Social Distance Reduces the Biases of Overweighting Small Probabilities and Underweighting Large Probabilities

Abstract

People often exhibit biases in probability weighting such as overweighting small probabilities and underweighting large probabilities. Our research examines whether increased social distance would reduce such biases. Participants completed valuation and choice tasks of probabilistic lotteries under conditions with different social distances. The results showed that increased social distance reduced these biases in both hypothetical (Studies 1 and 2) and incentivized (Study 3) settings. This reduction was accompanied by a decrease in emotional intensity and an increase in the attention to probability in the decision-making process (Study 4). Moreover, the bias-buffering effect of social distance was stronger in the gain domain than in the loss domain (Studies 1–4). These results suggest that increasing the social distance from the beneficiaries of the decisions can reduce biases in probability weighting and shed light on the relationship between social distance and the emotional-cognitive process in decision-making.

Keywords

probability weighting bias social distance emotional intensity probability neglect judgment and decision-making

Probability weighting influences judgment and decision-making. The fourfold pattern of cumulative prospect theory reveals that people tend to make (a) riskier choices involving small-probability gains but more cautious choices involving small-probability losses due to overweighting small probabilities (e.g., the impulsive purchase of lottery tickets, overinvestment in insurance for rare illnesses), and (b) more cautious choices involving large-probability gains but riskier choices involving large-probability losses because of underweighting large probabilities (Tversky & Kahneman, 1992). More broadly, these characteristics of probability weighting may apply to any choice—from financial to consumer to medical—that involves risk and uncertainty or contains either a positive or negative prospect (Newell et al., 2015).

However, the extensive research on probability weighting has focused exclusively on personal decisions—choices that people make for themselves. Consequently, conclusions regarding the characteristics of probability weighting have ignored possible differences between choices made for oneself and those made for others. In real life, people make not only personal decisions but also interpersonal decisions. A growing body of research shows self–other differences in decision-making (Andersson et al., 2014; Kray, 2000; Polman, 2012; Stone & Allgaier, 2008; Sun et al., 2017).

Despite this, research on probability weighting has not included interpersonal decisions. From personal decisions to interpersonal decisions, the social distance between decision-makers and decision recipients increases (Liviatan et al., 2008). In this article, we test how social distance influences probability weighting.

Probability Weighting

The biases of probability weighting refer to deviations between the subjective perception of the likelihood of an event (weight of probability: w(p)) and the objective likelihood (p) of such an event. Cumulative prospect theory reveals that people often overweight small probabilities, w(p) > p; p < .5, and underweight large probabilities, w(p) < p; p ≥ .5, which can be captured graphically by an inverse S-shaped probability weighting function (Tversky & Kahneman, 1992). People believe that low-probability events have a subjectively higher chance of occurring (e.g., 1% chance of winning US$100), leading to risk-seeking choices in gain frames and cautious choices in loss frames. Likewise, people believe that high-probability events have a subjectively lower chance of occurring (e.g., 99% chance of winning US$100), leading to risk-averse choices in gain frames and risk-seeking choices in loss frames. These biases explain why people make choices that violate expected utility theory, such as concurrently purchasing lottery tickets and insurance.

Probability Neglect

The biases of probability weighting stem from both probability neglect and the emotional intensity of probable events. The probability neglect account proposes that these biases are caused by attention to outcome and neglect of probability (Suter et al., 2016). Consider the following two decisions.

Choose between Options A (1%, US$100; 99%, US$0) and B (100%, US$1).

Choose between Options C (99%, US$100; 1%, US$0) and D (100%, US$99).

Individuals who compare the outcomes and disregard the corresponding probabilities will prefer Option A over B because the difference between US$100 and US$1 is larger than that between US$0 and US$1, leading to an overestimation of small probabilities. These individuals will also prefer Option D over C because the difference between US$100 and US$99 is smaller than that between US$0 and US$99, leading to an underestimation of large probabilities. By contrast, if individuals consider both outcomes and probabilities, the biases of probability weighting will be attenuated. The same logic holds true for Options C and D.

Empirical studies provided evidence for this account. Pachur et al. (2018) traced participants’ focus on outcomes and probabilities during the decision-making process and found an association between the degree of probability-weighting biases and the tendency to pay more attention to outcomes and less to probabilities. In addition, overestimation of the probability of terrorist attacks is found to be caused by their focus on the outcomes of these attacks and their ignorance of the likelihood of such attacks (McGraw et al., 2011). When individuals pay more attention to outcomes during the decision-making process, biased probability weighting is observed more often (Suter et al., 2016). In contrast, when they devote more attention to probabilities, biased probability weighting is found less often (Pachur et al., 2018).

Emotional Intensity

The emotional intensity account states that the intensity of emotional reactions to outcomes drives the biases of probability weighting (Brandstätter et al., 2002; Pachur et al., 2014). People overweight small probabilities because of their anticipated elation after having won a very unlikely outcome (e.g., US$100 in Option A). They underweight large probabilities because of their anticipated disappointment at failing to win a very likely outcome (e.g., US$100 in Option C). The biases of probability weighting induce the fourfold pattern of risk preferences mentioned above.

In line with this account, in Sun et al. (2018), participants who experienced more anticipated disappointment after having suffered from a very unlikely loss overweighted small probabilities more. Those who experienced more anticipated elation after having avoided a very likely loss underweighted large probabilities more. Rottenstreich and Hsee (2001) showed a more S-shaped probability weighting function for lotteries involving affect-rich than for those involving affect-poor outcomes. Furthermore, the fourfold pattern of risk preferences is more pronounced when the anticipated emotions become more intense (Brandstätter et al., 2002; Suter et al., 2016).

Social Distance in Interpersonal Decisions

Social distance describes the perceived closeness between oneself and others (Trope & Liberman, 2010). Making decisions for others induces larger social distance than making decisions for oneself. Social distance influences how people make decisions (Liviatan et al., 2008). To the best of our knowledge, however, no research has tested how social distance affects probability-weighting biases.

Social Distance and Probability Neglect

According to construal level theory, psychological distance influences the level at which people construe events (Trope & Liberman, 2010). People represent psychologically close events at a lower level, focusing on concrete features, whereas they represent psychologically distant events at a higher level, integrating several parts into a whole and focusing on abstract and integral features. For instance, in Wakslak et al. (2006), participants were asked to identify what a certain picture was about. The global picture was composed of several local blocks. Participants were more likely to see the whole picture when they were more psychologically distant from these pictures. As one dimension of psychological distance, social distance leads to a high construal level and enables people to integrate different parts (e.g., the “trees”) into a global one (e.g., the “forest”).

