Empirical studies have demonstrated a robust four-fold pattern of risk preferences when people make decisions under different domains and probabilities: (1) risk-seeking over small-probability gains; (2) risk-averse over large-probability gains; (3) risk-averse over small-probability losses; and (4) risk-seeking over large-probability losses (Tversky and Kahneman, 1992; Fox and Poldrack, 2009). For example, when facing a choice between “a 1% chance of winning $200” and “a 100% chance of winning $2,” people tend to choose the former, riskier, option; between “a 99% chance of winning $200” and “a 100% chance of winning $198,” people tend to choose the latter, risk-free, option. Conversely, when asked to choose between “a 1% chance of losing $200” and “a 100% chance of losing $2,” people tend to choose the latter, risk-free, option; between “a 99% chance of losing $200” and “a 100% chance to lose $198,” people tend to choose the former, riskier, option.

The notion of risk-as-feelings (Loewenstein et al., 2001) provides an explanation for this four-fold pattern: people often experience emotional reactions to risk and make choices that are driven partially by anticipated emotions (Rottenstreich and Hsee, 2001; Brandstätter et al., 2002; Kliger and Levy, 2008; Tyszka and Sawicki, 2011; Suter et al., 2015). With a small probability of potential gains/losses, the status quo may serve as a salient reference point; compared to this status quo, the possibility of a gain/loss stimulates elation/disappointment. In contrast, with a large probability, the salient reference point may be the potential gain/loss, and the possibility of an unrealized gain/loss can result in disappointment/elation. In other words, with small-probability gains or large-probability losses, the anticipated elation after having won a very unlikely prize or having avoided a very likely loss makes people risk-seeking; with large-probability gains or small-probability losses, the anticipated disappointment after having failed to win a very likely prize or having suffered from a very unlikely loss makes people risk-averse (Brandstätter et al., 2002). Consistent with the notion of risk-as-feelings, this four-fold pattern of risk preferences has been shown to be more pronounced when the anticipated emotions become more intense (Rottenstreich and Hsee, 2001; Kliger and Levy, 2008; Suter et al., 2015).

People often fail to accurately predict others' preferences and decisions in many situations, such as product valuations (Kurt and Inman, 2012), driving behaviors (Svenson, 1981), and medical decision-making (Garcia-Retamero and Galesic, 2012). Studies have suggested that the empathy gap between the predictor and the actor plays an important role in generating this prediction discrepancy—that is, a predictor may underestimate the intensity and impact of the actor's emotional state (Loewenstein, 1996; Van Boven and Loewenstein, 2003; Faro and Rottenstreich, 2006; Williams et al., 2014). For instance, Williams et al. (2014) report that people predicting the decisions of others experienced less anticipated elation in response to positive events and less anticipated disappointment in response to negative events than those who made decisions for themselves. Likewise, recent neuroimaging studies observed that the amygdala, a key neural structure related to emotional activity (Morrison and Salzman, 2010), was less active when people tried to predict others' decisions than when they made decisions for themselves (Albrecht et al., 2010; Jung et al., 2013).

These studies suggest that anticipated emotions are less intense for the predictor than they are for the actor. Therefore, we hypothesize that, due to the less intense anticipated emotion experienced by the predictor, the prediction would exhibit an attenuated four-fold pattern. That is:

Hypothesis 1 Individuals predict others' decisions to be more risk-neutral than they actually are.

Hypothesis 1 can be tested in four different situations: (1) In small-probability gains, an individual would predict others to be less risk-seeking; (2) in small-probability losses, an individual would predict others to be less risk-averse; (3) in large-probability gains, an individual would predict others to be less risk-averse; and (4) in large-probability losses, an individual would predict others to be less risk-seeking.

