Explaining Individual Differences in Advantageous Inequity Aversion by Social-Affective Trait Dimensions and Family Environment

Note: Article in press at Social Psychological and Personality Science (https://doi.org/10.1177/19485506211027794)

Explaining individual differences in advantageous inequity aversion by social-affective trait dimensions and family environment

Hongbo Yu 1, Chunlei Lu2, Xiaoxue Gao3,10, Bo Shen2,3, Kui Liu2, Weijian Li2, Yuqin Xiao4, Bo Yang4, Xudong Zhao5,6, Molly. J. Crockett7, Xiaolin Zhou2,3,6,8,9

1 Department of Psychological and Brain Sciences, University of California Santa Barbara, Santa Barbara, California, U.S.A. 2 Institute of Psychological and Brain Sciences, Zhejiang Normal University, Zhejiang, China 3 School of Psychological and Cognitive Sciences, Peking University, Beijing, China 4 School of Sociology, China University of Political Science and Law, Beijing, China 5 Pudong Mental Health Centre, Tongji University School of Medicine, Shanghai, China 6 Department of Psychology, Tongji University, Shanghai, China 7 Department of Psychology, Yale University, New Haven, Connecticut, U.S.A. 8 Beijing Key Laboratory of Behavior and Mental Health, Peking University, Beijing, China 9 PKU-IDG/McGovern Institute for Brain Research, Peking University, Beijing, China 10 Current affiliation: Shanghai Key Laboratory of Mental Health and Psychological Crisis Intervention, School of Psychology and Cognitive Science, East China Normal University, Shanghai, China

Correspondence and requests for materials should be addressed:

Dr. Hongbo Yu Department of Psychological and Brain Sciences University of California Santa Barbara Santa Barbara, CA, USA Email: [email protected] ORCID: https://orcid.org/0000-0002-3384-7772

Dr. Xiaolin Zhou

1 School of Psychological and Cognitive Sciences Peking University Beijing, China Email: [email protected] ORCID: https://orcid.org/0000-0001-7363-4360

Abstract

Humans are averse to both having less (i.e., disadvantageous inequity aversion) and having more than others (i.e., advantageous inequity aversion). However, the social-affective traits that drive individual differences in inequity aversion (IA) are not well understood. Here, by combining a modified Dictator Game and a computational model, we found in a sample of incarcerated adolescents (N = 67) that callous-unemotional traits were specifically associated with low advantageous but not disadvantageous IA. We replicated and extended the finding in a large- scale university student sample (N = 2,250) by adopting a dimensional approach to social- affective trait measures. We showed that advantageous IA was strongly and negatively associated with a trait dimension characterized by callousness and lack of social emotions (e.g., guilt and compassion). A supportive family environment negatively correlated with this trait dimension and positively with advantageous IA. These results identify a core set of social- affective dimensions specifically associated with advantageous IA.

Keywords: Dictator Game, computational model, advantageous inequity aversion, dimensional approach, family atmosphere

3 Introduction Humans are inequity averse. There are two types of inequity aversion (Charness & Rabin, 2002; Fehr & Schmidt, 1999): Advantageous inequity aversion (IA) refers to negative responses to receiving more than others, while disadvantageous IA refers to negative responses to receiving less than others. Although both types of IA could lead to a state of equality, advantageous IA is regarded as a hallmark of a full-blown sense of fairness and morality (Tomasello, 2019). Some theorize that advantageous IA is a manifestation of a joint commitment and a sense of obligation that older children and adult human beings feel towards other members of the same moral community (Ci, 2009). This feeling serves as a cognitive and affective mechanism that curbs individuals’ selfish motivations in the interest of harmonious interpersonal relationships and the common good (Tomasello, 2019, 2020).