In risky decisions, an expected-value calculation that includes payoff and probability should be more abstract than a predominant focus on just the payoff. Therefore, social distance should decrease probability neglect and increase greater integration of probability and payoff. Fernandez-Duque & Wifall (2007) asked actors or observers to play or observe a card game containing 10 face-down cards, among which nine were good (led to a US$1 gain for each card) and one was bad (caused the loss of all gained money). Participants decided how many cards to turn or predicted how many the player would turn. The researchers found that actors paid more attention to outcomes and less attention to probabilities, whereas observers promoted greater integration of the probability into the subjective value.

In sum, increased social distance enables integrating probabilities and outcomes. Given the relationship between probability neglect and the biases of probability weighting, we propose that the degree of probability-weighting biases will be reduced with social distance.

Social Distance and Emotional Intensity

Making decisions for others requires understanding the feelings of other people who are in different emotional states. However, empathizing with others’ emotions is difficult. People believe that others experience less-intense emotion than others actually do. For instance, people underestimate the intensity of other people’s embarrassment in an awkward situation (Van Boven et al., 2005) and other people’s hopes and fears when making risky decisions (Faro & Rottenstreich, 2006).

Williams et al. (2014) showed that social distance decreased the intensity of both positive and negative emotions. In one study, the participants imagined getting a ticket to watch either a socially close or socially distant musical act in concert and rated their likelihood of attending the concert, which served as an index of emotional intensity. Results showed that the likelihood of attending the concert was higher in the condition of close social distance than in the condition of distant social distance. The effect of social distance on emotional intensity has a neural mechanism. The amygdala, a brain region related to emotional intensity, was less activated when individuals made choices for a socially distant person than for a socially close person (Jung et al., 2013). In sum, social distance reduces the emotional intensity related to events. Given the relationship between emotional intensity and the biases of probability weighting, we propose that the degree of probability-weighting biases will be reduced with social distance.

Overall, our hypotheses are as follows:

Hypothesis 1 (H1). Social distance will reduce the biases of overweighting small probabilities and underweighting large probabilities.

Hypothesis 2 (H2). Social distance will reduce the biases of probability weighting by decreasing emotional intensity and enhancing attention to probabilities.

Research Overview

We conducted four studies to explore the effect of social distance on the biases of probability weighting. In each study, participants evaluated a series of probable events. As social distance can be reflected by self versus other and close versus distant others (Polman & Emich, 2011), we manipulated social distance in two ways. In Study 1, social distance was reflected by choices for oneself and others. In Study 2, social distance was reflected by choices for close and distant others. In Study 3, participants made consequential decisions. H1 was tested in these studies. Study 4 tested H2, measuring both emotional intensity to outcomes and attention to probabilities during the decision-making process.

To detect a medium effect size (Cohen’s f = 0.25) at 80% power (α = .05), we ensured at least 64 participants in each treatment (self vs. other) in Studies 1, 3, and 4. In Study 2, to detect a medium effect size from the regression on social distance (Cohen’s f² = 0.15) at 80% power (α = .05), we needed at least 55 participants.

Study 1: Choices for Oneself Versus Others

In Study 1, we compared the difference in probability weighting between choices for oneself and for others, to test whether increased social distance reduced the biases of overweighting small probabilities and underweighting large probabilities.

Method

Participants and design

One hundred eighty-one undergraduates (88 women; M_age = 20.17 years, SD = 1.34) enrolled in a course were randomly assigned to one condition in a 2 (Social Distance: Self or Other) × 2 (Domain: Gain or Loss) mixed design. Social distance varied between subjects and domain varied within subjects.

Procedure and materials

Participants were informed that the study aimed to investigate decision-making habits. The participants in the self condition were asked to make decisions for themselves, whereas those in the other condition were asked to make decisions for a typical student on their campus who was facing those decisions. Afterward, they completed a valuation task for probabilistic lotteries, which measured the biases of probability weighting (Tversky & Kahneman, 1992). Participants indicated an amount of cash such that they would be indifferent between receiving that cash amount for sure and taking the gamble in each lottery. Consider two examples.

Example 1: Please indicate an amount of cash ¥________ such that you would be indifferent between receiving that cash amount for sure and taking the gamble in the lottery for a 5% chance of obtaining ¥200¹ and a 95% chance of obtaining ¥0.

Example 2: Please indicate an amount of cash ¥________ such that you would be indifferent between receiving that cash amount for sure and taking the gamble in the lottery for a 95% chance of obtaining ¥200 and a 5% chance of obtaining ¥0.

In Example 1, if the answer is 10, it reflects accurate probability weighting (5% × ¥200 + 95% × ¥0 = ¥10). If the value is greater (vs. lower) than 10, it shows an overweighting (vs. underweighting) of the probability of gaining ¥200. In Example 2, if the answer is 190, it reflects accurate probability weighting (95% × ¥200 + 5% × ¥0 = ¥10). If the value is lower (vs. greater) than 190, it shows an underweighting (overweighting) of the probability of gaining ¥200.

Each lottery offered some chance of obtaining the cash: with a probability of p_i to obtain x_i and a probability of (1 − p_i) to obtain y_i. In different scenarios, p_i took the values of 1%, 5%, 10%, 25%, 50%, 75%, 90%, 95%, or 99%, whereas (x_i, y_i) took the values of (±50, 0), (±100, 0), (±200, 0), (±400, 0), (±100, ±50), or (±200, ±100). In all scenarios, x_i was greater than y_i. Both the order of probabilities and the outcomes were counterbalanced across the participants. In addition, we conducted a manipulation check by asking the participants to rate the individual for whom they made decisions on a 9-point scale (1 = deciding for yourself entirely, 9 = deciding for others entirely) after completing their tasks. Then, we collected demographic information. Finally, the participants were thanked, debriefed, and paid. See Supplemental Material A for original materials.

Results and Discussion

Manipulation check

The participants in the other condition (M = 7.33, SD = 1.00) scored higher than those in the self condition (M = 1.97, SD = 0.93) on the manipulation check, t(179) = 37.19, p < .001, Cohen’s d = 5.54, 95% confidence interval (CI) = [4.89, 6.18], suggesting the successful manipulation of social distance.

