Introduction

How people evaluate risk and decide between risky alternatives is a fundamental problem in decision making—one that should perhaps take on renewed importance in light of the recent financial crisis [1]–[3]. Risk sensitivity in humans is most commonly evaluated by asking people to decide between explicitly described, hypothetical choice scenarios [4]–[5]. Yet frequently in life, we make repeated choices, and our knowledge about uncertain outcomes is gleaned from experience, rather than from explicitly described scenarios. Recently, researchers have begun to evaluate risky choice based on experience, and several studies have reported that experience-based choices may differ from choices based on verbal descriptions. In particular, a description-experience gap has been revealed in people's sensitivity to rare outcomes [5]–[14]. When making decisions based on verbal descriptions, people overweight rare events, but they underweight those rare events when making decisions based on experience. In this paper, we show how this difference between decisions from description and experience extends beyond rare events, such as the proverbial black swan, and occurs even for events that are equally probable, such as tossing a coin.

When given a choice between explicitly described options, people tend to be risk averse for gains and risk seeking for losses. For example, when presented with a choice between a guaranteed win of $100 or a 50/50 chance of winning $200, most people will select the sure win and take the $100. Alternatively, if given a choice between a sure loss of $100 or a 50/50 chance of losing $200, most people will gamble and take the risky option. This shift from risk aversion for gains to risk seeking for losses is known as the reflection effect and is a foundational result in behavioral economics [4], [15]–[16]. This reflection effect is often interpreted, within the guise of prospect theory, as reflecting an s-shaped utility curve, whereby the subjective utility of gaining $200 is less than twice as good as the subjective utility of gaining $100, and the subjective utility of losing $200 is less than twice as bad as the subjective utility of losing $100. As a result, people tend to avoid the gamble in the gain case, but seek out the gamble in the loss case. This asymmetry can arise even when the objective expected value of both options in both choice settings is identical [4], [16]–[19].

If, however, one of the two outcomes is comparatively “rare”, usually defined as less than 20% chance of occurrence, then a different pattern of results emerges when people are asked to decide based on their experiences [6], [11]. For example, Hertwig et al. [10] (Problems 1 and 4) presented people with a choice between 100% chance at gaining $3 or an 80%/20% chance at gaining $4/$0. The description group received a verbal description of the contingencies. The experience group was allowed to repeatedly sample from the different alternatives and get feedback before making a single rewarded choice. They found that the experience group chose the risky alternative much more often than the description group (i.e., the experience group was more risk seeking). In contrast, when the choice was changed to be between losses, but keeping the amounts and probabilities the same, the experience group chose the risky alternative much less often the description group (i.e., the experience group was more risk averse). These results are commonly interpreted as an underweighting of the rare outcome in the experience-based decision process, possibly due to estimation error or a recency bias [11]. These results, however, hint at something even more fundamental: Perhaps the entire s-shaped curve mapping from objective value to subjective utility is altered when people learn about risky contingencies from experience. As a result, differences between description- and experience-based decisions should appear even in the absence of rare events. To evaluate this possibility, we designed two experiments that examine decisions from experiences without any rare outcomes, where the risky option always led to one of two equiprobable (50%) outcomes.

In this pair of experiments, we demonstrate that the differences between described and experienced risky choices are not limited to rare events. We developed a novel task for decisions from experience and description, wherein the same participants were repeatedly tested for risky choice in both ways (Fig. 1). In the experience conditions, participants chose between two colored doors and then immediately gained or lost points. One door led to a guaranteed win of 20 points, whereas a second door was followed by a 50/50 chance of winning 0 or 40 points. The final two doors used the same contingencies, but were followed by losses instead of gains. In the description conditions, the same participants chose between losing (or winning) a guaranteed number of points and a gamble where they could lose (or win) twice as many points. No immediate feedback was given on the outcome of this described gamble. Based on traditional prospect theory, we would expect risk aversion for gains and risk seeking for losses in both conditions. If, however, decision making from experience does not conform to prospect theory, even in the absence of rare events, then we would expect a difference between the experience and description conditions.

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Figure 1. Schematic of the method used in the experiments.

