a relative negative impact\n(reduce risky choice with feedback) rather than a no difference (0 effect)? Would a 0.5 probability not be the one that should\nlead to a zero effect according to regret? It would be good to explain the mechanism underlying the pattern of results here\nbeyond just the linear increase (that is, why are we getting these specific magnitudes?).\n2. I recommend showing the results of Exp 5 and of Exp 6 in Figure 4 rather than showing aggregated results across Exp 1-\n6. Otherwise, a reader may get the impression that the results of exp 5 and 6 are occluded due to the non-significant finding\nin Exp 6.\n3. For non-significant effects of importance (such as no-effect of trial t on trial t+1) I suggest adding a Bayes Factor to show\nthe non-effect is reliable.\n4. The exclusion rate is pretty high – approximately 110 subjects are excluded (of 620) and more for the model fitting.\n5. Unclear how R is calculated in the temporal analysis – is it R across subjects on each trial? Please state.\n6. Why are people not learning? People should be learning from outcomes, why do the authors suppose this is not the case\nhere?\nMinor comments:\nFigure 3 E - Y axis is not labeled, X axis is not fully labeled.\nTypos:\n199. should be: ‘to identify’\n175. should be: ‘cautious’\n175. delete ‘is’", "reviewer_2": "In this submission Nasioulas and colleagues examine the impact of choice feedback (versus no feedback), expectations\nabout feedback, and feedback type (partial, meaning only the chosen option, versus complete, meaning feedback from both\nthe chosen and foregone option) upon risky decision-making behavior in a decision-from-experience type paradigm across\nseveral experiments.\nThe authors find that the mere presence of feedback increases the overall rate of risky choice (particularly when the risky\nchoice was superior in terms of EV). Informing participants that they would receive feedback via instructions appeared to\nyield the same effect, but these increased risk preferences were present on the first trial (before any feedback could be\nexperienced). These results are interpreted as favoring a ‘dispositional’ view of feedback, whereby individuals choose risky\noptions in order to resolve curiosity, rather than a ‘learning’ view in which feedback serves to help update individuals’\nunderstanding of (described) outcome probabilities.\nMoreover, this feedback effect persisted even with full feedback, obviating the need to choose the risky to gain outcome\ninformation, which is interpreted as favoring a regret minimization hypothesis.\nIn general, I found the theoretical question worthy of study here, and the authors’ approach and conclusions here to be well\nthought out and (generally) clear. In that sense I think this is a solid study that elucidates a few interesting phenomena in\nrisky choice. Whether this constitutes the sort of advance appropriate for Nature Communications is a matter of editorial taste\n(and so I will defer to the editor on that question). Below are a few presentational concerns I had about the work.\n- The dispositional hypothesis, while I can understand it, is rather oddly named. A disposition as defined by the Oxford\nEnglish Dictionary refers to ‘a person's inherent qualities of mind and character’ which suggests an immutability or trait-like\naspect of risk preferences. Given that the authors show a (within-subject) malleability of risk preferences by feedback\ninformation, is this really the right word to describe an experimentally evoked state? I would strongly suggest giving this\nhypothesis a different name.\n- The authors seem to be a bit fixated on choice optimality as a dependent measure, at least in the first several experiments.\nWhy is choice optimality important or germane to the theories being tested here? It’s well known that people fail at making\nexpected-value maximizing choices under many circumstances. The important thing to me here seems to be shifts in risk\npreferences.\n- I was surprised to see the re-analysis of the Erev et al. (2017) dataset after the rather lengthy literature review and pseudo-\nmeta-analysis in the beginning of the paper, in my understanding, concluded that there were no existing datasets that could\nadjudicate between the learning versus dispositional hypotheses. If the Erev et al. data can shed useful light on this question\n—as evinced by the statement “Overall, all the behavioral analysis that we could replicate in Erev et al. (2017) lead to similar\nresults and conclusions as the ones performed on our own new data.” (p 21)—then why conduct and report these 7\nexperiments?\n- The General Discussion struck me as both odd and wordy. Typically, these should lead with some restatement of the key\nconceptual/theoretical question tested, the approach taken to test it, and what the findings suggest. Instead, I felt like this\nsection meandered through a large body of risky decision-making research without achieving a useful level of generality *or*\nspecificity for the reader. I think the authors could do much better here with a more traditional\nDiscussion structure.\nMore minor:\n- Where are inferential statistics accompanying the analysis of trial-by-trial feedback dynamics (Fig 6)? I expected to see\nregression tables.\n- How is the experimental setting (lab vs online) in Experiment 7 described “core characteristic” -- But not that these choice\npairs had equal EVs (unlike the previous experiments) ?\n- I found the diagram in Fig 1D was confusing, in particular the column headers. Is there a more intuitive way to represent\nthis information?\n- There were some other odd word choices that led to statements that I simply couldn’t follow. For example: the use of the\nword ‘Rationalizes’ (p 3 and 11) and the phrase ‘natural instantiation of the learning hypothesis’ (p 17). What is an\n‘ecological setting’ (p 19) ? I would find other, more intuitive ways to explain these ideas.", "reviewer_3": "This paper presents a series of experiments testing different hypotheses about how the presence of feedback might affect\nrisky choice behavior. Strikingly, the experiments quite consistently speak against feedback-dependent learning, the\ndominant account in the literature. Specifically, differences between feedback and no-feedback conditions are already\npresent before any feedback is experienced. Moreover, trial-by-trial analyses indicate that participants rather become less\n(vs. more) likely to choose a risky option after experiencing its most desirable outcome. The authors interpret these findings\nas pointing towards mechanisms of anticipatory regret and/or epistemic curiosity.\nThe experiments are meticulously designed to provide diagnostic tests pitting different candidate hypotheses regarding the\neffects of feedback against each other. Thereby, they allow the authors to fill in some quite striking but thus far overlooked\nblind-spots in the literature, which existed because factors such as risk and EV were typically not fully orthogonalized in prior\nwork. Moreover, the behavioral results are highly consistent across the different reported experiments and also analyses of\nexisting data, speaking towards the robustness of the findings. Although overall, this is already an excellent manuscript, I do\nhave a few questions and comments that should be addressed in a revision (see details below).\n1. From a conceptual stance, it may be problematic to characterize the present findings as „dispositional“ changes in risk\npreference. After all, „dispositional“ seems to imply that these effects might be long-lasting over time and/or concern a\nrelatively stable disposition to take/avoid risks. Given such an interpretation of the term, one would maybe expect the effects\nof feedback on one block to carry over to subsequent blocks—potentially even to blocks without feedback. However, this\nintuitive interpretation of the term does not seem to be what the authors mean to refer to here. It rather seems that the\nreported choice patterns are adapted from block to block to the currently experienced task structure, rather than reflecting\n„dispositional“ changes in risk preference. Thus, changing the terminology might be advisable. Though „merely“ concerning\nterminology, this point seems important to address, in the light of recent discussions in the risky choice literature about\nwhether risk preference is indeed a stable disposition, and whether this disposition can even be measured using behavioral\ntasks.\n2. The authors highlight that anticipated regret should affect complete feedback decisions. Do they mean it should\n*exclusively* play a role given complete feedback? After all, it seems that anticipated regret might also arise in partial\nfeedback situations where the participant considers choosing the risky option, but anticipates that the lower outcome might\nbe obtained. Here it is possible to experience (or anticipate) regret, even without feedback about the safe option, because\nthe realized outcome of the safe option can be inferred with certainty. Therefore I wonder, to what extent might anticipated\nregret explain behavior in the partial feedback conditions? (How) can one disentangle this type of anticipatory regret from\nepistemic curiosity here? Could the authors please present additional analyses to assess the relative contribution of\nanticipatory regret and epistemic curiosity in the partial feedback conditions?\n3. The author’s notion that learning should generally increase EV maximization rests on the assumption that the process of\nlearning itself adheres to a normative standard. However, there are experiments, for instance in the realm of Bayesian\nupdating, that have demonstrated that people do not necessarily integrate new information in an optimal manner. Instead,\nthey sometimes over- or under-adjust their expectations in the light of new information. In this light, can one really argue that\nlearning should *generally* render choice behavior more optimal?\n4. Did the emergence of the abrupt effect of feedback after the first trial depend on which option was chosen on the first trial,\nand on which feedback was received? Arguably, under learning, the direction of the effect should probably depend on these\nfactors. If there is an invariable increase in risk taking, this would provide further evidence against learning.\n5. Regarding p.15, Figure 3. In Experiments 3-4, the R-rate is below .5, even in the p=50 condition. It seems that under\nanticipated regret, as presented by the authors, one would expect an R-rate of pretty much exactly 50% here, because the\nsafe and the risky option each minimize regret in 50% of the trials (likewise, the R-rate should be >50% in the p = 90\ncondition). How can one explain that this does not seem to be the case in the data?\n6. It is quite surprising that the authors find no differences between gain and loss conditions in Experiment 7. People seem to\nbehave slightly risk-averse in the no-feedback condition and risk-neutral in the feedback condition, regardless of domain\n(gain/loss). How can these findings be reconciled with many findings in the risky choice literature indicating that\npreference patterns typically reverse between domains (the reflection effect)?