Developmental and comparative studies have demonstrated that relative to disadvantageous IA, advantageous IA develops later in life (McAuliffe et al., 2017) and has only been consistently observed in humans (Brosnan & de Waal, 2014). Consistently, neuroimaging research has shown that advantageous and disadvantageous IA are associated with distinct underlying neural processes (Fliessbach et al., 2012; Gao et al., 2018; Güroğlu et al., 2014; R. Yu et al., 2014). These lines of research indicate that advantageous and disadvantageous IA may rely on dissociable underlying neurocognitive mechanisms (Gao et al., 2018; R. Yu et al., 2014). One way to further probe the underlying mechanisms is to examine the social and affective factors associated with advantageous and disadvantageous IA.

Although prior research on fairness-related behaviors and inequity aversion have documented individual differences of advantageous and disadvantageous IA (Engel, 2011; Gao et al., 2018; Tisserand et al., 2015; R. Yu et al., 2014), systematic investigations into the core social and affective factors that may distinguish advantageous and disadvantageous IA have been lacking. One possibility is that these two types of IA rely differently on the ability and tendency to take others’ well-being into consideration (Tsoi & McAuliffe, 2020). Specifically, we hypothesized that other-regarding social-affective traits (e.g., empathic concern and guilt) and their antithesis (e.g., callousness and interpersonal manipulation) are associated with advantageous IA but not disadvantageous IA. We note that advantageous and disadvantageous IA in the strictest sense is a

4 description of certain behavioral patterns in a specific economic game, and it may or may not be associated with aversive emotional responses (Binmore & Shaked, 2010; Fehr & Schmidt, 2010). We use these terms in their descriptive sense.

Other-regarding social-affective traits, such as empathic concern and guilt proneness, predispose individuals to be more attentive to the distress of others and motivate altruistic behaviors (Blair & Mitchell, 2009; Kimonis et al., 2019; Thielmann et al., 2020). For example, past research has shown that individuals with high guilt proneness are less likely to commit unethical behaviors (e.g., lying in negotiation) and are more likely to take reparative measures after transgression (Cohen et al., 2011, 2012; Giner-Sorolla et al., 2011; Tangney et al., 2000). Similarly, numerous empirical studies have offered supportive evidence for the empathy-altruism hypothesis, which posits that at least some forms of empathy motivate observers to help victims for the sake of the victims’ well-being (Batson, 2011; Batson et al., 2007; Davis, 2015; Dovidio et al., 1990; Penner et al., 2005; Stocks et al., 2009; Wilhelm & Bekkers, 2010; Zaki, 2019, 2020).

In contrast, deficits in prosocial affective traits, both in clinical and general populations, have been associated with antisocial behaviors and a lack of care and altruistic responses to others’ distress (Blair, 2008, 2013; Blair et al., 2005; Glenn & Raine, 2014; Gregory et al., 2015; Yang et al., 2015). For instance, in general adult populations, self-reported psychopathic features have been associated with higher tendency to gain financial reward for oneself by harming another person in laboratory settings (Crockett et al., 2014), as well as more violent/aggressive behaviors in everyday life (Neumann & Hare, 2008). In adolescents, callous-unemotional (CU) traits have been shown to predict conduct problems, criminal offending, and delinquency (Frick & Viding, 2009). A recent meta-analysis reveals that CU traits are strongly and negatively associated with prosocial behavioral traits (Waller et al., 2020).

Although past research has established the link between social-affective traits and prosocial behaviors (or the lack thereof), two questions remain unclear. First, these previous studies have been primarily focused on behavioral outcomes and therefore remain agnostic about what underlying cognitive processes are influenced by prosocial emotions and social-affective traits. A seemingly prosocial behavior (e.g., allocating resources fairly) may be driven by multiple,