(A) On experience-based choice trials, participants were faced with a choice between two of four possible colored doors. Two doors always led to losses, and the other two always led to gains. Their choice was immediately followed by a gain or loss of a fixed or variable number of points throughout Experiment 1 and during the pre-training trials only in Experiment 2. (B) On description-based choice trials, participants were presented with verbal and pictorial descriptions of different choices between fixed or variable number of points. No feedback was given until all trials in a run were complete to prevent participants from learning from their experience.

https://doi.org/10.1371/journal.pone.0020262.g001

In this first experiment, experience-based choices always produced immediate feedback, and described choices never resulted in immediate feedback, perhaps leading to differential emotional states during the experienced and described choices. A second experiment controlled for the possibility that participants may have been in a more emotionally aroused or “hot” state during the experience-based choices. Risky decision making has been shown to vary in emotional states [23]–[24], suggesting that perhaps any differences between experience and description may arise from differential engagement of emotional and cognitive systems [25]. The second experiment was designed to eliminate the possibility that participants were in a different “hot” state during the experienced trials. The experiment started with a separate training period during which participants learned the contingencies between the doors and potential outcomes. All subsequent testing for both experienced and described trials was conducted without any further feedback. In addition, all test runs contained both a block of experienced trials and a block of described trials. These two changes should help ensure similar emotional states during the test period.

Methods

Results

Experiment 1: Partial Feedback

Contrary to the prediction of prospect theory, we found a reversal of the reflection effect for the experienced problems, even with equiprobable outcomes in Experiment 1. Figure 2A shows how people gambled more for gains than losses when the outcomes were learned from experience, but not when they were described. The reflection scores, calculated as the probability of gambling on loss trials minus the probability of gambling on gain trials, were significantly higher on described trials than on experienced trials (t(55)  = 4.45, p<.001, d = .60). The reflection scores for experience-based decisions trended downward across trials (see Fig. 2B), indicating that this reversal became more established as the relationships between cues and rewards were learned more accurately, although the visible downward trend was not statistically reliable (F(2,106)  = 1.98, p = .14, η²_p = .04). Figure 2C shows that this difference between the experienced and described trials represents a full reversal of the reflection effect (condition × choice type interaction, F(1,55)  = 19.9, p<.001, η²_p = .27). On gain trials, participants flipped from risk aversion on described problems to risk seeking on experienced problems. On loss trials, participants flipped from risk seeking on described problems to risk aversion on experienced problems (p<.031 for all pairwise comparisons).

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Figure 2. Results from Experiment 1.

(A). Reflection scores as a function of experimental condition. Participants displayed reliably higher reflection scores for described vs. experienced problems (p<.001). (B). Reflection scores on experienced trials as a function of block in the experiment. There was a trend toward a greater reverse reflection effect as the potential outcomes were learned. (C). Gambling quotient as a function of experimental condition and choice type. For gains, participants were risk seeking for experienced problems, but risk averse for described problems. In contrast, for losses, participants were risk averse in experienced problems, but risk seeking in described problems. *  =  p<.05. (D). Percentage correct on catch trials as a function of experience training block. Performance increased across blocks, but was high throughout, peaking at 97.6% on the final training block.

https://doi.org/10.1371/journal.pone.0020262.g002

Figure 2D depicts mean performance on the experienced catch trials across the three experience runs of the experiment. Six participants scored less than 60% correct on these catch trials (4 in Group 1 and 2 in Group 2); data from these participants have been removed from all analyses. For the remaining 54 participants that received all 3 training runs, performance was high throughout, but improved slightly across the runs (F(2,106)  = 14.99, p<.01, η²_p = .22). In the final run, on which the primary comparisons between described and experienced trials are based, mean performance on catch trials was 97.6% correct. Across the whole experiment, the empirical probabilities of receiving the better outcome on the risky option were 51.6±.8% and 50.3±1.2% for gain and loss trials respectively, which were not statistically different than 50%, nor from each other (all ps>.05).