Parameter estimation

Based on Tversky & Kahneman’s (1992) method, we modeled our data to calculate participants’ biases of probability weighting. The cash equivalent (CE) indicated by the participant was determined as follows:

v (C E) = w (p_{i}) v (x_{i}) + [1 - w (p_{i})] v (y_{i})

(1)

This function reflects that the CE was determined by participants’ subjective weighting of probability p_i (w(p_i)) and subjective value of outcomes x_i and y_i (v(x_i) and v(y_i)). w(p_i), v(x_i), and v(y_i) are defined, respectively, as

\begin{matrix} w^{+} (p) = \frac{p^{γ_{1}}}{{(p^{γ_{1}} + {(1 - p)}^{γ_{1}})}^{1 / γ_{1}}} w^{-} (p) \\ = \frac{p^{γ_{2}}}{{(p^{γ_{2}} + {(1 - p)}^{γ_{2}})}^{1 / γ_{2}}} \end{matrix}

(2)

\begin{array}{l} v (x) = {\begin{matrix} x^{a_{1}}, if x \geq 0 \\ - λ {(- x)}^{a_{2}}, if x < 0 \end{matrix} \\ v (y) = {\begin{matrix} y^{a_{1}}, if y \geq 0 \\ - λ {(- x)}^{a_{2}}, if y < 0 \end{matrix} \end{array}

(3)

In Equation 2, the parameters γ₁ and γ₂ govern the sensitivity to differences in probabilities in the gain and loss domains, respectively. They are assumed to be between 0 and 1, with lower values yielding a more inverse S-shaped curvature of the function (indicating larger biases of overweighting small probabilities and underweighting large probabilities). When γ₁ (γ₂) = 1, the perceived probability is the same as the actual probability, w(p) = p. Figure 1 visualizes probability-weighting biases. The horizontal axis represents probability (p) and the vertical axis represents subjective probability (w(p)). The solid line (γ = 0.85) is closer to the diagonal (γ = 1) than the dotted line (γ = 0.65), reflecting less biased probability weighting.

Figure 1.

Illustration of probability-weighting biases.

In Equation 3, the parameters α₁ and α₂ model diminishing sensitivity to the change in the outcome for gains and losses, respectively. They are constrained between 0 and 1, with lower values yielding a more concave value function for gains and a more convex value function for losses (less sensitive to the change in the outcome as the size of the change increases). When α₁ (α₂) = 1, the perceived outcome is the same as the actual outcome, v(x) = x. The parameter λ denotes the coefficient that reflects the magnitude of loss aversion (λ ≥ 1); a higher λ indicates a higher level of loss aversion. As our study did not include a mixed prospect (a prospect with both loss and gain outcomes), λ could not be estimated. We estimated the parameters in Equations 2 and 3 for each participant by using a nonlinear least-squares regression procedure.

Biases of probability weighting

Given that probability weighting may be different between gains and losses, we took the domain into consideration and conducted a 2 (Social Distance: Self or Other) × 2 (Domain: Gain or Loss) analysis of variance (ANOVA) on biases of probability weighting (reflected in γ; a higher γ indicates smaller biases of probability weighting). The results yielded a main effect for the social distance, F(1, 179) = 44.90, p < .001, η_p² = .20, 95% CI = [0.11, 0.20]. The probability-weighting biases in choices for others (M = 0.91, SD = 0.36) were smaller than those in choices for oneself (M = 0.63, SD = 0.19). These results supported our hypothesis that increasing social distance reduced the probability-weighting biases. The main effect for the domain was not significant, F(1, 179) = 1.79, p = .183, η_p² = .01, 95% CI = [0.00, 0.06].

The interaction between social distance and domain was also significant, F(1, 179) = 10.27, p = .002, η_p² = .05, 95% CI = [0.01, 0.13]. The bias-buffering effect of social distance on probability weighting was stronger in the gain domain (M_other = 0.98, SD = 0.45; M_self = 0.60, SD = 0.22) than in the loss domain (M_other = 0.85, SD = 0.38; M_self = 0.65, SD = 0.28), F(1, 179) = 52.06, p < .001, η_p² = .23, 95% CI = [0.13, 0.32] and F(1, 179) = 16.38, p < .001, η_p² = .08, 95% CI = [0.02, 0.17], respectively. Figure 2 displays the probability-weighting function.²

Figure 2.

Probability-weighting function as a function of social distance and domain in Study 1.

Biases of outcome sensitivity

A 2 (Social Distance) × 2 (Domain) ANOVA on the bias of diminishing sensitivity to outcome change (reflected in α) yielded a main effect for the social distance, F(1, 179) = 5.53, p = .002, η_p² = .03, 95% CI = [0.01, 0.09]. The bias in the other condition (M = 0.86, SD = 0.12) was smaller than that in the self condition (M = 0.82, SD = 0.12). The main effect for the domain was significant, F(1, 179) = 6.30, p = .013, η_p² = .03, 95% CI = [0.01, 0.10]. The bias in the loss domain (M = 0.82, SD = 0.15) was larger than those in the gain domain (M = 0.85, SD = 0.13). The interaction between the social distance and domain was not significant, F(1, 179) = 0.09, p = .759, η_p² < .01, 95% CI = [0.00, 0.02]. These results suggested that deciding for others (vs. oneself) reduced the utility curvature.

Study 1 revealed that increasing social distance from self to other attenuated the biases of overweighting small probabilities and underweighting large probabilities, supporting H1.

Study 2: Choices for Socially Close Versus Distant Others

In Study 2, we compared probability weighting between choices for socially close and distant others to further test whether increased social distance reduced the biases of overweighting small probabilities and underweighting large probabilities.

Method

Participants and design

Two hundred one undergraduates (96 women; M_age = 20.02 years, SD = 1.19) participated in Study 2, in which social distance, the independent variable, was treated as a continuous variable.

Procedure and materials

The participants imagined a list of the 100 people closest to them in the world, ranging from the closest friend at position 1 to a mere acquaintance at position 100. Each participant was then randomly assigned a number from 1 to 100 and was asked to write down the name of the friend or acquaintance by that assigned number. The participants imagined that that person was facing decisions and were asked to make decisions for her. The decision scenarios were identical to those in Study 1.

We performed a manipulation check by asking the participants to rate the closeness between themselves and the person whose name they had written down on the “inclusion of the other on the self” scale (Figure 3). The scale measures perceived closeness by the degree of overlap between two circles, with a lower score indicating a closer relationship. The participants were then thanked, debriefed, and paid. See Supplemental Material C for original materials.

Figure 3.

Inclusion of others on the self-scale in Study 2.

Results and Discussion

Manipulation check

The ranking of friends was correlated with the score of the manipulation check question, r = .90, p < .001, suggesting the successful manipulation of social distance.