5 sometimes conflicting underlying cognitive processes (e.g., an aversion toward inequality, guilt when getting more than one should, envy when the other party receives more than oneself, etc.). Specifically, in one of the most widely adopted experimental tasks for probing prosociality, namely the Dictator Game (DG; (Engel, 2011; Forsythe et al., 1994)), participants decide how they want a pool of money to be divided between themselves and a receiver, while the receiver has to accept what is allocated to them. In a modified version of DG, participants face a series of binary choice in which one option is always a fixed fair division, while in the other option the amount for the participants and the amount for the receiver are orthogonalized (for details, see Methods and Materials). Combined with an established computational model for inequity aversion, this paradigm has the advantage of statistically dissociating advantageous and disadvantageous IA, thereby allowing us to examine the factors that drive individual differences in these two latent cognitive processes (Fehr & Schmidt, 1999; Gao et al., 2018).

Second, past research on the individual differences in fairness-related behaviors with adult populations has largely overlooked the link between the social-affective traits predictive of prosocial behaviors and features of the environment where these traits develop. The environments where individuals socialize (e.g., the individuals’ family environment) play a key role in the development of the individuals’ personality (Di Pierro et al., 2012; Hoffman, 1991; Loehlin & Nichols, 2012). An understanding of potential environmental antecedents of these social-affective traits may have implications for interventions aimed to bolster the development of the traits that are conducive to prosocial behaviors and discourage those that may hinder prosocial behaviors (Singer & Klimecki, 2014). To fill this gap, we explored the effect of a potential environmental factor – the extent to which family members are encouraged to express their thoughts and feelings, support, care and empathize with each other (Ferguson & Stegge, 1995; Hinde, 2002; Stuewig & McCloskey, 2005; Tangney & Dearing, 2003). Indirect evidence from research on the relationships between parenting style and children’s and adolescents’ empathy-related traits, guilt proneness and prosociality suggests that positive and emotionally responsive parenting facilitates the development of empathy, care and a sense of guilt (Eisenberg & Valiente, 2002; Kochanska, 1991, 1997; López et al., 2008; Miklikowska et al., 2011). In this study, we test the prediction that a supportive family environment, as measured by a self- reported questionnaire (see Methods and Materials for detail; Kang et al., 2001), is associated

6 with more other-regarding social-affective traits, which in turn results in higher advantageous, but not disadvantageous, IA.

We carried out two studies to better understand the social-affective factors that drive individual differences in advantageous (relative to disadvantageous) IA. In Study 1, we administered the modified DG to a sample of incarcerated adolescents (N = 67). The rationale of including this sample was to maximize the range of the distribution of callous-unemotional traits, as it has been demonstrated that these traits have a wider distribution in institutionalized samples than in the general population (Byrd et al., 2013; Essau et al., 2006; Kimonis et al., 2008; Pihet et al., 2015). In Study 2, we aimed to replicate and extend the findings from Study 1 in a large sample of undergraduate students (N = 2,250) in a Chinese university. The size of this sample allows us to adopt a dimensional (or ‘trans-diagnostic’) approach to personality traits in computational psychiatry (Gillan et al., 2016), running factor analysis on individual items from various partially overlapping questionnaires and using the resultant factor scores, rather than questionnaire total scores, as predictors of the latent cognitive processes underlying the DG choices.

Methods and Materials

Participants. Study 1. To examine how callous-unemotional (CU) trait modulates prosocial motivation, we paid a visit to a correctional institution and administered a resource allocation task (modified Dictator Game; see below) to a group of 67 incarcerated male adolescent participants (mean age: 16.3 ± 0.8, age range: 14 – 17) in the institution. In the country where the data was collected, a correctional institution is a type of confined facility for juvenile offenders under the age of 18. The types of criminal offenses this sample of participants committed can be found in Table S1. The procedure used in the present study was approved by the authors’ university ethics committee, and was administered as part of the institution’s psychological intervention program. The size of the incarcerated sample was determined by who took part in the institution’s psychological intervention program and were available on the day of data collection.