Experiment 2: No Feedback

As in Experiment 1, people again gambled more for gains than losses when these contingencies were learned from experience, but not when they were described, even when immediate feedback was no longer being provided about the experience-based choices. Figure 3A depicts how the reflection scores were significantly lower in the experienced trials, (t(26)  = 2.79, p<.01, d = .54). These reflection scores were consistent across the 6 non-feedback runs for both experienced and described trials, as shown in Figure 3B. A two-way ANOVA confirmed a main effect of trial type (F(1,27)  = 7.83; p<.01, η²_p = .23), but no effect of run, nor any interaction (both ps>.25). The difference between experienced and described trials was present for both gains and losses. As depicted in Figure 3C, when choosing between gains, participants gambled more in the experienced case, and when choosing between losses, participants gambled more in the described case (condition × choice type interaction, F(1,26)  = 7.82; p = .01, η²_p = .23; both pairwise comparisons, p<.038). In addition, there was a significant reversal of the reflection effect for the experienced trials (p<.01); however, the reflection effect for the described condition failed to reach significance (p>.05). Finally, performance on the catch trials was high throughout, even peaking at 100% correct on the 5^th run (see Fig. 3D).

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Figure 3. Results from Experiment 2.

(A). Reflection scores as a function of experimental condition. Participants displayed reliably higher reflection scores for described vs. experienced problems (p<.001). (B). Reflection scores on experienced and described trials as a function of block in the experiment. On each block, reflection scores were higher for described than for experienced trials. PT  =  pre-training for the experienced trials, where feedback was obtained after each trial. (C). Gambling quotient as a function of experimental condition and choice type. For gains, participants were risk seeking for experienced problems, but risk averse for described problems. In contrast, for losses, participants were risk averse in experienced problems, but nominally risk seeking in described problems. *  =  p<.05. (D). Percentage correct on catch trials as a function of experience training block. Performance was relatively stable across test blocks, peaking at 100% on test block 5.

https://doi.org/10.1371/journal.pone.0020262.g003

Discussion

In a pair of experiments, we show that the classic reflection effect from behavioral economics is reversed when participants learn the reward contingencies from experience. These results significantly extend the recent discovery of a description-experience gap in the assessment of rare events [5]–[14]. For the variable options in our experiments, both outcomes were equiprobable, meaning that neither event was more rare than the other. Despite this elimination of rare events from the experiment, we still found a profound difference between people's risky choices in described and experienced cases. This finding suggests that the description-experience gap is more general than previously thought and cannot be solely explained by an overweighting of rare events [11]. Moreover, by using a within-subject design, our study is one of few studies to show differences between experience and description in the very same participants [7]–[13]. Our novel finding demonstrates a serious limitation to current theories of risky choice in behavioral economics, which are mostly based on described choices [4]–[5].

In prospect theory, the subjective utility curve grows sub-linearly, leaving extreme values proportionally underweighted [4], [16]. That is, a reward that is objectively twice as large (e.g., $200 vs. $100) is perceived as subjectively less than twice as big. In contrast, our results suggest that the subjective utility curve based on experienced outcomes may overweight extreme values, growing perhaps supra-linearly (i.e., faster than linear). Thus, extreme values (big wins or big losses) carry proportionally more weight in decisions based on experience, leading to risk seeking for gains and risk aversion for losses. This extrema hypothesis supposes that, in the experienced case, the largest and smallest rewards in a given context are given undue importance in the decision-making process. One possibility is that people remember the big wins and the big losses best, and, as a result, their decision making is swayed by those extreme outcomes, perhaps through an affect [26] or availability heuristic [27]. In our experiments, this memory bias towards extreme values would result in gambling for gains and risk aversion for losses, but only when the outcomes were learned from experience (as seen in Figs. 2 and 3).

The somatic marker hypothesis also provides a potential mechanism for this weighting scheme that gives a disproportionately large weight to extreme values [28]–[29]. This hypothesis contends that emotional, bodily reactions to rewarding events drive subsequent decision making. Larger rewards (good or bad) would thus elicit relatively more potent and memorable emotional responses, driving subsequent decision-making, but only in the experienced, retrospective case. We did not, however, record any physiological measures as a proxy for emotional reactions and thus cannot definitely claim that the extreme values were indeed more emotionally salient. An extended range of values beyond those presented here would also help formulate a hypothesis as to exactly what function might describe this experience-based weighting.