Biases of probability weighting

The biases of probability weighting (reflected in γ—a higher γ indicating smaller biases of probability weighting) were fitted as in Study 1. Considering that social distance in Study 2 was a continuous variable, a hierarchical regression was conducted to test the effect of social distance on probability weighting (Table 1). In the first step, the score of both the social distance and the domain (gain = 0, loss = 1) was entered into the model. In the second step, the product of social distance and domain (gain vs. loss) was entered. Social distance was positively correlated with parameter γ (β = .34, p < .001, R_p² = .10), indicating that increased social distance reduced the biases of overweighting small probabilities and underweighting large probabilities. Consistent with Study 1, the product of social distance and domain was negatively correlated with parameter γ (β = −.14, p = .036, R_p² = .01), suggesting that the domain served as a moderator between social distance and probability weighting. As shown in Figure 4, the bias-buffering effect of social distance on probability weighting was stronger in the gain domain (β = .47, p < .001, R_p² = .22) than in the loss domain (β = .23, p = .001, R_p² = .05).³

Table 1.

Hierarchical Regression Results for Probability-Weighting Biases (Study 2).

Variables	Probability-weighting biases (parameter γ)
Variables	Step 1 β	Step 2 β
Social distance	.34***	.44***
Domain	.01	.01
Social Distance × Domain	–	−.14*
∆R²	.12	.01
∆F(df)	25.91*** (2, 399)	4.44* (1, 398)
R² (adjusted R²)	.12 (.11)	.13 (.12)
Overall F(df)	25.91*** (2, 399)	18.90*** (3, 398)

Note. The values represent standardized regression coefficients.

p < .05. ***p < .001.

Figure 4.

Scatter plots and regression lines of probability-weighting biases as a function of social distance and domain in Study 2.

Biases of outcome sensitivity

A similar hierarchical regression with the bias of diminishing sensitivity (reflected in α) as the dependent variable revealed that social distance was positively correlated with parameter α (β = .20, p < .001, R_p² = .04), indicating that increased social distance diminished the bias of outcome evaluations. The domain was negatively correlated with parameter α (β = −.10, p = .050, R_p² = .01). The bias of outcome evaluations was larger in the loss domain than in the gain domain. The product of social distance and domain was not correlated with parameter α (β = −.07, p = .319, R_p² < .01).

Study 2 showed the difference in probability weighting in choices for different others and revealed that increasing social distance from close to distant others reduced the biases of overweighting small probabilities and underweighting large probabilities, supporting H1.

Study 3: Consequential Choices

We had so far found that social distance reduced probability-weighting biases and we proposed that emotional intensity and probability neglect caused this effect. However, an alternative explanation existed. Typically, people who make decision for themselves maximize their payoffs. However, people who make decisions for others do not necessarily aim to maximize others’ payoffs. Rather, prosocial individuals may want to maximize others’ payoffs, whereas antisocial individuals may want to minimize them. Therefore, social preferences may explain the observed self–other differences in Studies 1 and 2 (Olschewski et al., 2019). To rule out this explanation, we measured participants’ social preferences. If the bias-buffering effect is held for both antisocial and prosocial participants, this alternative explanation would be excluded. Moreover, participants were incentivized in this study.

Method

Participants and design

One hundred fifty-seven participants were randomly assigned to one condition in a 2 (Social Distance: Self or Other) × 2 (Domain: Gain or Loss) mixed design. Social distance was a between-subjects variable, whereas domain varied within subjects. Fifteen participants who failed comprehension checks were excluded, leaving 140 participants (97 women; M_age = 21.82 years, SD = 3.20).

Procedure and materials

Participants made four decisions. In each one, they were given a ¥15 initial endowment and imagined that they got a lottery ticket. Among the four decisions, two tickets were lucky, bringing a 5% or 95% probability of gaining ¥15, and two were unlucky, bringing a 5% or 95% probability of losing ¥15. Participants should pay to buy the lucky lottery tickets to obtain the probability of gaining money; otherwise, they would not win money. In contrast, participants should pay to destroy the unlucky lottery tickets to avoid the probability of losing money; otherwise they would probably lose money. Participants indicated the maximum amount of money they would pay for each lottery.

We adopted the Becker–DeGroot–Marschak procedure (Becher et al., 1964) to make the decisions incentive compatible. The participants were told that the system would also randomly place a bid from ¥0 to ¥15. For lucky lottery tickets, if the participants’ bid was higher than or equal to the system bid, they would pay the system bid to receive the ticket. If the participants’ bid was lower than the system bid, they cannot purchase the ticket. For unlucky lottery tickets, if the participants’ bid was higher than or equal to the system bid, they would pay the system bid to destroy the ticket. If not, they cannot destroy the ticket. The order of the four tickets was randomized.

The participants in the self condition made decisions for themselves, whereas those in the other condition made decision for the next participant. Before making decisions, the participants answered four comprehension questions. The participants were told that one lucky ticket and one unlucky ticket would be randomly selected after their choices. Their choices in these two tickets would determine their own payoffs or the next participant’s payoffs.

After the lottery task, the participants completed the manipulation check as in Study 1 and filled out the 6-item version of the social value orientation scale (SVO; Murphy et al., 2011). In each item, participants distributed money for themselves and another person (Supplemental Material E). These choices were not incentivized. Finally, the participants provided their demographic information and were thanked, debriefed, and paid.

Results and Discussion

Manipulation check

The participants in the other condition (M = 7.98, SD = 0.88) scored higher than those in the self condition (M = 1.68, SD = 0.73) on the manipulation check question, t(138) = 46.41, p < .001, Cohen’s d = 7.90, 95% CI = [6.89, 8.88], suggesting the successful manipulation of social distance.

Biases of probability weighting

We subtracted the expected value of small probability lottery tickets (5% × 15 = 0.75) from participants’ willingness to pay to reflect the bias of overweighting small probability. Thus, a larger value indicates a larger bias. We subtracted participants’ willingness to pay from the expected value of large probability lottery tickets (95% × 15 = 14.25) to reflect the bias of underweighting large probability. Thus, a larger value indicates a larger bias. Social preferences were captured by SVO angle that was calculated as the inverse tangent of the ratio between the mean allocation for the other person and for oneself. A larger angle indicates a higher degree of prosociality.