7 Study 2. First-year undergraduate students at a university in southeast China participated in the study as part of the university’s mental health prescreening. The study was approved by the authors’ university ethics committee. Participants gave their consent electronically prior to the experiment. A total of 4,888 participants completed the study as part of their mental health assessment program mandated by their university authority. Among them 2,638 participants were excluded from data analysis due to failure in comprehension or attention check questions, leaving a sample of N = 2,250 (mean age: 18.2 ± 0.7; age range: 17 – 22; 1,679 were female; see below for detailed exclusion criteria). Note that adopting different exclusion criteria does not change the pattern of results (see Supplementary Materials, p. 8). The sample size was determined by the number of first-year undergraduate students at the university where the data collection took place.

Experimental Design and Measurements Overview. For Study 1, participants’ Callous-Unemotional (CU) traits were assessed prior to this experiment session via interviews conducted by trained research assistants ((Essau et al., 2006; Kimonis et al., 2008); the Chinese version of the assessment scale was adopted from Chen, 2013). A high CU group (N = 32) and a low CU group (N = 35) were defined based on median split of the overall CU score (Table 1) (cf. (Pihet et al., 2015)). A computer program was installed in the computers in the testing room. This program would present the DG task to the participants and record their responses (i.e., button press). For Study 2, participants first performed the modified DG task with an anonymous co-player who was also a participant in the same study session. The participants then completed several personality questionnaires and provided demographic information (see below for details). The task and the questionnaires were computerized and presented to the participants via an online survey platform (https://www.wjx.cn/).

Modified Dictator Game (DG). We instructed the participants that they would be paired with an anonymous co-player in the same room. The participants’ task was to allocate monetary points between themselves (hereafter, Self) and the anonymous co-player (hereafter, Other), in the form of binary choice (Fig. 1; for participant payment, please see Supplementary Material, p. 6). Specifically, one of two options always offered 10 points to each player. The other option

8 came from a set of test options varying in the payoff of Self (Ms) and the payoff of Other (Mo) (see Fig. S1 for the full list of options used in this study). Participants made a series of 50 choices and one of them would be randomly selected and made real at the end of the experiment. From the participants’ perspective, in 48 of the 50 trials, the test option was either advantageous (i.e., Ms > Mo; Fig. 1a) or disadvantageous (i.e., Ms < Mo; Fig. 1b). The test options were generated such that Ms, Mo, and the absolute inequity (i.e., |Ms – Mo|) were decorrelated (rs < 0.07, ps > 0.66) (Gao et al., 2018; Saez et al., 2015). Two of the 50 trials were catch trials where the test option was also a fair division. Specifically, Ms = Mo = 2 for one, and Ms = Mo = 18 for the other.

Figure 1. Binary choice in the modified Dictator Game (DG). One of the two options was always a fixed, fair division where both Self and Other would get 10 points. The other option came from a set of test options varying in the payoff of the participants themselves (Ms) and the payoff of Other (Mo). Example trials from the advantageous frame (a) and the disadvantageous frame (b) are shown.

Computational modeling of choice in the modified DG. We modeled participants’ trial-by- trial choices by adapting a two-player inequity aversion model (Fehr & Schmidt, 1999) (see also Charness & Rabin, 2002) that had been validated for these types of binary choice task (Gao et al., 2018; Sáez et al., 2015). This allowed us to quantitatively isolate two motivations underlying participants’ choices:

� = �� − � ∙ � ∙ (�� − ��) − � ∙ � ∙ (�� − ��) where Ms and Mo are participants’ payoff and the recipient’s payoff in a given option, respectively. p and q indicate whether the option involves advantageous inequity or ‘aheadness’ (p = 1 when Ms > Mo, p = 0 otherwise) or disadvantageous inequity or ‘behindness’ (q = 1 when

9 Mo > Ms, q = 0 otherwise). Note that in some literature, the meaning of p and q are reversed (Gao et al., 2018). α and β are free parameters indicating the degree of disadvantageous inequity aversion and advantageous inequity aversion, respectively. We used a softmax function to convert utility difference between the two options (ΔU = Uunequal – Uequal) into probability of choosing the unequal option:

1 �(��) = 1 + �

Here, the inverse temperature parameter (λ) captures the steepness of the softmax function: higher value means that the softmax curve is closer to a step function, which in turn indicates that the participant’s choice is more sensitive to the change in utility difference. Given the relatively small sample and noisier choice behaviors of the incarcerated sample (see Supplementary Materials, p. 7), we only estimated α and β at the group level for Study 1 (cf., Gao et al., 2018; Zhu et al., 2014). For Study 2, we estimated α and β for each individual participant. A maximal likelihood estimation was used to find the combination of free parameters that best fit the observations. Two hundred iterations were performed for the group-level estimation (Study 1), while 50 iterations were performed for each individual participant (Study 2). The computational model quite accurately predicted the participants’ choices (69% for the high CU participants, 68% for the low CU participants, 85% for the college student sample).

Self-reported personality questionnaires and demographic information. For Study 1, participants completed the Interpersonal Reactivity Index (IRI; Davis, 1983) on a separate day prior to the experimental session. For Study 2, participants completed a battery of personality questionnaires assessing their social-affective traits, including the IRI, a 30-item self-reported psychopathy scale (Bartels & Pizarro, 2011), the Guilt and Shame Proneness Scale (GASP; (Cohen et al., 2011; Young et al., 2019)), the Self-Compassion Scale (SCS; (Neff, 2003)) and the Toronto Alexithymia Scale (TAS; (Bagby et al., 1994)). Participants’ attitudes and beliefs regarding justice and fairness were assessed using the General Belief in a Just World Scale (GBJWS; (Dalbert, 1999)). The Self-rating Scale of Systemic Family Dynamics (SSFD; Kang et al., 2001) was included to assess participants’ perception of their family environment. The SSFD

10 characterizes the organization and patterns of communication and interaction within a family. The scale has 4 dimensions (see Supplementary Material, p. 2, for the original Chinese version and its English translation) and we specifically focused on the FA subscale, which indicates a caring and supportive family atmosphere (e.g., “My family members can easily express warmth and concern for each other”). Participants also provided demographic information, including their age, sex assignment at birth, whether they are an only child in their family, the highest education of their parents, the environment where they grow up (urban vs. rural), and their subjective social economic status (SES). These variables were used as covariates in data analyses.

Data exclusion criteria for Study 2. Initially, we included three mechanisms to make sure that the participants understand the DG task and maintain sufficient attention throughout the task (Supplementary Material, p. 5). First, after the participants read the instruction for the DG task, they need to answer 8 comprehension questions about the DG task. Second, we included two “catch trials” in the DG task, where one option is obviously more profitable than the other both for the participant (i.e., decider) and the recipient. Third, we inserted three attention check questions in the personality questionnaires that were obvious and objective. Participants who correctly answered all the comprehension check questions in the DG task and the attention checks in the personality questionnaires were included in data analysis. Our results are almost identical under different data inclusion criteria (Supplementary Material, p. 8).

Results

All de-identified data and data analysis codes related to the results reported in this paper can be accessed at https://osf.io/fge9v. We have reported all measures, conditions, data exclusions, and how we determined the sample sizes.

In Study 1, we tested the hypothesis that high callous-unemotional (CU) trait is associated with advantageous, but not disadvantageous, inequity aversion. Supporting this hypothesis, the advantageous inequity aversion of the high CU group (M±s.d. = 0.75±0.07, credible interval

11 (89% Highest Density Interval) = [0.662, 0.863]) was almost 50% lower than that of the low CU group (1.14±0.09, credible interval = [1.007, 1.253]) (Fig. S2a, Table S2). This was not the case for disadvantageous inequity aversion (high CU group: 0.52±0.10, credible interval = [0.344, 0.655]; low CU group: 0.59±0.12, credible interval = [0.420, 0.773]) (Fig. S2b). This pattern indicates that getting more than one’s fair share is less of a concern for individuals with high CU than those with low CU, but they are equally averse to getting less than their fair share. The inverse temperature parameter of the high CU group (0.13±0.02, credible interval = [0.116, 0.168]) was higher than that of the low CU group (0.10±0.01, credible interval = [0.079, 0.115]) (Fig. S2c).