\n7. The analysis of trial-by-trial changes in behavior (p.19 f.) indicates that people adapt their behavior to feedback in a way\nreminiscent of a gambler’s fallacy. That is, indeed, some feedback-dependent adaptation of behavior on the trial-level seems to be present in the data. Because this adaptation seems to be based on a misconstrued notion of non-independent\noutcomes (i.e., gambler’s fallacy), the finding may speak against learning in the sense of moving closer to optimal behavior,\nand this is also the key inference the authors draw. However, the mere fact that such trial-by-trial effects exist also indicates\nthat „dispositional“ changes alone are insufficient to fully explain the consequences of feedback. This should be mentioned\nand discussed.\nMinor issues:\n- On p.4., the authors argue that anticipated regret may entail more choices of the risky option, because it (typically) offers the\npossibility of obtaining the best outcome in a choice problem. However, the opposite can also be the case (sometimes the\nsafe option minimizes regret), as the authors explain later (on p.15). In my opinion, this should already be pointed out in the\nintroduction to avoid confusion and doubts regarding the argument on anticipatory regret.\n- Sometimes the authors refer to non-risky options as „safe“, other times as „sure“. This distinction is only explained on p.16.\nPlease explain it earlier to avoid confusion.\n- Panel B of Figure 1 (and corresponding panels presenting choice problems in other figures) is a bit difficult to parse; could\nthis information be presented in a more straightforward manner?\n- Table 4: it is not immediately clear what the numbers 1, 2, 3,10 characterize in row C (probably trial-numbers).\nPlease provide additional information in Table-note.\n- Panel B of Figure 6 is quite difficult to decipher (esp. the middle part of each subplot).\n- p. 21 „trivial problems decisions“ —> „trivial decision problems“\n- p. 26 „a proper instruction-induce first trial effect“ —> „a proper instruction-induced first trial effect“\n- p. 26 „a dispositional influences“ —> „a dispositional influence“"}, "author_response": "R1.0\nWe thank the reviewer for their positive appreciation and the opportunity to clarify why we\nbelieve the paper addresses one of the most pressing questions in behavioral decision-making\nresearch.\nWe acknowledge that we may have been a bit reserved in outlining the broader implications\nof our study for decision-making research as a whole, as well as its potential applications to\nreal-life decision-making contexts.\nLet us begin by discussing the relevance of our paper to what is arguably the most complex\nissue in behavioral decision-making research: the \"great rationality debate” (GRD). The GRD\ncontrasts two perspectives: on the one hand, the “heuristics and biases” framework, originally\nchampioned by Tversky, Kahneman, and Thaler, which views human decision-making as\ninherently limited and error-prone. On the other hand, the adaptive rationality framework\n(championed by Gigerenzer, Hertwig and Erev, among others) posits that the “irrational\nbehaviors” identified by the heuristics and biases framework are mostly artefactual (and\nhumans display a form of “adaptive” rationality – i.e., responses that are adapted to their\nbehavioral/ecological “niche”). Apparent irrational behaviors arise from the fact that the tasks\nused in the heuristic and biases framework research are not ecological and are somewhat\nartificial. This is particular true for the “one-shot” decisions, most frequently used in behavioral\neconomics. A key tenet of the “adaptive rationality” framework is that findings of irrationality\noften arise in situations where participants are not provided feedback about their choices,\nmaking it impossible for them to improve their strategies and converge toward rational (or\noptimal) behavior. We believe the “adaptive rationality” framework is correct in asserting that\necological situations do not only involve abstract descriptions of decision variables and one-\nshot decisions, but also concrete and repeated feedback on the consequences of decisions.\nA common example is doctors prescribing medications: while they follow certain guidelines,\nthey also experience the consequences of treatments in their patients.\nHowever, our findings provide clear and unequivocal evidence that feedback does not improve\nrationality. Even more strikingly, the effect of feedback in decision-making under risk is not\nexclusively mediated by learning mechanisms, which challenges a key argument of the\nadaptive rationality framework. This has significant implications for the GRD.\nThe relevance of our study to the broader field of behavioral decision-making research has\nbeen further clarified in the revised version of the paper, where we have added additional\nanalyses and figures. These updates show that our results decisively falsify one of the most\nsuccessful models of decision-making in the presence and absence of feedback: the Best\nEstimates and Sampling Tools (BEAST) model 1. The centrality of the BEAST model is\nunderscored by the fact that it is frequently cited in recent high-impact papers in decision-\nmaking, including those published in Science and Nature Human Behaviour, where it is\nregarded as the standard model for describing human behavior 2,3.\nIn brief (see the following points and the revised manuscript for more details), the BEAST\nmodel posits that, once feedback is provided, the experienced distribution of outcomes is used\nto shape decision-making. In other words, the BEAST model is a learning model. As such, it\nfails to account for many key findings, including the first-trial effect and the negative recency\neffect. Our paper, therefore, presents a cautionary tale against the utilization of data-driven\napproaches in behavioral research (choice-prediction competitions, machine learning) and\nestablishes new behavioral benchmarks against which future models of decision-making can\nbe compared. On final note, we would like to point a recent paper in the economics literature\n(Oprea & Vieider, 2024) that, not only is based on the same paradigm as our study (the\ndescription + experience, thus showing the continuous relevance of this behavioral task), but\nalso keeps defending a version of the learning hypothesis (thus further illustrating the\nimportance of our conclusions).\nWe have made substantial revisions to the paper (including the abstract, introduction, results,\nand discussion) to more effectively highlight the contributions of our study to the great\nrationality debate and behavioral decision-making models (see many points below and\nmanuscript with changes highlighted). One such example is the following (from the updated\ndiscussion):\nTaken together, our observations significantly challenge any cognitive model relying\non learning process as a mechanism of the effect of feedback on decision-making\nunder risk, be it routed in reinforcement learning4, Bayesian5 or decision-by-sampling\ntheories6. Concretely, we found the influential BEAST model, which supposes that\nonce feedback is available values are constructed by (mentally) sampling outcomes\nfrom the empirical distribution falls short of capturing critical features of behavioral\nresults, such as the first trial effect and the negative recency effect. Also of note, while\nthe BEAST model does capture the role of regret, it is not equipped to deal with the\nshape of effects highlighted in the partial feedback condition. Our results, therefore,\nsuggest that the BEAST model to be continued used as a valid model of human\ndecision-making should undergo major restructuring vis-à-vis several key structure\nfeatures7–9. Our findings also tell a cautionary tale against validating computational\ncognitive models using choice prediction, data-driven competitions, which, focusing on\nquantitative metrics and aggregate data, may miss critical features of human behavior\nthat can be highly diagnostic of the underlying cognitive mechanisms10,11.\n1. Figure 3E right panel – would a regret account not predict that 0.1 probability will lead to a\nrelative negative impact (reduce risky choice with feedback) rather than a no difference (0\neffect)? Would a 0.5 probability not be the one that should lead to a zero effect according to\nregret? It would be good to explain the mechanism underlying the pattern of results here\nbeyond just the linear increase (that is, why are we getting these specific magnitudes?).\nR1.1\nThis is a good observation. The reviewer is right that if we present a simple definition of regret\nthat only considers outcome probabilities in complete feedback experiments, one should not\nonly expect a monotonic effect of the effect of feedback as a function of the probability of the\nrisky outcome, but also a negative effect in the p=0.1 condition (when the risky option is not\nrewarded most of the times). To avoid getting into too many technicalities, we opted for a\nsimplistic version of the regret account in our original paper, which, as R1 correctly points out,\ncannot fully explain the behavioral pattern.\nWhile proposing a new, complete model of regret is beyond the scope of our manuscript, we\nwould like to take the opportunity of this revision to briefly sketch how we believe regret should\nbe calculated in decision-making under risk scenarios, to account for the observed behavioral\npattern. In short, the simple regret account (which we used in the submitted version) is\nincomplete because it depends only on the probabilities of the considered options (probability\nof giving their best outcome) and not on the magnitudes of the outcomes.\nTo build an intuition of why -and how- magnitude can affect the direction and magnitude of\nregret premium, consider three of the decision problems we use in our paper, with High,\nMedium, Low and pRisky, respectively (magnitude, probability):\nH: (40, 0.9; 0, 0.1) vs (34, 1.0)\nM: (40, 0.5; 0, 0.5) vs (19, 1.0)\nL: (40, 0.1; 0, 0.9) vs (3, 1.0)\nMost theories of regret consider the potential states of the world resulting from the factorial\ncombination of the lottery outcomes (see Diecidue and Somasundaram, 2017 12).\nIn the H decision problem, one can anticipate that 9 out of 10 times, the risky Lottery yields 40\nwhile the safe option yields 34. The Risky option gives the relatively best outcome most of the\ntime, hence, it should get the regret premium, according to most theories of regret. Besides,\nnote that this relatively most frequent best outcome is also the highest possible outcome in\nthe decision problem in absolute term. In our account, this potentiates the regret premium to\nthe Risky option because both the probability and the magnitude contribute to the anxiety of\nmissing out on this option.\nNow consider the L decision problem: 9 out of 10 times, the risky Lottery yields 0 while the\nsafe option yields 3. The Safe option gives the relatively best outcome most of the time and,\ntherefore, should get the regret premium (thereby reducing risky choice in the feedback\ncondition, as mentioned by the Reviewer). However, this time, note that the relatively most\nfrequent best outcome (3) is quite negligible compared to the highest outcome in the decision\nproblem (40), in absolute term. Therefore, because of this magnitude dimension, the risk\npremium for the Safe Option is significantly reduced – to the point of being non-detectable.