Considering that social preference was a continuous variable, hierarchical regressions were conducted to test the effect of social distance on the biases of overweighting small probability and underweighting large probability (Table 2). In the first step, the social distance (0 = self, 1 = other), domain (lucky lottery tickets = 0, unlucky ones = 1), and social preference were entered into the model. In the second step, the product of the social distance and domain, the product of the social distance and social preference, and the product of the domain, and social preference were entered. In the third step, the product of the social distance, domain, and social preference was entered. As expected, social distance was negatively correlated with the biases of overweighting small probabilities (β = −.28, p < .001, R_p² = .09) and underweighting large probabilities (β = −.25, p < .001, R_p² = .06). The product of social distance and domain was positively correlated with the biases of overweighting small probabilities (β = .18, p = .042, R_p² = .02) and underweighting large probabilities (β = .21, p = .038, R_p² = .02), which suggested the moderating effect of domain. Specifically, the bias-buffering effect of social distance on the bias of overweighting small probabilities was stronger for the lucky lottery tickets (β = −.57, p < .001, R_p² = .32) than for the unlucky lottery tickets (β = −.17, p = .046, R_p² = .03). Similarly, the bias-buffering effect of social distance on the bias of underweighting large probabilities was stronger for the lucky lottery tickets (β = −.39, p < .001, R_p² = .15) than for the unlucky lottery tickets (β = −.13, p = .124, R_p² = .02). None of the effects regarding social preference was significant.

Table 2.

Hierarchical Regression Results for Probability-Weighting Biases (Study 3).

Variables	Bias of overweighting small probabilities			Bias of underweighting large probabilities
Variables	Step 1 β	Step 2 β	Step 3 β	Step 1 β	Step 2 β	Step 3 β
Social distance	−.28***	−.30*	−.18	−.25***	−.31*	−.24
Domain	.41***	.36***	.46**	.04	−.12	−.06
Social preference	−.04	.03	.09	−.06	−.06	−.03
Social Distance × Domain	–	.18*	−.02	–	.20*	.09
Social Distance × Social Preference	–	−.11	−.27	–	−.08	−.17
Domain × Social Preference	–	−.06	−.19	–	.07	−.01
Social Distance × Domain × Social Preference	–	–	−.25	–	–	.14
∆R²	.25	.01	.004	.07	.02	.001
∆F(df)	30.95*** (3, 276)	1.67 (3, 273)	1.53 (1, 272)	7.19*** (3, 276)	1.76 (3, 273)	0.40 (1, 272)
R² (adjusted R²)	.25 (.24)	.27 (.25)	.27 (.25)	.08 (.06)	.09 (.07)	.09 (.07)
Overall F(df)	30.95*** (3, 276)	16.42*** (6, 273)	14.32*** (7, 272)	7.19*** (3, 276)	4.50*** (6, 2743)	3.91*** (7, 272)

Note. The values represent standardized regression coefficients.

p < .05. **p < .01. ***p < .001.

Notably, the observed self–other differences in valuation might be resulted from self–other differences in outcome sensitivity or in probability weighting. If the former was true (i.e., participants in the self condition showed a more diminishing sensitivity to outcomes than those in the other condition), the willingness to pay in the self condition should be always lower than that in the other condition, across the four lottery tickets. If the latter was true (i.e., the participants showed larger biases of overweighting small probabilities and underweighting large probabilities in choices for oneself than for others), the willingness to pay in the self condition should be higher than that in the other condition for small-probability outcomes, yet lower than that in the other condition for large-probability outcomes. Our findings supported the latter (Table 3).

Table 3.

Willingness to Pay for the Four Lottery Tickets (Study 3).

Conditions	Willingness to pay (¥)
	Close social distance		Distant social distance
	(Self)		(Other)
Low probabilistic gain	2.97 (1.26)	>***	1.32 (1.08)
High probabilistic gain	10.27 (2.67)	<***	12.18 (1.58)
Low probabilistic loss	4.29 (2.36)	>*	3.52 (2.15)
High probabilistic loss	10.59 (2.04)	=	11.19 (3.09)

p < .0. ***p < .001.

Therefore, Study 3 showed that social distance reduced the biases of probability weighting in an incentivized setting and this effect cannot be explained by social preferences.

Study 4: Probability Attention and Emotional Intensity

To test H2, we measured both probability attention and emotional intensity during the decision-making process in Study 4. We used a choice task in which participants chose between two options to measure the probability-weighting biases. Based on cumulative prospect theory (Tversky & Kahneman, 1992), the more obvious the fourfold pattern of risk attitude was the greater the biases of overweighting small probabilities and underweighting large probabilities.

Method

Participants and design

One hundred thirty-five undergraduates (64 women; M_age = 20.63 years, SD = 1.27) were randomly assigned to one condition in a 2 (Social Distance: Self or Other) × 2 (Domain: Gain or Loss) mixed design. Social distance was a between-subjects variable, whereas domain varied within subjects.

Procedure and materials

(a) Probability weighting. The participants were instructed to complete a choice task (Pachur et al., 2014) that included a series of decision problems. Each problem had two options: a risky option (i.e., with a probability of p_i of obtaining x_i and a probability of [1 − p_i] of obtaining nothing); and a safe option (i.e., 100% probability of obtaining z_i). Participants were asked to make a choice between the two options. For low probabilistic (p < .5) gains, the expected value of the safe option is slightly greater than that of the risky option. For high probabilistic (p ≥ .5) gains, the expected value of the risky option is slightly greater than that of the safe option. For low probabilistic (p < .5) losses, the expected value of the risky option is slightly greater than that of the safe option. For high probabilistic (p ≥ .5) losses, the expected value of the safe option is slightly greater than that of the risky option (see Table 4 for examples).⁴

Table 4.

Examples for the Choice Task (Study 4).

Conditions	Choices	Examples	Probability-weighting biases
Low probabilistic gain	Risky option: p_i, x_i; 1 − p_i, 0	Risky option: 5%, 50; 95%, 0	The preference for the risky option indicates the bias of overweighting small probabilities over gains
	Safe option: z_i for sure	Safe option: 5 for sure
	Expected value: p_ix_i < z_i	Expected value: 5% × 50 < 5
High probabilistic gain	Risky option: p_i, x_i; 1 − p_i, 0	Risky option: 95%, 50; 5%, 0	The preference for the safe option indicates the bias of underweighting large probabilities over gains
	Safe option: z_i for sure	Safe option: 45 for sure
	Expected value: p_ix_i > z_i	Expected value: 95% × 50 > 45
Low probabilistic loss	Risky option: p_i, x_i; 1 − p_i, 0	Risky option: 5%, −50; 95%, 0	The preference for the safe option indicates the bias of overweighting small probabilities over losses
	Safe option: z_i for sure	Safe option: −5 for sure
	Expected value: p_ix_i > z_i	Expected value: 5% × (–50) > −5
High probabilistic loss	Risky option: p_i, x_i; 1 − p_i, 0	Risky option: 95%, −50; 5%, 0	The preference for the risky option indicates the bias of underweighting large probabilities over losses
	Safe option: z_i for sure	Safe option: −45 for sure
	Expected value: p_ix_i < z_i	Expected value: 95% × (–50) < −45

In different scenarios, p_i takes the values of 1%, 5%, 10%, 25%, 50%, 75%, 90%, 95%, or 99%, whereas (x_i, y_i) take the values of (±50, 0), (±100, 0), (±200, 0), or (±400, 0). Both the order of probabilities and the outcomes were counterbalanced across the participants. Based on cumulative prospect theory (Tversky & Kahneman, 1992), the more obvious the fourfold pattern of risk preference was the greater the biases of overweighting small probabilities and underweighting large probabilities.