Table 1. Demographic and personality measures of the high and low CU groups

Measure High CU Low CU t-value p-value

M (s.d.) M (s.d.)

16.3 (0.8) 16.3 (0.8) -0.18 0.86 Age Education 2.1 (1.1) 2.0 (0.5) 0.30 0.77

Father education 1.8 (1.0) 1.9 (1.3) -0.56 0.58

Mother education 2.0 (1.5) 1.6 (0.7) 1.24 0.22

Family gross income 3.3 (1.5) 3.7 (1.4) -1.02 0.31

Callous-unemotional 10.3 (1.5) 8.3 (2.1) 4.63 < 0.001

IRI-Perspective 1.9 (0.6) 2.2 (0.5) -2.08 0.04 taking IRI-Empathic 2.1 (0.6) 2.6 (0.4) -3.98 < 0.001 concern IRI-Personal distress 2.2 (0.5) 2.1 (0.5) 0.98 0.33

In Study 2, we aimed to 1) conceptually replicate the differential effects of callousness-related traits on advantageous versus disadvantageous inequity aversion, and 2) to examine the specificity of the effects of callousness-related traits in a larger non-institutionalized sample. We found that the scores of the callous-affect and interpersonal manipulation sub-scales of the self-

12 reported psychopathy questionnaire (Bartels & Pizarro, 2011) were strongly and negatively correlated with advantageous IA. Moreover, the correlations with advantageous IA were significantly stronger (i.e., more negative) than those with disadvantageous IA (Table S3). This pattern, however, was not specific to callousness-related traits. In fact, most of the social- affective personality traits that we measured showed a similar pattern (for details, see Methods and Materials and Table S3). Given the conceptual and statistical overlap among the questionnaires, including their total scores in the same regression model to predict inequity aversion parameters is both uninformative and problematic.

To address this issue, we adopted a dimension approach to personality measures (Gillan et al., 2016) and used the composite dimensional scores to predict participants’ behavioral preferences in the DG task. Specifically, we carried out a factor analysis on the 126 individual items from the 6 personality questionnaires. Using the Cattell-Nelson-Gorsuch (CNG) test implemented by the ‘nFactors’ package in R (Raiche & Magis, 2010), our analysis identified a 3-factor latent structure (Figure 2a). Based on the highest loading items (|loading| > 0.25), we labeled the factors as ‘Emotion Perception and Regulation’ (Factor 1; Table S4, an example item “Being in a tense emotional situation scares me”, loading = 0.54), ‘Compassionate Social Emotions’ (Factor 2; Table S5, an example item “I often have tender, concerned feelings for people less fortunate than me”, loading = -0.31), and ‘Expanded Self and Belief in Justice’ (Factor 3; Table S6, example items “I try to see my failings as part of the human condition”, loading = 0.57 and “I think basically the world is a just place.”, loading = 0.32)1. Of particular interest, ‘Compassionate Social Emotions’ (Factor 2) picked up almost all the individual items from the Interpersonal Manipulation (M ± s.d. = 0.43±0.06) and the Callous Affect (0.34±0.11) subscales of the self-reported psychopathic questionnaire, and all the items from the guilt and shame proneness scale pertaining to guilt (-0.40±0.09) and shame experience (-0.39±0.09) (Table S7). Therefore, higher scores on this dimension indicates a lack of dispositional compassionate social emotions.