\nFinally, for the M decision problem, if we only consider outcome probabilities, the regret should\nbe equally split between the two options, each yielding the relatively best outcome half of the\ntime. This should nullify all regret premium, as anticipated by the reviewer. Yet, when we\nconsider the magnitude of the outcomes in these most likely scenarios, the Risky option yields\nthe best absolute outcome (40), while the safe option half as much (19). Thereby, the\nmagnitude tips the scale in favor of the Risky option, such that a noticeable regret premium\nwill increase the proportion of risky choices in the presence of feedback – though smaller than\nin the H decision problem because the probability dimension does not contribute to it as much.\nNow, remember that in our experiments, decision problems were generated with a constraint\non the difference in expected value between the sure/safe and the risky option being small\n(Figure 1B). Because the worst outcome of the risky lottery is always 0, for very risky options\n(i.e. options with small probabilities and substantial magnitude), the magnitude of the safe\noption had to be considerably smaller than the best outcome of the risky lottery. Therefore,\nthe Low probability Risky options systematically had their regret premium reduced by the\nmagnitude dimension.\nImportantly, the BEAST model (Erev et al, 2017) provides a (complex) way to capture this\n(simple) intuition by incorporating a regret tool that depends both on probabilities and\nmagnitudes of the options and that contributes more to decisions in the presence of feedback.\nAs a matter of fact, simulated predictions of the BEAST model using fitted parameters give\nrise to the same pattern of behavioral data, thereby further corroborating the above\ndemonstration (Rebuttal Figure 1).\nComplete feedback\n(Exp,3,4,6)\nBehavioral data\nBEASTmodelsimulations\nRebuttal Figure 1: the effect of feedback on R-rates (namely, the difference of R-rates between Feedback and no-\nFeedback conditions) as a function of the probability of the best outcome of the risky option. The graphs present\nboth the BEAST model simulations (using fitted parameters), as well as our empirical data, only in the complete\nfeedback experiments (Experiments 3,4,6).\nNote, that by relaxing the constraints on the decision problems (and specifically by including\nmixed gambles), one can theoretically observe negative feedback effect (i.e. significant regret\npremium to the safe options), which the Reviewer anticipated to see in the Low-probability\ndecision problems. We can actually substantiate this point with the re-analysis of Erev et al.\n(2017) whose choice-set include options and lotteries with mixed positives and negative\noutcomes, expanding the range of considered decision problems – and actually allowing\nscenarios where the (absolute) magnitude of safe option outcomes in low-probability decision\nproblems is more significant. Recall that we classify risky options as Low, Medium or High with\nrespect to the probability of the best outcome of the risky lottery, which means that lotteries\nwith a high probability of a loss are actually referred as Low probability in the following analysis.\nTo appreciate this point, consider the following gambles:\nL_gain: (40, 0.1; 0, 0.9) vs (3, 1.0)\nL_mixed: (40, 0.1; -3, 0.9) vs (3, 1.0)\nIn this case, the small safe outcome has to be compared with a negative one, thereby\nincreasing its perceived desirability (and probably even more so, because usually “losses loom\ngreater than gains”). Consistent with this idea, in Erev et al. (2017) data, results show that in\nthe Low probability condition of to gain-only decision problems, there is no detectable effect ‒\nwhich is fully compatible with our data and with the BEAST simulations (see Rebuttal Figure\n2; left). On the other hand, there is a significant negative effect of feedback (i.e. a regret\npremium to the safe option) in the Low probability decision-problems containing losses see\nRebuttal Figure 2; right), supporting our theoretical account.\nRebuttal Figure 2: the effect of feedback on R-rates as a function of the probability level (of the best outcome of\nthe risky option) and the decision domain, in the Erev et al. dataset. Gain: decision problems with only positive or\nneutral outcomes (hence, similar to those investigated in our Experiments 1-to-6 ). Mixed-loss: decision problems\ninvolving a negative outcome in the risky option.\nIn summary, refining our initial regret account to consider outcome magnitudes -in addition to\nthe probabilities- allows us to explain the behavioral pattern of our data (as well as the\nbehavioral pattern of Erev et al (2017) data and the predictions of their BEAST model).\nWe modified the paper in order to make this point clearer:\nWe propose that at the decision stage, the option that gives the best outcome most of\nthe time gets the regret “premium”. This premium is further modulated by the ratio\nbetween the more frequent best outcome (by comparison to the alternative) and the\nrange of the possible outcomes (i.e., the difference between the best and worst\npossible outcomes) in the decision problem. Hence, the regret premium of an option\ndepends both on the probability that the option delivers an outcome greater than the\nalternative and on its magnitude relative to the outcome range.\nNote that according to this definition, in our design, the options with the greater regret\npremium are those associated with a high (90%) probability of delivering the risky\noutcome because: 1) they deliver the best possible outcome compared to the\nalternative 9 times out of 10, and 2) since the risky outcome is the largest in a decision\npair, its value relative to the range of available outcomes is high (r~=1). Conversely, in\ndecision problems where the probability of delivering the risky option is low (10%), the\noption that delivers the best outcome most of the time is the safe one. However, its\nregret premium is drastically reduced because the value of the safe outcome is\ngenerally much smaller than the range of the available outcomes (<<1).\n[…]\nNote, that since the regret “premium” is also proportional to the relative magnitude of\nthe best outcome of the regret-minimizing option and given that the magnitude of the\nsure option is very small when we are in the low-probability case (because the sure\noption’s magnitude is close to the Expected Value of the risky option (see Figure 1B)),\nthe regret premium we would expect in this case is negligible. And this is exactly what\nwe observe in the behavioral data (Figure 3D & 3E, P = 10%).\n[…]\nNote, that the negative effect observed in the low condition is also consistent with the\nregret account we described above and it is a result of Erev’s data set including\ndecision problems with negative outcomes. Indeed, if we split the low-probability\nproblems in those containing only non-negative outcomes (as in our design) and those\ncontaining negative outcomes, we see that in the former set the effect is absent (as in\nour data), while the latter set exhibits a negative effect. This could originate from the\nfact that in the decision problems including negative outcomes the magnitude of the\nsafe option is bigger relative to a range that extends in the negative domain.\n2. I recommend showing the results of Exp 5 and of Exp 6 in Figure 4 rather than showing\naggregated results across Exp 1-6. Otherwise, a reader may get the impression that the\nresults of exp 5 and 6 are occluded due to the non-significant finding in Exp 6.\nR1.2\nWe thank the reviewer for this suggestion, as it was certainly not our intention to hide anything\n(the results of Experiment 5 and Experiment 6 were actually presented in tables and described\nin the same detail as the other experiments in the previous submission’s main text). We are\ntherefore very happy to include visual representations of Experiments 5 and 6 in the revised\nsubmission.\nSpecifically, we have modified Figure 1 to include a concise visual summary of some of the\nmain results from all individual experiments (i.e., the effect of feedback on risk propensity and\noptimality; see Rebuttal Figure 3 below).\nRebuttal Figure 3: panels C and D of the revised Figure 1. (C) where we show per experiment the effect of\nfeedback on Risky-choice rate (R-rate) and Optimal-choice rate (O-Rate). Note that as per design of Experiment\n7, options did not differ in terms of Expected Value, therefore, the O-rate could not be calculated. (D) the effect of\nfeedback on R-rates as a function of whether the sure or the risky option has higher Expected Value.\nWe also include now in the supplementary materials (Figure S1) a figure analog of Figure 3,\nwhich only focuses on Experiments 5 and 6, as requested:\nRebuttal Figure 4: detailed results concerning Experiment 5 and Experiment 6 as now presented in the\nsupplementary materials. Specifically concerning the main effect of feedback, across trials and across probabilities\nlevels.\n3. For non-significant effects of importance (such as no-effect of trial t on trial t+1) I suggest\nadding a Bayes Factor to show the non-effect is reliable.\nR1.3\nWe thank the reviewer for suggesting the use of Bayes Factors (BFs) as a way to substantiate\nclaims regarding the absence of an effect. Before diving into the new results which we have\nincorporated into the revised version based on their suggestion, we would like to clarify that\nour claim concerning the first trial effect is not based on the absence of a feedback effect in\nthe first trials of the experiments without instructions. Rather, it is based on the presence of an\neffect in the first trial of the experiments with instructions and the fact that this effect differs\nbetween the two instruction treatments.\nAs a result, our claim is grounded in positive statistical evidence for differing means (i.e., the\neffect of feedback in the “instructions” experiments is significantly different from zero and\nsignificantly different from the feedback effect in the “no instructions” experiments in the first\ntrial; see Rebuttal Figure 5, below). Since this claim is based on the presence of an effect,\nrather than its absence, we believe that the use of BFs is not warranted in this case.\nDifferent from noInstr\n****Different from zero\nRebuttal Figure 5: Quick summary of the contrast of the effect of feedback on R-rates across the Experiments not\nfeaturing block-wise instructions (noInstr) and those featuring block-wise instructions (Instr). ****p<0.0001 against\nzero (one-sample two-tailed test) and between conditions (two-sample two-tailed test).\nWith that clarification in mind, we acknowledge that one of our claims does rely on the absence\nof an effect, specifically the assertion that feedback has no beneficial impact on EV-\nmaximizing choices. To clarify further, we were particularly confident in making this claim not\nonly due to the lack of a significant effect, but also because, if anything, the trend moves in\nthe opposite direction —O-Rate is, if anything, marginally higher in the no-Feedback condition\n(59.4 ± 0.6%) compared to the Feedback condition (58.3 ± 0.5%). However, in line with the\nreviewer’s suggestion, we have now also calculated the Bayes Factor (BF) for this comparison\nand report the evidence supporting the null effect:\nBayesian evidence suggest a strong to very strong (depending on the scale used - e.g.