The empathy gap can influence the prediction discrepancy through two possible channels: (a) underestimation of the intensity of the emotional state; and (b) underestimation of the impact of the emotional state (Loewenstein, 1996; Van Boven et al., 2000). The second channel can influence prediction discrepancy because, even if predictors correctly predict the intensity of the actors' emotional state, they may underestimate how much that emotional state would impact the actors' decisions. While previous studies have demonstrated the effect of the empathy gap, they do not examine the relative importance of these two channels. We propose the following two hypotheses related to the effect of the empathy gap:

Hypothesis 2 The prediction discrepancy is caused by the predictors' underestimate of the intensity of the actors' emotional state.

Hypothesis 3 The prediction discrepancy is caused by the predictors' underestimate of the impact of the actors' emotional state.

In a related study, Faro and Rottenstreich (2006) provide some initial evidence for patterns of the prediction discrepancy that are consistent with our Hypothesis 1. Using a pricing task, participants were asked to indicate the amount of cash that made them indifferent between receiving the cash and playing a lottery with a certain probability (0.001 or 0.99) of winning $4000. The results showed that the predictions were more risk-neutral than the choices. Further, they found that participants with high levels of self-reporting empathy made more-accurate predictions.

There are some important questions that Faro and Rottenstreich (2006) did not explore. First, they investigated only the effect of empathy gaps in the gain domain and did not distinguish the effects of different types of emotions on the prediction discrepancy. Second, without a direct measure of emotions, they could not compare the relative importance of the two channels (intensity underestimation vs. impact underestimation) through which the empathy gap can work. Third, they used only lotteries with extreme probabilities (0.001 and 0.99). As studies have suggested that extreme probabilities are not well-behaved in the probability weighting function (Kahneman and Tversky, 1979), it is important to investigate whether Faro and Rottenstreich's conclusions can be extended to less extreme probabilities. Finally, Faro and Rottenstreich (2006) used pricing tasks to measure risk preferences—that is, participants were asked to indicate their certainty equivalents for lotteries. Many studies have shown that pricing tasks and choice tasks (choosing between a lottery and a certain amount of cash) could lead to drastically different measures of risk preferences (Harbaugh et al., 2010). Therefore, it is unclear whether we would observe the same pattern of prediction discrepancies in choice tasks.

By answering the aforementioned questions, our study greatly complements, and extends Faro and Rottenstreich's 2006 study. In our experiment, participants were asked to complete a series of choice tasks that involve a wide range of probabilities in both the loss and gain domains. By directly eliciting emotional intensities, we investigated the correlation between emotional states and prediction discrepancies, which can shed light on the relative importance of the two channels.

Five participants, all of whom were predictors, failed the manipulation check: they reported that they had been making decisions for themselves instead of predicting the decisions of others. Thus, we excluded them from the analysis. The actors and predictors did not differ from one another in terms of gender, χ²(1, N = 133) = 0.41, p = 0.523, and age t₍₁₃₁₎ = 1.50, p = 0.137, Cohen's d = 0.23, respectively.

Following previous studies (Hsee and Weber, 1997; Krishnamurthy and Kumar, 2002), we calculated the proportion of risky options among each participant's choices to serve as the risk preference (RP) index⁴. The RP index had a range between 0 and 1. Risk-neutral individuals should have an RP index close to 0.5, while larger values of RP index indicate stronger risk-seekingness. To simplify the analysis and to avoid the complication presented by the correlation between decisions by the same participant, we divided the decisions into four conditions (small probability gain, small probability loss, large probability gain, and large probability loss). Following Tversky and Kahneman (1992), we defined p < 0.5 as small probability and p ≥ 0.5 as large probability⁵. For each condition, we calculated the proportion of risky choices for each participant as the individual RP index under that condition.

