In this section, we critically review studies of decisions under risk among fully-described gambles, which features decision problems opposing a risky and a sure option, and which compare choices in the presence versus absence of feedback. With these criteria, we identified 9 studies that otherwise differed greatly in the composition of the decision problems (probabilities and outcomes), in the number of repetitions of each decision problem, in the number of subjects and in the general design (between- versus within-subjects manipulation of the presence of feedback; see Table 1; Table S1 for more details).
To inform our research question, we focus on 1) whether the presence of feedback affects decisions under risk in a systematic direction, with regard to risk preferences, and, 2) when applicable, whether the presence of feedback improves decisions, in the sense of increasing the capacity of participants to make expected-value maximizing choices.
Our critical literature review points toward a relatively consistent effect of feedback on increasing risk-taking. Most of the literature has adopted, implicitly or explicitly, the intuition that feedback acts through the updating of, otherwise distorted, subjective probabilities (learning hypothesis) (Jessup et al., 2008; Marchiori et al., 2015; Yechiam & Barron, 2005). Yet, two studies which report results coherent with this general picture, adopted a specific experimental design choice which, when taken into account in the interpretation of the results, challenges this view (Josephs et al., 1992; Rigoli et al., 2019). By revealing the effects of feedback in the context of unique (one-shot) decisions set-up, which prevents an option-specific learning effect, these studies raise the possibility of a more general dispositional effect of feedback, for instance in the form of curiosity (Rigoli et al., 2019). Furthermore, the fact the effect of feedback is generally stronger for high-probability risky options is consistent with a form of regret avoidance, understood as the drive to choose the option that gives the highest possible outcome most of the time (Cohen et al., 2020; Erev et al., 2017).
To sum up, a critical survey of the available literature does not allow clear-cut conclusions concerning the psychological mechanisms of the effect of feedback and their behavioral consequences. The effects of feedback on risky or optimal choice rate were not systematic in direction and often quite negligible in size. Our assessment of the literature also allowed us identifying several – frequent – methodological shortcomings that limit the questions that can be addressed. More specifically, we noted that experimental designs often fell short of orthogonalizing key dimensions of options, such as risk, probability and expected value and to control for an equal number of trials with and without feedback.
To address our research question, while eluding the shortcomings identified in the literature, we ran a series of six online (N = 100 for each experiment before the application of strict exclusion criteria ‒ see Methods) and one laboratory incentivized experiment (N = 30). The six online experiments were variants of the experimental paradigm that we will describe below.
One novelty of our experimental design is using a factorial design with a within-subjects 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 exception (Erev et al., 2017). 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 itself (Couto et al., 2020). Trials featuring the same decision problem were clustered in blocks of 10 trials. Feedback and no-feedback blocks were randomly interspersed.
We used a binary choice task featuring a sure and a risky option in each trial. The risky option had the form of (p,m; 1-p,0), namely giving m points with probability p and zero points otherwise. In addition to feedback (present or absent), we also factorially manipulated the choice 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. This allowed to orthogonalize risk preference and decision optimality ‒two features that have been often confounded in the literature. Finally, we manipulated within-subjects the probability of gain associated with the risky option (three levels, namely 0.1, 0.5, and 0.9), 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 subject, 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 effect (GLME) model with the task factors (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 (P < 0.001; Table 3.A), which was characterized by an increased propensity to choose the risky option when trial-by-trial feedback was present (Fig. 2A; Table 4.A). 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) (Table 4.D), such that there was no detectable main effect of feedback on the optimal choice rate (Tables 3.B & 4.B; Fig. 2B). In other terms, there was a significant interaction between feedback and option optimality: feedback increased the O-rate when the risky option was the EV-maximizing one, but decreased it otherwise (interaction P < 0.001; Table 3.B).
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 the 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 (P > 0.05; Fig.
2C; Table
4.
C), R-rate in feedback and no-feedback conditions abruptly diverged in the second trial and the difference remained constant until the end of the block (P < 0.01 in all trials).
Overall, the results of this first experiment appeared, at the macroscopic level, in line with most of the existent literature generally showing an increase of 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 seems abrupt rather than gradual could be rationalized 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 disposition 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 a dispositional 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 in which, at the beginning of each block, participants received explicit instructions (hence block instructions) mentioning whether they will 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 (Fig.
2D and
2E; Tables
3 &
4). Yet, the between-experiment manipulation of the block instruction produced a significant difference in the effect of feedback on first-trial R-rates (P < 0.01; two-sample t-test; 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 (P < 0.01; Table
4.
C; Fig.