\nJeffreys13 or Kass and Raftery14) support in favor of the null hypothesis of O-rate not\nbeing increased by feedback against the alternative hypothesis that feedback\nincreases O-rates (BF10 = 0.015 with uninformed Cauchy prior with scale 0.707; BF10\n= 0.017 with informed Normal prior with mean and std calculated by the empirical data\nof Erev_2017).\n4. The exclusion rate is pretty high – approximately 110 subjects are excluded (of 620) and\nmore for the model fitting.\nR1.4\nWe thank the reviewer for raising this important point. First, we want to clarify that our\nexclusion criteria are independent of any effect of interest. Our primary exclusion criterion is\nbased on data quality and task completion (i.e., missing trials). Another is based on\nparticipants' choices in a block of trivial/dominated options, akin to an attention check (e.g., 30\npoints with a 100% probability versus 5 points with a 100% probability). This second criterion\nis crucial when dealing with decision-making under risk protocols, as it ensures a minimum\nlevel of engagement and understanding of the decision variables (points and probabilities)\namong participants in the experimental sample (which is particular important, since Exp1-6\nwere performed online). These criteria were pre-registered as part of the submission and\nvalidation procedures for the master’s thesis of Antonios Nasioulas, and were mentioned in\nthe methods section.\nThat being said, to address the reviewer’s concern, we reanalyzed all our data using the quasi-\nfull sample (including all participants that had less than ten missing trials and at least 6/10\ncorrect answers in the trivial/dominated choice block; this left us with 609/620). We are\npleased to report that all the main results remain significant (main effect of feedback, first trial\neffect with instructions, interaction with probability level in the complete feedback experiments,\nand negative recency effect), as shown in Rebuttal Figures 6 and 7.\nInstruction-induced first trial effect Interaction between feedback typeand probability of the risky outcome\nRebuttal Figure 6: Recap of the main results in a full sample (i.e., with minimal exclusion – see above). As shown\nin the figure: 1) feedback increases Risky-choice rate, 2) the effect is present in the first trial when instructions are\navailable (dispositional effect) and 3) the effect interacts with probability level, only in the complete feedback\nexperiment (curiosity vs. regret).\nInteraction between feedback typeand probability of the risky outcome\nRebuttal Figure 7: Recap of the main results in a full sample (i.e., w/o excluded subjects). Specifically, the graph\nshows that the negative recency effect (“gambler fallacy”) still hold in the sample.\nWe now included this information in the methods of the revised manuscript (when we explain\nthe exclusion criteria):\nTo ensure the high quality of the data of the online experiments, we applied the\nfollowing exclusion criteria (which were explicitly pre-registered in the master thesis\npre-planning document produced by the first author): […]\nIt is worth noting that all our main results replicate when we drastically lower our\nexclusion criteria (keeping participants with less than ten missing trials and with an\naccuracy in the catch block of at least 6/10), thereby including 609/620 participants in\nthe analysis.\n5. Unclear how R is calculated in the temporal analysis – is it R across subjects on each trial?\nPlease state.\nR1.5\nIn our paper, the letter \"R\" designate the risk-choice rate (i.e., the probability of selecting the\nriskier of the two options presented). Conversely, \"O\" refers to the optimal choice rate (i.e., the\nprobability of choosing the option that maximizes the expected value between the two\npresented). Importantly, by design, these two quantities are orthogonal. Regarding the\ntemporal analysis specifically, as the reviewer mentions, we compute the R-rate of each\nsubject on each trial of a block (averaged across repetitions of similar condition) and then the\nline plot depicts the mean of these values ± s.e.m across subjects. To avoid any\nmisunderstanding, the meaning of these abbreviations is now systematically clarified in all\nfigure legends.\nFor example:\nIn (C) and (F), the central bold line is the mean of the individual averages in each\ncondition and the shaded area above and below the mean is plus and minus,\nrespectively, the s.e.m. of the individual averages.\n6. Why are people not learning? People should be learning from outcomes, why do the authors\nsuppose this is not the case here?\nR1.6\nFirst, the very fact that R1 is surprised by the participants' lack of learning confirms that the\nwidely held assumption is, as the Reviewer puts it, \"people should be learning from outcomes.\"\nThis is also the intuition behind many influential models of feedback effects in risk decision-\nmaking, including the BEAST model (see above).\nBy confirming that the learning hypothesis is the intuitive and dominant one, the Reviewer\nindirectly underscores the relevance and \"ground-breaking\" nature of our findings, as well as\ntheir suitability for a general audience outlet like Nature Communications (see R1.0 and R2.0).\nThe reason why participants do not learn, we believe, is largely elucidated by our trial-by-trial\nanalysis, which shows that participants exhibit a negative recency effect. We speculate this is\ndue to a biased, naïve understanding of probabilistic and stochastic processes, similar to the\nwell-known \"gambler's fallacy.\" Crucially, we believe that this prevalent misconception of\nstochastic processes is exacerbated by the explicit description of the gambles. In other words,\nthe explicit description of event probabilities inhibits the learning from stochastic processes.\nImportantly, we also demonstrate that, despite the absence of learning, feedback still\ninfluences risk preferences, but through complex pathways, which differ between partial and\ncomplete feedback conditions (e.g., curiosity vs. regret).\nIn response to this comment, we have substantially revised the discussion to clarify these\ninterpretations.\nEvidence for an attitudinal influence (as manifested by the first-trial effect) does not\nrule out the possibility that learning processes operate in parallel and influence\nchoices. To test this hypothesis, we looked at feedback-induced trial-by-trial choice\nadjustments. We reasoned that virtually all instantiations of learning, be they rooted in\nBayesian update or Reinforcement learning15, generate positive recency effects, i.e.\npredict that the probability of choosing a risky option should increase following a\nrewarded risky choice. Critically, this is also true for decision-by-sampling models, such\nas the BEAST, which supposes that mental samples of the outcomes are drawn from\nthe empirical (i.e., experienced) distribution. Accordingly, having experienced positive\noutcomes in the past should increase the likelihood of repeating the same choice. In\nstriking contrast with the prediction of the learning hypothesis, our analysis revealed a\nnegative recency pattern: a positive feedback in the preceding trial reduced the chance\nof repeating a risky option. Our re-analysis of Erev et al. 2017 provided further support\nin favor of a negative recency (gambler’s fallacy) effect. This prima facie puzzling\nbehavioral effect can be understood as a manifestation of what is called the gambler’s\nfallacy, i.e., the fact that human subjects tend to misrepresent the independence of\nprobabilistic outcomes16–18. This interpretation is further confirmed by the fact that this\neffect interacted with the probability of the risky outcome, such that the negative\nrecency effect was stronger when the probability of the risky outcome was lower: a\nsituation where the gambler fallacy intuition suggests that two consecutive lucky strikes\nappear almost impossible. These results not only rule out the possibility that residual\nfeedback-induced learning effects are at play, but also suggest that an explicit\ndescription of the probabilistic process may create (biased) prior expectations that\nprevent learning processes.\nMinor comments:\nFigure 3 E - Y axis is not labeled, X axis is not fully labeled.\nTypos:\n199. should be: ‘to identify’\n175. should be: ‘cautious’\n175. delete ‘is’\nThank you very much, we fixed all these points.\nReviewer #2 (Remarks to the Author):\nIn this submission Nasioulas and colleagues examine the impact of choice feedback (versus\nno feedback), expectations about feedback, and feedback type (partial, meaning only the\nchosen option, versus complete, meaning feedback from both the chosen and foregone\noption) upon risky decision-making behavior in a decision-from-experience type paradigm\nacross several experiments.\nThe authors find that the mere presence of feedback increases the overall rate of risky choice\n(particularly when the risky choice was superior in terms of EV). Informing participants that\nthey would receive feedback via instructions appeared to yield the same effect, but these\nincreased risk preferences were present on the first trial (before any feedback could be\nexperienced). These results are interpreted as favoring a ‘dispositional’ view of feedback,\nwhereby individuals choose risky options in order to resolve curiosity, rather than a ‘learning’\nview in which feedback serves to help update individuals’ understanding of (described)\noutcome probabilities.\nMoreover, this feedback effect persisted even with full feedback, obviating the need to choose\nthe risky to gain outcome information, which is interpreted as favoring a regret minimization\nhypothesis.\nIn general, I found the theoretical question worthy of study here, and the authors’ approach\nand conclusions here to be well thought out and (generally) clear. In that sense I think this is\na solid study that elucidates a few interesting phenomena in risky choice. Whether this\nconstitutes the sort of advance appropriate for Nature Communications is a matter of editorial\ntaste (and so I will defer to the editor on that question). Below are a few presentational\nconcerns I had about the work.\nR2.0\nWe thank the reviewer for their positive appreciation of our work. We also take this opportunity\nto highlight the key advances in our paper and the modifications undertaken to better\nemphasize them. We also refer R2 to additional arguments which we have provided in\nresponse to Reviewer 1’s similar concerns (see R1.0).\nFirst, we note that adding feedback to decisions based on descriptions makes the\nexperimental setup very relevant from an \"ecological\" point of view, as many real-life decisions\ninvolve both descriptions and feedback. Understanding how these two dimensions interact is\ntherefore fundamental, if not paramount, not only for theories of human decision-making but\nalso for the application of such theories outside the lab (e.g., nudges, decisions system\nengineering, etc.).