Table 1 provides the statistics of the risk preferences and anticipated emotions for both the actors and the predictors, separately for the four different conditions. The level of anticipated emotion is normalized so that its value is between 0 and 1. To assess whether there were prediction discrepancies in risk preference, we performed a 2(decision maker's role) × 2(domain) × 2 (probability) analysis of variance (ANOVA) on the RP index and found a main effect for probability, F_{(1, 131)} = 92.88, p < 0.001, η_p² = 0.42, such that the participants were more risk-seeking in large-probability condition (M = 0.49, SD = 0.14) than in small-probability condition (M = 0.40, SD = 0.13). Consistent with cumulative prospect theory (Tversky and Kahneman, 1992), we also obtained an interaction between domain and probability, F_{(1, 131)} = 633.09, p < 0.001, η_p² = 0.83. In small-probability condition, the participants were more risk-seeking in the gain domain (M = 0.53, SD = 0.18) than in the loss domain (M = 0.27, SD = 0.15), F_{(1, 131)} = 247.80, p < 0.001, η_p² = 0.65, whereas in large-probability condition, the participants were more risk-seeking in the loss domain (M = 0.62, SD = 0.16) than in the gain domain (M = 0.35, SD = 0.16), F_{(1, 131)} = 371.30, p < 0.001, η_p² = 0.92, which suggests that both choices and predictions exhibit the four-pattern risk preferences⁶.

Crucially, we observed an interaction among decision maker's role, domain and probability (Table 1), F_{(1, 131)} = 77.98, p < 0.001, η_p² = 0.37. In small-probability gains, the participants who predicted decisions of others (M = 0.47, SD = 0.16) were less risk-seeking than those who made decisions for themselves (M = 0.58, SD = 0.18), F_{(1, 131)} = 14.21, p < 0.001, η_p² = 0.10, whereas in large-probability gains, the participants who predicted decisions of others (M = 0.39, SD = 0.17) were less risk-averse than those who made decisions for themselves (M = 0.31, SD = 0.15), F_{(1, 131)} = 7.80, p = 0.006, η_p² = 0.06. Conversely, in small-probability losses, the participants who predicted decisions of others (M = 0.32, SD = 0.15) were less risk-averse than those who made decisions for themselves (M = 0.23, SD = 0.13), F_{(1, 131)} = 14.71, p < 0.001, η_p² = 0.10, whereas in large-probability losses, the participants who predicted decisions of others (M = 0.58, SD = 0.15) were less risk-seeking than those who made decisions for themselves (M = 0.66, SD = 0.15), F_{(1, 131)} = 9.21, p = 0.003, η_p² = 0.07. The prediction discrepancies are consistent with our hypotheses: predictors are significantly more risk-neutral (RP index closer to 0.5) under all four conditions. No other main effects and interactions were significant, ps > 0.16.

Looking at Table 1 for the four different conditions, we can notice that the prediction discrepancy is highly correlated with the difference in anticipated emotion. Note that the actual and predicted levels of elation from reaching the desired outcome under small probability loss and large probability gain, as well as the actual and predicted levels of disappointment from reaching the undesired outcome, are not statistically significant–these levels of anticipated emotion can be considered as the baseline level. In contrast, the anticipated emotion in all other situations demonstrates a significant difference: predictors do not fully appreciate the anticipated elation experienced by the actors for small probability gains [F_{(1, 131)} = 8.46, p = 0.004, η_p² = 0.06] and large probability losses [F_{(1, 131)} = 23.04, p < 0.001, η_p² = 0.15]; on the other hand, predictors fail to fully appreciate the anticipated disappointment experienced by the actors for small probability losses [F_{(1, 131)} = 5.96, p = 0.016, η_p² = 0.04] and large probability gains [F_{(1, 131)} = 12.44, p = 0.001, η_p² = 0.09].

The difference between actual and predicted emotion intensity demonstrates an empathy gap between the actor and the predictor (Loewenstein, 1996). While predictors correctly predict the type of emotional state the actors would experience, they underestimate its intensity. The empathy gap can aggravate the prediction discrepancy if predictors underestimate the impact of the emotional state—given an equally intense emotional state, the predictors underestimate the actors' reaction to it.

We can use the following regressions to understand the connection between the anticipated emotion and the prediction discrepancy and to disentangle the two channels through which the empathy gap can work.