2F). Thus, it seems that the mere anticipation of feedback information induced by the block instructions was enough to change risk preference 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 feedback instruction in Exp.2 favor the dispositional hypothesis. Overall, this pattern of results is consistent with a dispositional 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.
Curiosity cannot be the only determinant of the effect of feedback on risk preference: a role for regret
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. 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 in absence of feedback) and the risky one (whose result cannot be inferred with certainty in absence of feedback) 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 (Tables 3.A & 4.A), and had no effect on the O-rate (Tables 3.B & 4.B).
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 (P < 0.01 from 3rd trial onwards; Fig. 3A; Table 4.C). 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 (P < 0.01 in all trials; Fig. 3Β; Table 4.C). As in Exp.1 versus Exp.2, the between-experiment manipulation of the block instruction produced a significant difference in the effect of feedback on first-trial R-rates in Exp.3 versus Exp.4 (P < 0.01; two-sample t-test; inset of Fig. 3Β).
While these results are once again consistent with a feedback-induced dispositional change in risk preference (the effect arose before any feedback is 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 systematic comparison is possible only in the complete feedback condition, where regret is experienced whenever the forgone outcome is higher than the obtained one. However, a regret-minimizing account demands that the effect of feedback on risk preference should interact with the probability of obtaining the high-value outcome from the risky option (Cohen et al., 2020; Erev et al., 2017). This is because, if the highest-value outcome of the risky option (hence referred to as the best-risky outcome) is rare (say 10%), picking the sure option actually minimizes regret 90% of the time. The converse is true if the best-risky outcome is frequent (e.g. 90%): in this case, choosing the risky option minimizes regret 90% of the time. Thereby, to assess the anticipated regret hypothesis, we evaluated the effect of feedback 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 (Fig. 3E; P < 0.01; Table 3.C), 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 (P < 0.001; Table 3.C) but being stable in the partial feedback experiments (P > 0.05; Table 3.C).
Extending the results to moderate risk options?
Next, we attempted to 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 paradoxes (Tversky & Kahneman, 1986) -yet, Plonsky et al. showed that their findings stay essentially unchanged when adding noise in sure lotteries in experience-only decisions (Plonsky & Teodorescu, 2020). In the next two experiments, we therefore assessed the robustness of our results to variation in task conditions, specifically to contexts where the non-risky option is not certain. To do so, we designed Experiment 5 and Experiment 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 one of the sure options (Fig. 1C). 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. 1). Consolidating our conclusions, all the main results identified in Exp.1–4 were replicated in this modified setup. Notably, the presence of feedback increased risk-taking from the first trial significantly in the partial feedback Exp. 5 and numerically in the complete feedback Exp.6, (Table 4.C), and this dispositional effect interacted with the probability of the risky option in the complete feedback condition (Table 3.D). 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 confirmed that the dispositional effect induced at the first trial was robustly elicited in the experiments featuring feedback instructions (Exps 2,4,5,6; Fig. 4B) and vanished in the absence of the said instructions (Exps 1,3; Fig. 4A). 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 (Exps 1,2,4; Fig. 4C), while significantly modulated by this factor in the complete feedback experiments (Figs. 4D & 4E). Finally, if anyting when pooling all the experiments, contrary to the more natural instantiation of the learning hypothesis, we found a small negative impact (~ 1%) of the presence of feedback on the optimal choice rate (Table S3).
Extending the results to the loss domain
Having robustly established our results in six web-based experiments focusing on gain prospects, we proceeded to conduct a final experiment (Exp.7) with significant variations in these two core characteristics. First, it was performed in the lab (N = 30), which allowed us to further probe the robustness of our conclusions in a more controlled set-up, while concomitantly using higher incentives (Exp.1–6: £5.72(0.1); Exp.7: €14.4(0.35)). Second, Exp.7 featured a valence manipulation: prospects were framed either as potential gains or losses, in lieu of the risky-better vs. risky-worst dimension. Keeping in line with the previous experiments, we manipulated the probability of the risky option (three levels, namely 20%, 50%, and 80%), and the magnitude of the risky option (three levels in the gain, three in the loss domain) (Fig. 5A). Finally, Exp.7 featured partial feedback and block-wise instructions, such that participants knew before starting each block whether or not they would receive feedback in the upcoming block.
Exp.7 once again confirmed a positive effect of feedback on the rate of risky choices (P < 0.001; Fig. 5B; Tables 3.E & 4.A). Notably, valence did neither have a main effect on the percentage of risky choices nor interact with feedback (P > 0.05; Table 3.E; Fig. 5C). Note that the design of this experiment (the two options having equal EVs) renders the analysis of optimal choice rate irrelevant.