\nSecond, the commonly held belief about how feedback influence decision-making under risk\nis that it occurs through a learning process. Statistically speaking, learning processes should\nhave a positive effect on decision optimality, measured by the rate of choosing expected-\nvalue-maximizing choices. This learning hypothesis, in addition to being verbally endorsed in\nmany previous studies, is computationally embedded in several models accounting for the\neffect of feedback on decisions from descriptions, including the very influential BEAST model,\nwhich is currently a key reference in the field (see its many citations and applications, for\nexample, in machine learning papers).\nThird, despite the prevalence of the learning hypothesis (see also R1.6), a deeper examination\nof the literature reveals no consensus about the direction of feedback's effect in decision-\nmaking under risk, and even less information about its role in optimality, which is rarely\nassessed in this branch of behavioral decision-making literature. This lack of a clear picture is\na significant obstacle to validating theories and proposing applications (see the first and\nsecond points above). On final note, we would like to point a recent paper in the economics\nliterature (Oprea & Vieider, 2024) that, not only is based on the same paradigm as our study\n(the description + experience, thus showing the continuous relevance of this behavioral task),\nbut also keeps defending a version of the learning hypothesis (thus further illustrating the\nimportance of our conclusions).\nIn light of these observations, we believe that our study represents a milestone, if not a turning\npoint, in this research field because we are able to:\n1. Demonstrate that the (dominant) learning hypothesis is false, while pointing to concrete\ndirections concerning the structure of the (complex) cognitive processes underlying the\neffect of feedback in description-based decision-making under risk;\n2. Establish clear empirical regularities characterizing the directionality of feedback’s\neffect on risk preferences and decision optimality under various experimental\ncircumstances (different feedback regimens, gains, losses, etc.).\nAs a result, we believe that our findings will be of the utmost relevance for any researcher or\npractitioner interested in the role of feedback in decision-making. We have made several\nimprovements to the manuscript to clarify the relevance of our study.\n- The dispositional hypothesis, while I can understand it, is rather oddly named. A disposition\nas defined by the Oxford English Dictionary refers to ‘a person's inherent qualities of mind and\ncharacter’ which suggests an immutability or trait-like aspect of risk preferences. Given that\nthe authors show a (within-subject) malleability of risk preferences by feedback information, is\nthis really the right word to describe an experimentally evoked state? I would strongly suggest\ngiving this hypothesis a different name.\nR2.1\nWe thank the reviewer for pointing this out. While we have presented this work internationally\nmany times and noted that the terminology used was generally well received and understood,\nwe acknowledge that, as non-native speakers, we may have missed some of the nuances\nassociated with the term “dispositional.” Therefore, following the reviewer’s suggestion and\nafter carefully reviewing the meaning, we have decided to change the term to “attitudinal.”\nWe hope the reviewer is as satisfied with this change in terminology as we are, since we\nbelieve that the notion of \"attitude\" implies something that can change as a result of new\nexperiences or situations (as in the phrase \"change of attitude\"), as is the case for the results\nwe want to describe.\n- The authors seem to be a bit fixated on choice optimality as a dependent measure, at least\nin the first several experiments. Why is choice optimality important or germane to the theories\nbeing tested here? It’s well known that people fail at making expected-value maximizing\nchoices under many circumstances. The important thing to me here seems to be shifts in risk\npreferences.\nR2.2\nWe were honestly a bit puzzled by this remark, especially since the term \"fixation,\" according\nto the Oxford Dictionary, refers to \"an obsessive interest in or feeling about someone or\nsomething\". The reason for our puzzlement is that, in the version of the manuscript reviewed\nby the Reviewer, 11 figure panels focused on risk preferences, but only 2 focused on the\noptimal choice rate. As a result, we believe that while our study adheres to the behavioral\ndecision-making tradition, which considers the risk choice rate as the more important variable,\nit also has the merit of including another key, often overlooked, variable: the rate of expected\nvalue maximization. The revised version maintains the same balance of focus between risk\npreferences and optimality, with an overwhelming emphasis on risk preference, which we\nhope will satisfy the reviewer’s perspective.\nThat being said, we maintain that our additional characterization of choice optimality\nrepresents an important and original contribution of our study. This is not only because\nassessing optimality informs the main research question (as the learning hypothesis is\nnaturally linked to the idea that feedback increases maximization), but also because answering\nthis question is necessary to explore the potential beneficial role of decision-enhancing\ninterventions based on delivering feedback. In fact, while it is well known that people fail at\nmaximizing EV under many circumstances, researchers have been attempting to identify\nconditions under which this can be improved and feedback has been often pointed out as a\npotential candidate.\nWe have revised the introduction and discussion of the paper to better emphasize this point.\nFor example:\nThe lack of clarity and investigation of the effect of feedback on choice optimality is\nsurprising since feedback is often suggested as a possible way to correct decision-\nmaking biases and improve decision-making 19,20.\n[…]\nThese results not only rule out the possibility that residual feedback-induced learning\neffects are at play but also suggest that an explicit description of the probabilistic\nprocess may create (biased) prior expectations that prevent learning processes.\n[…]\nIn particular, our results suggest that, contrary to what common sense could dictate,\nproviding feedback cannot be considered as a panacea to correct decision-making\nbiases, notably because the effects of feedback are at least partially mediated by\nattitudinal changes rather than purely driven by learning processes19–21.\n- I was surprised to see the re-analysis of the Erev et al. (2017) dataset after the rather lengthy\nliterature review and pseudo-meta-analysis in the beginning of the paper, in my understanding,\nconcluded that there were no existing datasets that could adjudicate between the learning\nversus dispositional hypotheses. If the Erev et al. data can shed useful light on this question—\nas evinced by the statement “Overall, all the behavioral analysis that we could replicate in Erev\net al. (2017) lead to similar results and conclusions as the ones performed on our own new\ndata.” (p 21)—then why conduct and report these 7 experiments?\nR2.3\nAgain, we count not help feeling disappointed by this remark, which we felt came across as\nsomewhat dismissive of our experimental and intellectual effort. The fact that some of our\nfindings were, retrospectively, confirmed in Erev et al. (2017) (E2017) does not imply that their\ndataset could definitively answer all the questions we address. To clarify this point, we would\nlike to highlight some limitations of the E2017 study that were overcome by our experiments:\n1. Regarding the feedback/no-feedback contrast, E2017 featured a different number of\ntrials between the two conditions (5 vs. 20), meaning that their effect of feedback is not\ncontrolled for the mere effect of choice repetition.\n2. In E2017 the no-feedback trials always preceded the feedback trials, creating a\npotential order effect that confounded their comparison.\n3. E2017 only considered the complete feedback regime, thus entirely missing the\nopportunity to show that very different psychological mechanisms are at play under the\npartial feedback regime (as demonstrated in our study).\n4. Finally, and most crucially, their study was not designed to adjudicate between the\nlearning and attitudinal hypotheses, as it lacked a proper \"instruction\" manipulation\n(which our study includes). The fact that their dataset was not well-suited to distinguish\nbetween these two hypotheses is evidenced by the emergence of the BEAST model—\na learning model—as the best possible explanation for their data. However, just a few\nyears later, we were able to fully falsify this model on several accounts.\nWe hope this rationale clarifies the clear added value of designing, running and analyzing our\nseven new experiments. It is worth mentioning that all the above were mentioned in the\nsubmitted manuscript; though, to be fair, they were probably not highlighted as much as they\ndeserve. For the sake of clarity, these points are now explicitly listed in the revised manuscript:\n…feedback was treated as a between-subjects factor in most of the previous studies,\nwith only one exception11 - our design improves over Erev et al., (2017) by equalizing\nthe number of repetitions for the two conditions (their design featured five repetitions\nfor no-feedback and twenty for feedback) and by counterbalancing the order of the\nconditions.\nWe re-analyze a previously published dataset that stands out as containing the largest\nsample size among the studies analyzed (N=446) and as proposing an influential\ncognitive model of decision-making (see next paragraph)8,9,11, despite featuring some\nimportant limitations (it involved only complete feedback, the feedback and no-\nfeedback conditions featured different number of trials and always appeared in the\nsame order, there was no clear manipulation of the instructions).\n- The General Discussion struck me as both odd and wordy. Typically, these should lead with\nsome restatement of the key conceptual/theoretical question tested, the approach taken to\ntest it, and what the findings suggest. Instead, I felt like this section meandered through a large\nbody of risky decision-making research without achieving a useful level of generality *or*\nspecificity for the reader. I think the authors could do much better here with a more traditional\nDiscussion structure.\nR2.4\nWe have substantially revised the Discussion section of the manuscript to address this\ncomment (as well as feedback from other reviewers). The section now begins with a summary\nof the results, and we believe the key general contributions are more clearly highlighted and\narticulated. Some of the more \"scholarly\" results and findings (which may only be of interest\nto a limited group of readers) have been moved to the supplementary materials. These have\nbeen replaced with a clearer depiction of what we believe are the far-reaching implications of\nour study.\nMore minor:\n- Where are inferential statistics accompanying the analysis of trial-by-trial feedback dynamics\n(Fig 6)? I expected to see regression tables.\nWe thank the reviewer for this important reminder. We now provide regression analyses for\nthe trial-by-trial feedback dynamics. Their specification can be found in the updated Main\nText/Methods/Statistical Analysis section and the results in Main Text/Table\n1/repeatRisky and Supplementary/Regression Table S3 (detailed version).