The participants in the self condition made choices for themselves, whereas those in the other condition made choices for a typical student on their campus who was facing those decisions. Before the participants made their choices, their probability attention was recorded, and their emotional intensity was measured.

(b) Probability attention. The Mouselab paradigm was used to record how participants acquired information. Specifically, the outcomes and probabilities of the options were hidden behind boxes (Figure 5, left panel). The participants clicked a box to uncover the information behind it and could click on each box repeatedly. Once the participants clicked a second box, the information in the former box disappeared; both the duration and frequency of their looking at the information in each box were recorded. A longer duration and a higher frequency of looking at a certain type of information indicated more focus on this type of information. The format of the boxes (horizontal or vertical), the order of information (probability first or outcome first), and the order of options (risky option = Option A or safe option = Option A) were counterbalanced across participants.

Figure 5.

The interface of measuring probability attention (left panel) and emotional intensity (right panel) in Study 4.

(c) Emotional intensity. Based on Brandstätter et al. (2002), we measured participants’ intensity of anticipated positive and negative emotions by asking them to indicate how joyful, excited, and surprised they anticipated feeling if they were to choose the risky option and reach their desired outcome (1 = not at all, 9 = extremely); and how upset, disappointed, and surprised they anticipated feeling if they were to choose the risky option and not reach their desired outcome (1 = not at all, 9 = extremely; Figure 5, right panel). The measuring order of emotion intensity and probability attention was counterbalanced across the participants.

Thereafter, the participants indicated their choice. A manipulation check of social distance was conducted, as in Study 1. Finally, the participants were thanked, debriefed, and paid. See Supplemental Material F for original materials.

Results and Discussion

Calculation of variables

(a) Biases of probability weighting. We calculated the proportion of options with lower expected value among each participant’s choices to serve as the index of probability-weighting biases. This index had a range between 0 and 1 (Pachur et al., 2014; Sun et al., 2017). For low probabilistic gains, we calculated the proportion of risky options among each participant’s choices to serve as the index of bias of overweighting small probability over gains. For high probabilistic gains, we calculated the proportion of safe options among each participant’s choices to serve as the index of bias of underweighting large probability over gains. For low probabilistic losses, we calculated the proportion of safe options among each participant’s choices to serve as the index of bias of overweighting small probability over losses. For high probabilistic losses, we calculated the proportion of risky options among each participant’s choices to serve as the index of bias of underweighting large probability over losses.

(b) Probability attention. For each participant, we calculated the duration of looking at the probabilities and that of looking at all the information in the boxes. The frequency of clicking the boxes with and without probabilities was also calculated. The proportions of the duration of looking at the probabilities and the frequency of clicking the boxes with probability information were computed according to Equations 4 and 5, respectively. An average score of the two indices was calculated to reflect probability attention. This index had a range between 0 and 1. Individuals who pay equal attention to probabilities and outcomes should have an index close to .5, whereas a larger value indicates more attention to probabilities.

D u r a t i o n = \frac{\begin{array}{l} The duration of looking \\ at the probability information \end{array}}{\begin{array}{l} The duration of looking \\ at all information \end{array}}

(4)

F r e q u e n c y = \frac{\begin{array}{l} The frequency for clicking \\ the boxes with probability information \end{array}}{\begin{array}{l} The frequency for clicking \\ all the boxes \end{array}}

(5)

(c) Emotional intensity. An average score of anticipated joy, excitement, and surprise was calculated as the index of intensity of positive emotion (α = .92), whereas an average score of anticipated upset, disappointment, and surprise was calculated as the index of intensity of negative emotion (α = .98).

Manipulation check

The participants in the other condition (M = 7.19, SD = 1.29) scored higher than those in the self condition (M = 1.58, SD = 0.72) on the manipulation check question, t(133) = 30.07, p < .001, Cohen’s d = 5.21, 95% CI = [4.49, 5.92], suggesting the successful manipulation of social distance.

Biases of probability weighting

Table 5 displays statistics for the probability-weighting biases, probability attention, and emotional intensity in all conditions. Social distance reduced the biases of overweighting small probability over gains, F(1, 133) = 58.31, p < .001, η_p² = .31, 95% CI = [0.18, 0.42], underweighting large probability over gains, F(1, 133) = 64.41, p < .001, η_p² = .33, 95% CI = [0.20, 0.44], overweighting small probability over losses, F(1, 133) = 30.94, p < .001, η_p² = .19, 95% CI = [0.08, 0.30], and underweighting large probability over losses, F(1, 133) = 16.06, p < .001, η_p² = .11, 95% CI = [0.03, 0.21], supporting H1. Furthermore, a 2 (Social Distance) × 2 (Domain) ANOVA on the index of probability-weighting biases revealed an interaction between the social distance and the domain, F(1, 133) = 18.56, p < .001, η_p² = .12, 95% CI = [0.04, 0.23]. The bias-buffering effect of social distance on probability weighting was stronger in the gain domain, F(1, 133) = 121.73, p < .001, η_p² = .48, 95% CI [0.36, 0.57], than in the loss domain, F(1, 133) = 45.65, p < .001, η_p² = .26, 95% CI [0.14, 0.37].⁵

Table 5.

Mean (± SD) for Biases of Probability Weighting, Emotional Intensity, and Probability Attention (Study 4).

Conditions	Biases of probability weighting			Probability attention			Intensity of positive emotion			Intensity of negative emotion
Conditions	Close social distance(Self)		Distant social distance(Other)	Close social distance(Self)		Distant social distance(Other)	Close social distance(Self)		Distant social distance(Other)	Close social distance(Self)		Distant social distance(Other)
Low probabilistic gain	0.46 (0.17)	>***	0.22 (0.18)	0.42 (0.11)	<**	0.48 (0.13)	6.32 (1.51)	>***	4.16 (1.70)	3.37 (1.04)	=	3.16 (1.07)
High probabilistic gain	0.58 (0.20)	>***	0.35 (0.13)	0.37 (0.11)	<***	0.49 (0.16)	2.96 (1.01)	=	3.13 (0.96)	6.34 (0.11)	>***	4.06 (0.11)
Low probabilistic loss	0.55 (0.14)	>***	0.41 (0.16)	0.43 (0.11)	<*	0.48 (0.13)	3.80 (1.02)	=	3.88 (0.95)	6.06 (1.13)	>*	5.04 (1.80)
High probabilistic loss	0.42 (0.15)	>**	0.32 (0.13)	0.46 (0.12)	<***	0.54 (0.10)	5.48 (1.75)	>***	4.27 (1.24)	3.07 (0.81)	=	3.08 (0.88)

Note. Statistical significance is based on ANOVA.

p < .05. **p < .01. ***p < .001.