Equation (1) is a simple regression of the RP index on the dummy variable Predictor, which takes 1 for the predicted values and 0 otherwise. If a prediction discrepancy exists, we would expect β11 to be statistically significant. Equation (2) includes anticipated emotions as explanatory variables. According to the notion of risk-as-feelings, we would expect β22 to be significantly positive and β22 to be significantly negative. If the prediction discrepancy is mainly caused by predictors underestimating the intensity, we would have an insignificant β12. Equation (2) investigates how the underestimate of emotional intensity influences prediction discrepancy, however, it does not take into consideration the possibility that predictors can underestimate the impact of the emotions, even if they accurately estimate the actors' emotional intensity. The two interactions terms (with coefficients β43 and β53) in Equation (3) allow us to investigate whether being a predictor moderates the effect of emotional states—that is, whether the predictors underestimate the impact of emotional states. If the prediction discrepancy can be attributed, in part, to the underestimated impact of emotional states, β43  would be statistically negative and β53 statistically positive.

Table 2 shows the regression results separately for each of the four conditions, controlling for the effect of gender and age. Models (1), (3), (5), and (7) provide results that are consistent with the statistic tests shown in Table 1. Models (2), (5), (8), and (11) investigate the effect of predictors underestimating emotional intensity on the prediction discrepancy. Note that the coefficient of “predictor” decreases significantly after including emotional intensity as explanatory variables, demonstrating that the underestimate of emotional intensity by the predictors is an important factor causing the prediction discrepancy.

Models (3), (6), (9), and (12) further include the interaction terms between the decision maker's role and the intensity of the anticipated emotions, capturing the effect of predictors' underestimating the emotional impact. The significance of the emotional intensity (coefficients of the variable “elation” and “disappointment”) is not influenced by the including these interaction terms. After controlling for the effect of the emotional state (both the intensity and the impact), action, and prediction do not show a significant difference, implying that the prediction discrepancy can be explained by the empathy gap. In all four models, the anticipated elation of reaching the desired outcome of the risky option makes people significantly more risk-seeking, while the anticipated disappointment of reaching the undesired outcome makes people significantly more risk-averse (p < 0.01). However, the effect of the anticipated disappointment is significant only for small-probability loss and large-probability gain, and the effect of the anticipated elation is significant only for small-probability gain and large-probability loss (marginally significant for large-probability gain).

These models also allow us to disentangle the two channels through which the empathy gap can influence prediction discrepancy. If the predictor underestimates the impact of the emotional state on the actor's choice, we would expect a moderating effect of the participant's role on the emotional state. However, the interactions between anticipated emotion and the participant's role are not significant, and a joint F-test of these two interaction terms is also insignificant, indicating that the effect of emotional intensity is not significantly moderated by participant's role. This provides strong evidence that the prediction discrepancy is caused primarily by the underestimation of the intensity (not the impact) of the emotional state⁷.

Table 2 also shows that male participants are slightly more risk-seeking, while older participants tend to be more risk-averse. However, these effects are small in size and not always statistically significant across different conditions. The regression results are almost identical if these two variables are excluded.

Figure 2 and Table 3 provide the path analysis that visualizes the mediating effects of the anticipated emotions on the prediction discrepancy and the relative importance of the two channels of empathy gaps. In each condition, the participant's role (actor = 0, predictor = 1) was treated as the independent variable and a potential moderator for the anticipated emotions. Anticipated elation and disappointment were treated as potential mediators. We used the bootstrapping procedure from Hayes and Preacher (2014) and the corresponding SPSS PROCESS macro to test for mediated moderation. The analysis shows that the prediction discrepancies were mediated mainly by the anticipated elation for small-probability gains and large- probability losses, as well as by the anticipated disappointment for small-probability losses and large-probability gains (Table 3). In the four models, the results showed no moderating effect of the decision-maker's role in the relationship between anticipated emotions and risk preferences, further suggesting that the primary cause of the prediction discrepancy is the underestimate of the intensity (not the impact) of the emotional state.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.