\nWe also took this opportunity to revise both the specifications and the presentation of all\nregression analyses. Regarding the specifications, the main update is that instead of treating\nall variables as continuous (as was the case in the original version we submitted), we now\ntreat as categorical the variables that naturally have this type (feedback, probability of the risky\noption, etc). Additionally, instead of including all interactions in the fixed effects structure at\nonce, to increase interpretability, we now run a basic model including only the main effects\nand we only include one interaction at a time, depending on the question at hand. Finally, to\navoid several fitting issues that emerged in this new specification (overfitting, singular fits, etc.)\nwe included only the main effects in the random effects structure -in contrast to the maximal\nstructure we used in the original version. All the details about the updated specifications of the\nmodels can be found in the Main Text/Methods/Statistical Analysis section.\nRegarding the presentation, we now include a summary table (Main Text/Table 1) for all the\ninvolved dependent variables containing the predictors discussed in the main text and detailed\nregression tables (Supplementary/Regression Tables S1-4). We hope that all these\nchanges make our paper in line with the standards of the economics literature.\nImportantly, none of these changes and improvement of the statistical methods changed our\npreviously reached conclusions.\n- How is the experimental setting (lab vs online) in Experiment 7 described “core characteristic”\n-- But not that these choice pairs had equal EVs (unlike the previous experiments) ?\nWe are not sure we understand the point, but, indeed, a key difference between Experiment\n1-6 and Experiment 7 is that we replaced the “choice optimality” factor with a modulation of\nthe valence of the decision problem (“gains versus losses”). We made sure that this is clearly\nexplained (we note that in the revised version Experiment 7 is now only presented in the\nsupplementary materials). We also replaced “core” with “key”, which may avoid some\nconfusion.\n- I found the diagram in Fig 1D was confusing, in particular the column headers. Is there a\nmore intuitive way to represent this information?\nWe agree for the Reviewer and following their suggestion, we substantially modified Figure 1\nto make it clearer.\nPlease find below the “design” section of the revised Figure 1:\nRebuttal Figure 8: Revised Figure 1, panels A & B, concerning the design aspects. (A) how the block instructions\nand the trials looked like across different versions of the tasks (with or w/o instructions and with or w/o partial or\ncomplete feedback. (B) Payoffs of the decision problems. Top: the design matrix concerning the outcomes of the\nrisky options; bottom: how the sure (Exp 1-4) and the safe (Exp 5-6) options were calculated.\n- There were some other odd word choices that led to statements that I simply couldn’t follow.\nFor example: the use of the word ‘Rationalizes’ (p 3 and 11) and the phrase ‘natural\ninstantiation of the learning hypothesis’ (p 17). What is an ‘ecological setting’ (p 19) ? I would\nfind other, more intuitive ways to explain these ideas.\nWe thank the Reviewer for pointing this out. We replaced, “rationalized” with “understood”, we\nreplaced “natural instantiation” with “expectations” of the learning hypothesis and we replaced\n“ecological setting” with “ecological (real-life) setting”.\nReviewer #3 (Remarks to the Author):\nThis paper presents a series of experiments testing different hypotheses about how the\npresence of feedback might affect risky choice behavior. Strikingly, the experiments quite\nconsistently speak against feedback-dependent learning, the dominant account in the\nliterature. Specifically, differences between feedback and no-feedback conditions are already\npresent before any feedback is experienced. Moreover, trial-by-trial analyses indicate that\nparticipants rather become less (vs. more) likely to choose a risky option after experiencing its\nmost desirable outcome. The authors interpret these findings as pointing towards mechanisms\nof anticipatory regret and/or epistemic curiosity.\nThe experiments are meticulously designed to provide diagnostic tests pitting different\ncandidate hypotheses regarding the effects of feedback against each other. Thereby, they\nallow the authors to fill in some quite striking but thus far overlooked blind-spots in the\nliterature, which existed because factors such as risk and EV were typically not fully\northogonalized in prior work. Moreover, the behavioral results are highly consistent across the\ndifferent reported experiments and also analyses of existing data, speaking towards the\nrobustness of the findings. Although overall, this is already an excellent manuscript, I do\nhave a few questions and comments that should be addressed in a revision (see details below).\nR3.0\nWe thank the reviewer for this very positive appreciation of our work.\n1. From a conceptual stance, it may be problematic to characterize the present findings as\n“dispositional“ changes in risk preference. After all, ”dispositional“ seems to imply that these\neffects might be long-lasting over time and/or concern a relatively stable disposition to\ntake/avoid risks. Given such an interpretation of the term, one would maybe expect the effects\nof feedback on one block to carry over to subsequent blocks—potentially even to blocks\nwithout feedback. However, this intuitive interpretation of the term does not seem to be what\nthe authors mean to refer to here. It rather seems that the reported choice patterns are adapted\nfrom block to block to the currently experienced task structure, rather than reflecting\n”dispositional“ changes in risk preference. Thus, changing the terminology might be advisable.\nThough ”merely“ concerning terminology, this point seems important to address, in the light of\nrecent discussions in the risky choice literature about whether risk preference is indeed a\nstable disposition, and whether this disposition can even be measured using behavioral tasks.\nR3.1\nWe thank the reviewer for this remark and note that Reviewer 2 expressed a very similar\nconcern (see R2.1). We agree that terminology is important. After careful consideration and\nconsultation with a native English speaker, we concluded that \"attitudinal\" is a more\nappropriate adjective for the effect we are describing, as \"attitude\" refers to more malleable\nstates, rather than stable traits (see the phrase “change of attitude”).\n2. The authors highlight that anticipated regret should affect complete feedback decisions. Do\nthey mean it should *exclusively* play a role given complete feedback? After all, it seems that\nanticipated regret might also arise in partial feedback situations where the participant\nconsiders choosing the risky option, but anticipates that the lower outcome might be obtained.\nHere it is possible to experience (or anticipate) regret, even without feedback about the safe\noption, because the realized outcome of the safe option can be inferred with certainty.\nTherefore, I wonder, to what extent might anticipated regret explain behavior in the partial\nfeedback conditions? (How) can one disentangle this type of anticipatory regret from\nepistemic curiosity here? Could the authors please present additional analyses to assess the\nrelative contribution of anticipatory regret and epistemic curiosity in the partial feedback conditions?\nR3.2\nThe Reviewer raises a valid point regarding the possibility that anticipated regret may shape\nrisk preferences even in partial feedback situations. We acknowledge that this perspective\naligns with prominent decision theory models that attribute a role to counterfactual emotions,\nsuch as regret and disappointment, in description-based choices, even in the absence of\nfeedback (see for example seminal work by Loomes et al22).\nThat said, based on our data, we do not have evidence to support the presence of regret in\nthe partial feedback condition. Indeed, in our design, anticipated or experienced regret should\ninduce a monotonic increase in the probability of choosing the risky option as a function of the\nprobability of the maximum outcome for that option (see additional information in R1.1 for a\nfuller explanation). This monotonic relationship is key for detecting (or disentangling) the\ninfluence of regret on risk preferences.\nWith this diagnostic pattern in mind, we examined our data to see if the influence of regret on\nrisk preferences can be detected in other conditions (even if below a significant threshold).\nFollowing the reviewer’s suggestion, we focused on:\n1. The \"No feedback\" conditions present in both the partial and complete feedback\nexperiments.\n2. The \"Partial feedback\" condition.\nAs illustrated in Rebuttal Figure 9 (below), a closer examination of these cases provides no\nevidence for the influence of regret. In fact, in the \"No feedback\" conditions (Case 1) and in\nthe \"Partial feedback\" condition, we observed a non-significant trend in the opposite\ndirection—a decrease rather than an increase. Therefore, while it is theoretically possible, as\nthe reviewer suggests, that anticipated regret could have influenced choices in the conditions\nwithout feedback or with partial feedback (potentially based on mental simulations of possible\noutcomes), the data indicate otherwise.\nThis aigns with the consensual idea23 that regret is, fundamentally, a comparison between\nobtained and forgone outcomes, and this comparison, as well as the anticipation of it, is more\nsalient in the complete feedback condition. Thus, it is not surprising that, while theoretically\npossible, we did not observe evidence of regret in the remaining conditions (no feedback or\npartial feedback), where outcome comparisons are not made explicit. Finally, while we are not\naware of any study examining the intensity of regret as a function of the saliency of outcomes’\ncomparison, it is worth mentioning that complete feedback has been shown to intensify the\nimpact of regret compared to when partial 24 or no 1 feedback is provided, as well as that\nexperience (namely, exposure to feedback) increases sensitivity to regret 1,25.\nFigure 4C and 4D results Zoom in\nPartial feedback experiments\nPartial\nfeedback\nconditions\nNo feedback\nconditions\nComplete feedback experiments\nppp===159000\np=10 p=50 p=90 p=10 p=50 p=90\nProbability\nProbability\nRebuttal Figure 9: Closely looking for a possible role of regret in other conditions other than “complete feedback”.\nOn the left, we reproduce the full result (taken from Figure 4) illustrating the effect of feedback on Risky choice rate\ninteracting with the probability level (of the high-value outcome of the risky option) across the partial (top panel)\nand the complete (bottom panel). On the right, we show a “zoom in” of the data after averaging across all\nexperiments to gain maximum statistical power. A robust monotonic trend can only be observed in the conditions\nwith complete feedback.