Probability attention

Participants paid more attention to probabilities in the other condition than in the self condition, for low probabilistic gains: F(1, 133) = 8.42, p = .004, η_p² = .06, 95% CI = [0.01, 0.15]; for high probabilistic gains: F(1, 133) = 29.99, p < .001, η_p² = .18, 95% CI = [0.08, 0.30]; for low probabilistic losses: F(1, 133) = 6.12, p = .015, η_p² = .04, 95% CI = [0.01, 0.13]; for high probabilistic losses: F(1, 133) = 14.20, p < .001, η_p² = .10, 95% CI = [0.02, 0.20]. As shown in Table 5, the index of probability attention was closer to 0.5 in the other condition than in the self condition, suggesting that participants paid more balanced attention to outcomes and probabilities in the other condition than in the self condition. This result indicated that social distance promoted integration of the probability into the subjective value.

Emotional intensity

For low probabilistic gains, social distance reduced the intensity of positive emotion induced by reaching desirable outcomes, F(1, 133) = 59.10, p < .001, η_p² = .31, 95% CI = [0.18, 0.42], but did not influence the intensity of negative emotion induced by missing desirable outcomes, F(1, 133) = 1.25, p = .265, η_p² = .01, 95% CI = [0.00, 0.07]. For high probabilistic gains, social distance reduced the intensity of negative emotion induced by missing desirable outcomes, F(1, 133) = 54.72, p < .001, η_p² = .29, 95% CI = [0.17, 0.40], but did not influence the intensity of positive emotion induced by reaching desirable outcomes, F(1, 133) = 0.95, p = .330, η_p² = .01, 95% CI = [0.00, 0.06]. For low probabilistic losses, social distance reduced the intensity of negative emotion induced by reaching undesirable outcomes, F(1, 133) = 14.55, p < .001, η_p² = .10, 95% CI = [0.02, 0.20], but did not influence the intensity of positive emotion induced by avoiding undesirable outcomes, F(1, 133) = 0.24, p = .626, η_p² < .01, 95% CI = [0.00, 0.04]. For high probabilistic loss, social distance reduced the intensity of positive emotion induced by avoiding undesirable outcomes, F(1, 133) = 21.71, p < .001, η_p² = .14, 95% CI = [0.05, 0.25], but did not influence the intensity of negative emotion induced by reaching undesirable outcomes, F(1, 133) < 0.01, p = .936, η_p² < .01, 95% CI = [0.00, 0.28].

Mediation analysis

We conducted bootstrapping analyses to test the potential mediating roles of probability attention and emotional intensity in the relationship between social distance and probability-weighting biases (Table 6). In each condition, social distance (0 = self, 1 = other) was treated as the independent variable. Probability attention, intensity of positive emotion, and intensity of negative emotion were treated as potential mediators. The probability-weighting bias was treated as the dependent variable. Results revealed that social distance reduced the biases of probability weighting by enhancing attention to probabilities and decreasing emotional intensity (intensity of positive emotion for low probabilistic gains and high probabilistic losses; intensity of negative emotion for high probabilistic gains and low probabilistic losses), which offered evidence for H2.

Table 6.

Direct and Indirect Effects of Social Distance on Probability-Weighting Biases (Study 4).

	Conditions	Direct effect	Mediating effects
	Conditions	Social distance	Probability attention	Intensity of positive emotion	Intensity of negative emotion
Low probabilistic gain	Bootstrap estimate (±SE)	−.27 (.07)*	−.07 (.03)*	−.22 (.06)*	.008 (.01)
Low probabilistic gain	95% CI	[−.40, −.13]	[−.15, −.02]	[−.34, −.12]	[−.004, .05]
High probabilistic gain	Bootstrap estimate (±SE)	−.25 (.07)*	−.11 (.03)*	.001 (.01)	−.21 (.05)*
High probabilistic gain	95% CI	[−.38, −.11]	[−.20, −.05]	[−.01, .02]	[−.32, −.13]
Low probabilistic Loss	Bootstrap estimate (±SE)	−.25 (.07)*	−.04 (.02)*	.001 (.01)	−.15 (.05)*
Low probabilistic Loss	95% CI	[−.38, −.12]	[−.09, −.01]	[−.01, .01]	[−.26, −.08]
High probabilistic loss	Bootstrap estimate (±SE)	−.06 (.07)	−.10 (.04)*	−.17 (.05)*	.00 (.01)
High probabilistic loss	95% CI	[−.20, .07]	[−.19, −.04]	[−.27, −.09]	[−.01, .02]

Note. Parallel multiple mediation analyses were conducted using the PROCESS macro (bootstrapping, 5,000 samples) for SPSS 18.0. The values represent standardized bootstrap estimates.

Significant effect.

Similar to Study 3, if the findings regarding choice stemmed from self–other differences in outcome sensitivity, the risky option should be less chosen in the self condition than in the other condition across all the choices in the gain condition. The risky option should be more chosen in the self condition than in the other condition across all the choices in the loss condition. If the findings stemmed from self–other differences in probability weighting, the risky option should be more chosen in the self condition than in the other condition over small-probability gains and large-probability losses, whereas the risky option should be less chosen in the self condition than in the other condition over large-probability gains and small-probability losses. The current findings supported the latter (Table 7).

Table 7.

Mean (± SD) for Proportions of Choosing Risky Option (Study 4).

Conditions	Proportion of choosing risky option
	Close social distance		Distant social distance
	(Self)		(Other)
Low probabilistic gain	0.46 (0.17)	>***	0.22 (0.18)
High probabilistic gain	0.42 (0.20)	<***	0.65 (0.13)
Low probabilistic loss	0.45 (0.14)	<***	0.59 (0.16)
High probabilistic loss	0.42 (0.15)	>**	0.32 (0.13)

Note. Statistical significance is based on analysis of variance.

p < .01. ***p < .001

General Discussion

Cumulative prospect theory and the fourfold pattern of risk attitude have focused exclusively on probability weighting in personal decisions when people make decisions for themselves, but they have ignored probability weighting in interpersonal decisions, in which people make decisions for others. Social distance between decision-makers and decision recipients increases from personal to interpersonal decisions. This research examined how social distance influenced probability weighting. The results showed that increased social distance reduced the biases of overweighting small probabilities and underweighting large probabilities by reducing emotional intensity and enhancing attention to probabilities during the decision-making process. In addition, this effect was stronger in the gain domain than in the loss domain.