In a recent review, Hertwig and Erev [11] proposed several psychological mechanisms that might account for the description-experience gap for rare events. Our finding that this gap can extend to equally probable outcomes suggests that some of these mechanisms are insufficient for explaining the differences between description and experience. For example, our results cannot easily be accounted for by limited sample sizes or estimation errors of the rate of occurrence of rare events. Indeed, the programmed and received outcomes for the risky outcomes always hovered near 50% in our experiment. In addition, the single-option trials ensured that all participants received both possible outcomes several times for both risky options, and many of our participants correctly identified the exact 50/50 probability in the post-experiment questionnaire. As compared to many other studies of decisions from experience [10], [13], our participants received more experience with the different options (>100 trials total as opposed to the usual 10–20) further limiting the possibility that a sampling bias could explain the results. This extensive training, however, raises a different concern in that our results only seemed to emerge after significant training with the experience-based options (see Fig. 2B). We do not know yet whether our results will generalize to other procedures for examining experience-based decisions that rely on fewer exposures to the potential outcomes.

A second possibility that Hertwig and Erev [11] suggest for explaining the description-experience gap with rare events is that recent events might carry more weight in the decision process, again biasing the weight toward the more frequently occurring outcome. In our experiments, however, there were no rare events, therefore neither the positive nor the negative outcome for the risky option should have received consistently increased weighting. Moreover, the results from Experiment 2, which explicitly separated the learning phase with feedback from the experience-based test trials, provide further evidence against this recency hypothesis.

Another possible difference between the described and experienced problems is that the probabilities of the various outcomes are known with certainty in the described problems, but start off uncertain or ambiguous for the experienced problems [30]–[31]. Thus, to the extent that participants have not learned the relationship between the stimuli and rewards, the experienced task incorporates elements of ambiguity. The trend towards increasingly negative reflection scores across the different blocks in Exp. 1 (Fig. 2D), however, suggests that ambiguity does not underlie the reversed reflection effect. As the contingencies are learned (see Fig. 2B) and the ambiguity in the experienced problems is attenuated, the difference between the experienced and described problems does not disappear. Indeed, the difference between experienced and described problems is most robust on the final experience run, after the contingencies are well learned (Fig. 2A and 2C).

Our findings suggest an alternate interpretation of the role of ambiguity in other tasks that involve ambiguous outcome probabilities, such as the Iowa Gambling Task. The Iowa Gambling task engages emotional processes to a greater extent than tasks with stated probabilities [28]–[29], [32]–[33]. This enhanced emotional engagement has been attributed to ambiguous decisions in those tasks. We suggest that the emotional engagement might instead derive from the fact that the outcomes for those ambiguous decisions are learned from experience.

Our results strongly reinforce the finding that patterns of human decision-making under uncertainty depend on how the decision problem is posed, as is often found in many areas of psychology [19], [34], [35], [36]. The canonical reflection effect can be reversed when participants learn the probabilities from experienced outcomes, even for moderate probabilities, indicating that how we decide may be fundamentally different when we think about the future (in described cases) than when we reflect on the past (in experienced cases). When considering future possibilities, we may underweight extreme outcomes, as per prospect theory, leading to the canonical reflection effect. When remembering past outcomes, we may be driven by the emotional, somatic effects of the more extreme values and overweight those outcomes in our decision making for risky outcomes, leading to a reversal of the usual reflection effect. This dichotomy between prospective and retrospective modes of evaluation suggests a fundamental extension to theories of risky choice.

Acknowledgments

The authors would like to thank Daniel Lee and Craig Anderson for help with data collection, Rich Sutton for inspiration without constraint, Chris Madan for many helpful discussions and ideas, and Adrian Camilleri for insightful suggestions and careful reading of an earlier draft. Door images were extracted from Irish Doors, by Joe Bonita, on fineartamerica.com and were used with permission of the artist. Much of this research was conducted while the first author was a research associate in the Department of Computing Science at the University of Alberta.