\n3. The author’s notion that learning should generally increase EV maximization rests on the\nassumption that the process of learning itself adheres to a normative standard. However, there\nare experiments, for instance in the realm of Bayesian updating, that have demonstrated that\npeople do not necessarily integrate new information in an optimal manner. Instead, they\nsometimes over- or under-adjust their expectations in the light of new information. In this light,\ncan one really argue that learning should *generally* render choice behavior more optimal?\nR3.3\nThe Reviewer is absolutely correct; there is ample evidence of biased reinforcement learning\nand Bayesian integration (including in our own studies). We have revised our paper to clarify\nwhat we believe are the predictions of the learning hypothesis. In light of this comment, we\nhave further qualified our claim that learning should increase maximization in both the\nintroduction and the discussion.\nWe also take this opportunity to emphasize that the absence of a beneficial effect of feedback\non maximization is not the only result that challenges the learning hypothesis. Specifically, the\nlearning hypothesis is contradicted by the first trial effect—the observation that the effect is\npresent before any feedback is experienced, implying that it is not mediated by experienced\nfeedback. Furthermore, the learning hypothesis is challenged by our trial-by-trial analysis,\nwhich shows that participants exhibit a \"negative recency effect,\" meaning they tend to not\nrepeat rewarded risky choices. Crucially, no learning process, however biased, would predict\nthis outcome.\nWe have copied below the relevant sections of the amended introduction and discussion:\nWe shall refer to this category of accounts as the learning hypothesis. Because the\nintegration of feedback in future choices is supposed to correct originally distorted\nsubjective probabilities, the learning hypothesis often assumes that the presence of\nfeedback should correct representational biases and, as a consequence, promote\noptimal (i.e., expected value maximizing) choices 26–28. Admittedly, though, these\nsimple predictions from the learning hypothesis can be challenged, e.g., by the\npresence of learning biases 29,30, or when the probabilities of the outcomes are extreme\nand the options are not sufficiently sampled: two conditions that lead the experienced\nand the actual frequency of the outcomes to diverge31.\n[…]\nCritically, in contrast to the learning hypothesis, which supposes that the effect of the\nfeedback should emerge gradually, the attitudinal hypothesis conceives that it can\nemerge even before any feedback is experienced – i.e., by anticipation. Because the\ntwo hypotheses differ in the temporal relation with respect to the time of choice and\noutcomes, fine-grained temporal dynamics can dissociate the two accounts: attitudinal\neffects precede choices while learning effects follow outcomes. In addition, the two\nhypotheses are also different in their relation to choice optimality. Learning\nmechanisms are generally supposed to correct representational biases and,\naccordingly, should increase expected value maximization. Attitudinal ones are more\nsilent in that respect.\n4. Did the emergence of the abrupt effect of feedback after the first trial depend on which\noption was chosen on the first trial, and on which feedback was received? Arguably, under\nlearning, the direction of the effect should probably depend on these factors. If there is an\ninvariable increase in risk taking, this would provide further evidence against learning.\nR3.4\nWe thank the reviewer for this valuable insight and suggestion. Indeed, we lacked a proper\ncharacterization of the abrupt emergence of the feedback effect on the second trial in the\nexperiments without instructions. Following the reviewer's suggestion, we examined this effect\nas a function of both the choice made and the outcome received on trial 1. The results are\npresented below in Rebuttal Figure 10. As shown in the figure, the feedback effect is present\non trial 2 across all cases, regardless of which choice was made or which outcome was\nreceived on trial 1.\nImportantly, as the reviewer suggested, this analysis further supports an attitudinal change\nmechanism and challenges the learning hypothesis. Since the effect is present in the second\ntrial regardless of the information received in the first trial, only the mere discovery of the\npresence of feedback (and consequent attitudinal change) could explain the effect. The main\neffect of feedback is observed regardless of the previous choice type (sure/safe, versus risky\nFigure R10 A&C), and additively to the main effect of the previous choice type on R-rates\n(Figure R10 B&D).\nWe believe this result is important, so we have mention it in the results section of the main text\nand also incorporate Rebuttal Figure 10 as part of Figure 5 (relevant panels are A-D) of the\nrevised manuscript.\nA follow-up question is whether the abrupt emergence of the feedback effect on the\nsecond trial in the experiments without block instructions was dependent on the choice\nmade on the first trial. We observe that the main effect of feedback is observed\nregardless of the previous choice type (sure/safe, versus risky), and additively to the\nmain effect of the previous choice type on R-rates (Figure 5A and 5C). Since the\nsecond-trial effect is present regardless of the choice made on the first trial, only the\nmere discovery of the presence of feedback (and consequent attitudinal change) could\nexplain the effect, challenging the learning hypothesis.\nNext, we wanted to check whether the abrupt effect of feedback between the first and\nthe second trial in experiments without block instructions was influenced by the\noutcome received on the first trial. While confirming the presence of a negative recency\neffect, the results also show that the effect of feedback is detectable, regardless of the\nnature of the outcome received on the first trial (Figure 5B and 5D). This result further\nsupports the idea of an outcome-independent attitudinal change in risk preferences.\nRebuttal Figure 10: Risky choice rate in the second trial of the experiments without instructions as a function of\nfeedback and of the choice made in the first trial (“safe” or “risky”; A) or of the outcome received at the first trial\n(“zero” or “positive; B). Plots (C) and (D) collapse the feedback dimension (by taking the difference) of plots A and\nB, respectively.\n5. Regarding p.15, Figure 3. In Experiments 3-4, the R-rate is below .5, even in the p=50\ncondition. It seems that under anticipated regret, as presented by the authors, one would\nexpect an R-rate of pretty much exactly 50% here, because the safe and the risky option each\nminimize regret in 50% of the trials (likewise, the R-rate should be >50% in the p = 90\ncondition). How can one explain that this does not seem to be the case in the data?\nR3.5\nWe thank the reviewer for allowing us to clarify this point. The reviewer's observation regarding\nthe p=50 condition (“under anticipated regret, as presented by the authors, one would expect\nan R-rate of pretty much exactly 50%”) would be correct if one assumed that regret is the sole\ndeterminant of risk preference. However, we believe that feedback-induced adherence to\nregret influences risk preferences on top of pre-existing tendencies, which can be adequately\ncaptured by standard models of risk aversion. To put it another way, we refer to regret to\nexplain relative differences on R-rates, rather than their absolute levels.\nWe believe this point is made even clearer in the revised manuscript, where we have\nexpanded the explanation concerning the role of regret and how it is computationally captured\nin standard models such as the BEAST (see R1.1).\n6. It is quite surprising that the authors find no differences between gain and loss conditions\nin Experiment 7. People seem to behave slightly risk-averse in the no-feedback condition and\nrisk-neutral in the feedback condition, regardless of domain (gain/loss). How can these\nfindings be reconciled with many findings in the risky choice literature indicating that\npreference patterns typically reverse between domains (the reflection effect)?\nR3.6\nWe agree with the Reviewer that differences in risk preference between the gains and losses\ndomains (Exp 7) could be anticipated based on what is known about loss aversion and the\nconsequent “reflection effect. Despite the robustness of the reflection effect in many contexts,\nit is also worth pointing out that the traditional demonstration of loss aversion and reflection\neffect emerged from one-shot paradigms; therefore, we can also consider that choice\nrepetition and the presence of feedback are additional experimental factors that may blunt or\nundermine the detection of them. In line with this, we found that E2017 reported only a weak\nreplication of the reflection effect in the “no feedback” condition and no effect—or even a\nreversed reflection effect—in the “feedback” condition.\nFurthermore, a closer look at the literature suggests that loss aversion—and, consequently,\nthe reflection effect—may not be as generalizable as originally proposed. Specifically, we refer\nto a few insightful studies led by Eldad Yechiam, which propose that loss aversion tends to\nmaterialize with larger losses rather than smaller ones. Given that our experiment involved\npayoffs in the range of only a few euros, it is plausible that we fall within this specific\ncircumstance.\nWe have mentioned these arguments in the supplementary discussion dedicated to\nExperiment 7’s results:\nIn our Experiment, we found no evidence of the reflection effect, which should translate\ninto higher risk seeking in the loss, compared to the gain domain. This may appear\nsurprising, as the reflection effect is traditionally attributed to loss aversion, which, in\nturn, is generally considered a robust feature of human decision-making32. Our findings\nbecome less surprising when one notices that the traditional demonstration of the\nreflection effect has been made in one-shot paradigms33. In contrast, in paradigms with\nchoice repetition and/or feedback (namely, paradigms closer to ours) the reflection\neffect is much less robust or even reversed (Erev et al., 2017 reported only a weak\nreplication of the reflection effect in the “no feedback” condition and no effect—or even\na reversed reflection effect—in the “feedback” condition; Rigoli et al., 2019 report\nnull/reversed results of risk attitudes as a function of decision domain too). Related to\nthe reflection effect, loss aversion has also been shown to have been overstated, as it\nseems to be present only for very large losses and only in a fraction of studies that\nreport it35.\n7. The analysis of trial-by-trial changes in behavior (p.19 f.) indicates that people adapt their\nbehavior to feedback in a way reminiscent of a gambler’s fallacy. That is, indeed, some\nfeedback-dependent adaptation of behavior on the trial-level seems to be present in the data.\nBecause this adaptation seems to be based on a misconstrued notion of non-independent\noutcomes (i.e., gambler’s fallacy), the finding may speak against learning in the sense of\nmoving closer to optimal behavior, and this is also the key inference the authors draw.\nHowever, the mere fact that such trial-by-trial effects exist also indicates that „dispositional“\nchanges alone are insufficient to fully explain the consequences of feedback. This should be\nmentioned and discussed.