Self–Other Differences in Risky Decisions

Previous findings about self–other differences in risky decisions were mixed. Some studies showed more risk-seeking in choices for others than in choices for oneself (Andersson et al., 2014; Stone & Allgaier, 2008; Sun et al., 2017), where others showed more risk-averse in choices for others than in choices for oneself (Fernandez-Duque & Wifall, 2007; Lu et al., 2018; Stone et al., 2013). Given the association between risk preference and probability weighting, our findings provide two possible reasons for these inconsistencies.

First, probability magnitude, which moderates the self–other difference in probability weighting, may reverse the self–other difference in risk preference (Sun et al., 2019). People may be more risk-seeking in choices for themselves (vs. others) involving low probabilistic gains (p < .5) because they overweight small probabilities more in choices for themselves (vs. others). In contrast, people may be more risk-averse in choices for themselves (vs. others) involving high probabilistic gains (p ≥ .5) because they underweight large probabilities more in choices for themselves (vs. others). Second, the domain (gain/loss) may also reverse the self–other difference in risk preference. For example, people who face a choice between gaining US$200 with probability .05 and gaining US$10 for sure will be more risk-seeking in choices for themselves (vs. others) because they expect more for reaching the desired outcome (a US$200 gain) in choices for themselves (vs. others). Conversely, people who face a choice between losing US$200 with probability .05 and losing US$10 for sure will be more risk-averse in choices for themselves (vs. others) because they are more fearful about reaching the undesired outcome (a US$200 loss) in choices for themselves (vs. others). In sum, our findings help explain the mixed findings about self–other differences in risky decisions.

Bias-Buffering Effect of Social Distance: A Gain–Loss Asymmetry

All four studies suggest a gain–loss asymmetry: The bias-buffering effect of social distance on probability weighting is stronger in the gain domain than in the loss domain. Recent studies show similar results. For example, Sun et al. (2017) observed a stronger self–other difference in making risky decisions in the gain domain than in the loss domain. Lu et al. (2018) found self–other differences in decision-making under risk over gains, but no difference over losses. Such asymmetry might be driven by the fact that empathizing with others’ losses is easier than empathizing with others’ gains (Martínez-Jauand et al., 2012). The results regarding emotional intensity in Study 3 support this speculation, as they show that emotional intensity diminishes more in the gain domain than in the loss domain as social distance increases (Table 5).

Practical Implications

As social distance reduces the probability weighting biases, investors who aim to avoid these biases and make wise decisions may well ask agents for advice. If that is difficult to do, investors should visualize their investments from the perspective of an observer. Moreover, to facilitate decisions free from probability-weighting biases, doctors should avoid treating themselves, their close friends, or their family members—a decision supported by the regulations of the American Medical Association (2014). Our result is also illuminating for organizations that face risky choices. To reduce probability-weighting biases, it may be helpful to turn to consulting companies when making important risky decisions. However, it should be noted that such biases might be less reduced in the loss domain.

Alternative Explanations, Limitations, and Future Directions

Study 4 showed that social distance decreased emotional intensity and made positive emotions less positive. An alternative explanation was that social distance reduced reliance on emotion during the decision-making process (i.e., people relied less on their emotions to make decisions). However, this possibility has little theoretical basis. Extant research shows that social distance reduces emotional intensity (Williams et al., 2014). There is no evidence that social distance can change the weight attached to emotion and probability during the decision-making process. To ensure that social distance does not change the weight attached to emotion, we analyzed whether social distance moderated the strength of the relationship between emotion intensity and the biases of probability weighting. If the alternative explanation is valid, social distance should decrease the strength of the relationship. The results revealed no moderating effects of social distance (Supplemental Material H), ruling out the alternative explanation.

Another alternative explanation is that social distance increases the overall information acquired (Liu et al., 2018) instead of increasing the proportion of probability information acquired. We analyzed the overall information that the participants acquired in Study 4 and found no difference between the self and other conditions (Supplemental Material I), ruling out this possibility.

Prior studies revealed that emotional intensity and probability neglect are not separate. For instance, the more blamed policy-makers feel, the more likely that they ignore the likelihood of terroristic attack, thereby leading to irrational budget priorities (McGraw et al., 2011). Likewise, affect-rich scenarios have a higher tendency than affect-poor scenarios to trigger probability neglect (Pachur et al., 2014). We found a high correlation between emotional intensity and probability neglect (Supplemental Material J). The relation between the emotional intensity and probability neglect mechanisms needs further investigation.

In addition to the probability neglect and emotional intensity accounts, probability-weighting biases also have other roots, such as focusing on salient values (Kahneman, 2003) and rank-based processing (Stewart et al., 2006). Future research may well investigate their roles in the bias-buffering effect of social distance on probability-weighting biases.

Conclusion

The present research reveals that increasing social distance reduces the biases of overestimating small probabilities and underestimating large probabilities by reducing emotional intensity and enhancing attention to probabilities during the decision-making process. In addition, the bias-buffering effect of social distance is stronger in the gain domain than in the loss domain.

Supplemental Material

Sun_Online_Appendix – Supplemental material for Social Distance Reduces the Biases of Overweighting Small Probabilities and Underweighting Large Probabilities

Supplemental material, Sun_Online_Appendix for Social Distance Reduces the Biases of Overweighting Small Probabilities and Underweighting Large Probabilities by Qingzhou Sun, Jingyi Lu, Huanren Zhang and Yongfang Liu in Personality and Social Psychology Bulletin

Supplemental Material

Supplementary_material_R4 – Supplemental material for Social Distance Reduces the Biases of Overweighting Small Probabilities and Underweighting Large Probabilities

Supplemental material, Supplementary_material_R4 for Social Distance Reduces the Biases of Overweighting Small Probabilities and Underweighting Large Probabilities by Qingzhou Sun, Jingyi Lu, Huanren Zhang and Yongfang Liu in Personality and Social Psychology Bulletin

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Natural Science Foundation of China (Numbers 71801193, 71771088, and 71942004), National Social Science Foundation of China (Number 15ZDB121), Zhejiang Provincial Natural Science Foundation of China (Number LY20C090011), and Humanity and Social Science foundation of Ministry of Education (Number 18YJC630155).

ORCID iDs

Qingzhou Sun

Jingyi Lu

Supplemental Material

Supplemental material is available online with this article.

Notes

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Supplementary Material

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