Furthermore, supporting the dispositional effect hypothesis, the difference in risky rates between feedback and no-feedback blocks was detectable from the very first trial (P < 0.01; Fig. 5D; Table 4.C). Thus, Exp7 confirms that the anticipation of feedback (induced by the block instructions) changes the behavior before any feedback is actually experienced, and generalizes this result to decision contexts involving losses as well as higher incentives.
Feedback-induced trial-by-trial adjustments
Having evidenced feedback-induced dispositional 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 average risky choice rate, because their effect depend on the previous trial choice and outcome. To investigate possible learning effects in trial-by-trial dynamics, we therefore 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 (non-zero) outcome, compared to receiving the worst possible (zero) outcome (Fig. 6A, left) (REF). We tested this hypothesis by analyzing this behavioral variable (probability of repeating a risky choice, p(Rt|Rt−1)) across all datasets. The results are in sharp contrast with the learning processes predictions (Fig. 6B). In fact, the probability of repeating a risky choice was lower after receiving positive feedback (means p(Rt|Rt−1=0) = 0.69 ± 0.27, p(Rt|Rt−1>0) = 0.62 ± 0.26, paired-difference test P < 0.001). The analysis of trial-by-trial dynamics thus show no support for any form of feedback-induced learning process, and rather strictly 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 laboratory Ayton & Fischer, 2004; Teoderescu et al., 2013; Barron & Leider, 2010 and in ecological setting Clotfelter & Cook, 1993), according to which participant would move away from a recently rewarded risky choice because they (wrongly) assume that the subsequent likelihood of positive feedback will be lower (Fig. 6B and Fig. 6C). This gambler’s fallacy interpretation is further confirmed by conditioning this analysis on the probability of the risky outcome (remind, in our task we featured three probability levels: 0.1, 0.5 and 0.9). This actually reveals that the effect is modulated by the underlying outcome probability and is maximal when outcomes are rare (p = 0.1: subjects perceive the likelihood of receiving two positive outcomes in a row lower than reality) and absent when the outcomes are common (p = 0.9; regression analysis revealed a highly significant interaction between the probability of the risky outcome and the outcome in the previous trial P < 0.001; in addition to a highly significant main effect of outcome of the previous trial: P < 0.001). 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 or disposition), 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 fallacy (Ayton & Fischer, 2004; Barron & Leider, 2010; Clotfelter & Cook, 1993; Teoderescu et al., 2013).
Checking our findings in 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 otherwise generally understood as stemming from a learning process (Table 1). 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 absence) we also found that the effects were mediated by a change of attitude (or disposition) of different nature in the partial (consistent with curiosity) and complete (consistent with regret) feedback condition; trial-by-trial dynamics analysis further ruled out that outcome-based learning play a role in these processes.
To close the loop, we conclude by re-analyzing a previously published dataset that stands out as the one containing the larger sample size among the studies analyzed (N = 446) and the wider spectrum of decision problems (150 decision problems) (Erev et al. 2017). In order 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 define risky choice rate), decisions involving options with different expected values (to define optimal choice rate) and decisions featuring non-extreme probabilities (excluding 1% or 99%) for the risky option. We also excluded trivial problems decisions in which one option dominates the other (see Supplementary Material for more details about the study and the decision problem selection).
This re-analysis of Erev et al. (2017) data was consistent with our own results on the absence of positive effect of feedback on the optimal choice rate (without feedback 0.66 ± 0.21; with feedback: 0.65 ± 0.17; P > 0.05; Fig. 7A), as well as on the increase in risk choice rate (without feedback: 0.38 ± 0.22, with feedback 0.42 ± 0.18; P < 0.001; Fig. 7B). 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\(\le\)0.25, medium: 0.25<prob<.075, high: prob\(\ge\)0.75) 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 (Fig. 7C; low: -0.053±0.317; medium: 0.052±0.198; high: 0.147±0.341). Moreover, we looked at the trial-by-trial dynamics and found a negative recency pattern, consistent with a gambler’s fallacy bias (Fig. 7D). Finally, while the manipulation of instructions was not present as such in Erev 2017, the different orders of presentation of decision problems allowed us to perform an analogous analysis, which further supports a first-trial/dispositional effect (for the details look Supplementary Material/ Erev et al. (2017) re-analysis & Figure S1). Overall, all the behavioral analysis that we could replicate in Erev et al. (2017) lead to similar results and conclusions as the ones performed on our own new data.