\nR3.7\nFirst, let us clarify that the attitudinal effect is revealed by a comparison between the feedback\nversus no-feedback condition, while the negative recency effect can only be assessed (by\ndefinition) in the feedback conditions. This being said, the Reviewer correctly appreciates that\nthe negative recency effect (similar to the Gambler’s fallacy) revealed in our data further\nchallenges the learning hypothesis. We also agree that these results indicate that feedback\ninfluences decision-making in ways that are not solely mediated by an attitudinal mechanism.\nWe have clarified this point in the discussion section of the revised manuscript.\nTo sum up, not only do we demonstrate that the effect of feedback on risk preference\nprecedes the reception of any feedback (and is, therefore, better understood as a\nchange in attitude), but we also disprove any residual role for feedback-induced\nlearning processes in the trial-by-trial dynamics by evidencing biased reactions to\nprobabilistic and stochastic events akin to the gambler’s fallacy16,17,36,37.\n[…]\nThese results not only rule out the possibility that residual feedback-induced learning\neffects are at play but also suggest that an explicit description of the probabilistic\nprocess may create (biased) prior expectations that prevent learning processes.\n[…]\nIn particular, our results suggest that, contrary to what common sense could dictate,\nproviding feedback cannot be considered as a panacea to correct decision-making\nbiases, notably because the effects of feedback are at least partially mediated by\nattitudinal changes rather than purely driven by learning processes19–21.\nMinor issues:\n- On p.4., the authors argue that anticipated regret may entail more choices of the risky option,\nbecause it (typically) offers the possibility of obtaining the best outcome in a choice problem.\nHowever, the opposite can also be the case (sometimes the safe option minimizes regret), as\nthe authors explain later (on p.15). In my opinion, this should already be pointed out in the\nintroduction to avoid confusion and doubts regarding the argument on anticipatory regret.\nSimilar concerns about the definition of regret were also pointed out in R1.1, we refer to this\nresponse for more details that we hope will also satisfy the Reviewer.\n- Sometimes the authors refer to non-risky options as “safe”, other times as “sure”. This\ndistinction is only explained on p.16. Please explain it earlier to avoid confusion.\nIn principle, we settled for using “safe” for lower variance options (Experiments 5-6) and “sure”\nfor no variance options (Experiments 1-4). Following the Reviewer’s remark, we double-\nchecked the manuscript to avoid confusion.\n- Panel B of Figure 1 (and corresponding panels presenting choice problems in other figures)\nis a bit difficult to parse; could this information be presented in a more straightforward manner?\nWe improved Figure 1 in a way that we believe circumvent this issue.\nRebuttal Figure 11: Revised Figure 1, concerning the design aspects. (A) how the block instructions and the trials\nlooked like across different versions of the tasks (with or w/o instructions and with or w/o partial or complete\nfeedback. (B) Payoffs of the decision problems. Top: the design matrix concerning the outcomes of the risky\noptions; bottom: how the sure (Exp 1-4) and the sage (Exp 5-6) options were calculated.\n- Table 4: it is not immediately clear what the numbers 1, 2, 3,10 characterize in row C\n(probably trial-numbers). Please provide additional information in Table-note.\nThis table was moved to the Supplementary material (Table S5) and we updated its legend to\nspecifically clarify what the numbers 1,2,3,10 refer to.\n- Panel B of Figure 6 is quite difficult to decipher (esp. the middle part of each subplot).\nThank you, the reviewer will find most figures and tables radically changed and hopefully\nthoroughly clarified.\n- p. 21 „trivial problems decisions“ —> „trivial decision problems“\n- p. 26 „a proper instruction-induce first trial effect“ —> „a proper instruction-induced first trial\neffect“\n- p. 26 „a dispositional influences“ —> „a dispositional influence“\nThank you, we corrected these typos."}, {"round": 2, "reviewer_comments": {"reviewer_2": "The authors have done a commendable job in responding to my comments and concerns and, as a result of their substantial revisions, I believe these findings will be much easier for readers to appreciate and understand .", "reviewer_3": "I thank the authors for their detailed and thoughtful rebuttal, as well as for the careful and convincing way in which they addressed the comments I raised in the first round of reviews. The revisions and improvements made to the manuscript in response to the initial feedback have significantly strengthened the paper. I do have some additional questions/comments regarding the data and code availability and documentation. If these points can be addressed I am supportive of publication.\nThe provided link (https://github.com/hrl-team) leads to the general GitHub page of the HRL team. It was not immediately evident to me which specific repository corresponds to the present study. I identified the repo psych201-nasioulas2024feedback to be the relevant one containing some code related to the presented work. The README is rather minimalistic, including links to the preprint and to another GitHub repository where the data are stored. Although I am not perfectly fluent in python my impression is that the uploaded code mainly serves to generate prompts for the experiment rather than reproducing data analysis. Unless I overlooked something the full analysis code should be added. Additionally, some more detailed documentation as well as a direct link to the relevant dataset and code repository/repositories would be helpful.\nMinor (typos/grammar):\np. 16 : „The existence of feedback-induced attitudinal effects on risk preferences does not rule exclude that additional feedback-induced learning processes co-exist.“ — either „rule out“ or „exclude“  p. 21 „ . This is an expected result, since the BEAST attitudinal changes occurring before any feedback are experienced play no role. „ — „in the BEAST“ or „for the BEAST“?\np. 26 „\"Our results, therefore, suggest that the BEAST model to be continued used as a valid model of human decision-making should undergo major restructuring vis-à-vis several key structure Features\" — rather „Our results, therefore, suggest that the BEAST model—if it is to continue being used as a valid model of human decision-making—should undergo major restructuring with respect to several key structural features.“ or something similar?"}, "author_response": "Reviewer #2 (Remarks to the Author):\nThe authors have done a commendable job in responding to my comments and\nconcerns and, as a result of their substantial revisions, I believe these findings will be\nmuch easier for readers to appreciate and understand.\nWe thank the reviewer for their positive remarks and the numerous\nconstructive comments that significantly improved our paper.\nReviewer #3 (Remarks to the Author):\nI thank the authors for their detailed and thoughtful rebuttal, as well as for the careful\nand convincing way in which they addressed the comments I raised in the first round\nof reviews. The revisions and improvements made to the manuscript in response to\nthe initial feedback have significantly strengthened the paper. I do have some\nadditional questions/comments regarding the data and code availability and\ndocumentation. If these points can be addressed I am supportive of publication.\nWe thank the reviewer for their positive remarks and the numerous constructive\ncomments that significantly improved our paper.\nThe provided link (https://github.com/hrl-team) leads to the general GitHub page of the\nHRL team. It was not immediately evident to me which specific repository corresponds\nto the present study. I identified the repo psych201-nasioulas2024feedback to be the\nrelevant one containing some code related to the presented work. The README is\nrather minimalistic, including links to the preprint and to another GitHub repository\nwhere the data are stored. Although I am not perfectly fluent in python my impression\nis that the uploaded code mainly serves to generate prompts for the experiment rather\nthan reproducing data analysis. Unless I overlooked something the full analysis code\nshould be added. Additionally, some more detailed documentation as well as a direct\nlink to the relevant dataset and code repository/repositories would be helpful.\nMinor (typos/grammar):\np. 16 : „The existence of feedback-induced attitudinal effects on risk preferences does\nnot rule exclude that additional feedback-induced learning processes co-exist.“ —\neither „rule out“ or „exclude“ p. 21 „ . This is an expected result, since the BEAST\nattitudinal changes occurring before any feedback are experienced play no role. „ —\n„in the BEAST“ or „for the BEAST“?\np. 26 „\"Our results, therefore, suggest that the BEAST model to be continued used as\na valid model of human decision-making should undergo major restructuring vis-à-vis\nseveral key structure Features\" — rather „Our results, therefore, suggest that the\nBEAST model—if it is to continue being used as a valid model of human decision-\nmaking—should undergo major restructuring with respect to several key structural\nfeatures.“ or something similar?\nThanks for spotting these minor typos, the sentences have been amended.\nReviewer #3 (Remarks on code availability):\nThe provided link (https://github.com/hrl-team) leads to the general GitHub page of the\nHRL team. It was not immediately evident to me which specific repository corresponds\nto the present study. I identified the repo psych201-nasioulas2024feedback to be the\nrelevant one containing some code related to the presented work. The README is\nrather minimalistic, including links to the preprint and to another GitHub repository\nwhere the data are stored. Although I am not perfectly fluent in python my impression\nis that the uploaded code mainly serves to generate prompts for the experiment rather\nthan reproducing data analysis. Unless I overlooked something the full analysis code\nshould be added. Additionally, some more detailed documentation as well as a direct\nlink to the relevant dataset and code repository/repositories would be helpful.\nWe updated the data and coding sharing files so that they are full available to\nthe community.\nData availability\nThe data supporting the findings of this study are available on GitHub at https://github.com/hrl-\nteam/riskyDecisionMakingFeedback. The file Nasioulas2024_data.csv contains the raw data from the\nnewly collected Experiments 1–7, and Erev2017_data.csv contains processed data reproduced from\nErev et al. (2017). The original datasets from Erev et al. (2017) are publicly available on Zenodo at\nhttps://zenodo.org/records/321652.\nCode availability\nAll analysis code is openly available on GitHub at https://github.com/hrl-\nteam/riskyDecisionMakingFeedback. The MATLAB script generate_figures_main.m reproduces all\nmain-text and supplementary figures, and the R script generate_glmm_main.R performs the logistic\nregression analyses reported in the manuscript."}]

Decision letter