1 Note that, for the first two factors, the scores indicate the opposite or the lack of the traits signified by their respective factor labels. For example, higher score on Factor 2 indicates a lack of compassionate social emotions. We decided not to label the factors this way to avoid wordy names.

13 Table 2. Associations between social-affective trait dimensions and inequity aversion parameters. Variables B (SE) and CI B (SE) and CI B (SE) and CI for advantageous IA for disadvantageous IA for inverse temperature

Factor 1: Emotion -0.28 (0.07)*** -0.23 (0.10)* 0.03 (0.01)* Perception and Regulation [-0.42, -0.13] [-0.42, -0.04] [0.01, 0.05] Factor 2: Compassionate -0.52 (0.07)*** -0.16 (0.10) 0.06 (0.01)*** Social Emotions [-0.66, -0.38] [-0.35, 0.30] [0.03, 0.08] Factor 3: Expanded Self -0.02 (0.07) -0.12 (0.10) 0.01 (0.01) and Belief in Justice [-0.17, 0.12] [-0.32, 0.07] [-0.01, 0.04] Sex (Male > Female) -0.52 (0.16)** -1.44 (0.22)*** 0.19 (0.03)*** [-0.84, -0.20] [-1.87, -1.007] [0.14, 0.24] Age 0.12 (0.11) 0.07 (0.15) -0.03 (0.02) [-0.09, 0.33] [-0.22, 0.35] [-0.06, 0.01] Single child (Single > -0.15 (0.15) -0.53 (0.20)** 0.05 (0.02)* Non-single) [-0.44, 0.13] [-0.91, -0.15] [0.01, 0.09] Urban environment 0.11 (0.17) 0.07 (0.22) -0.01 (0.03) (Urban > Rural) [-0.21, 0.44] [-0.37, 0.51] [-0.06, 0.04] Father education -0.08 (0.07) -0.21 (0.10)* 0.02 (0.01) [-0.22, 0.06] [-0.40, -0.03] [-0.06, 0.04] Mother education -0.08 (0.07) 0.00 (0.10) -0.01 (0.01) [-0.22, 0.06] [-0.18, 0.19] [-0.03, 0.01] Socioeconomic status -0.05 (0.05) 0.12 (0.07) -0.00 (0.01) [-0.15, 0.05] [-0.02, 0.26] [-0.02, 0.01] N 2,250 2,250 2,250

R-squared 2 0.05 0.05 0.07

* p < 0.05, ** p < 0.01, *** p < 0.001

We next ran two robust linear mixed-effect models (R package ‘robustlmm’; Koller, 2016) to examine the association between the factor scores and the advantageous and disadvantageous inequity aversion parameters, which were estimated independently of the factor analysis. The scores of all the three factors were included in the same model. Demographic variables were also included as covariates (Table 2). Both Factor 1 and Factor 2, but not Factor 3, were significantly

2 Robust linear regression relies on weighted least squares, with the weights determined by an iterative process. The r-squared for robust linear regression should be interpreted with caution. Here, we reported the r-squared of corresponding standard linear mixed-effects models as an approximation.

14 and negatively associated with the advantageous IA parameter (Table 2, Table S8; Fig. 2b). For the disadvantageous IA parameter, only Factor 1 was significantly correlated (Table 2, Table S8; Fig. 2c). Note that this latter association became non-significant under the most conservative data exclusion criteria, indicating that this effect was not as robust as the effects with the advantageous IA. Importantly, as the confidence intervals indicated, Factor 2 was significantly more predictive of advantageous IA than of disadvantageous IA. This differential predictive power, which was conceptually consistent with the finding of Study 1, was not observed for Factor 1 or Factor 3. We carried out a post-hoc power calculation based on the association between Factor 2 score and advantageous inequity aversion (f2 = 0.014). The size of the final analysis sample afforded a power of 99.9% in detecting this effect at p < 0.05.

15 Figure 2. Results of factor analysis. (a) The correlation matrix of 126 individual questionnaire items and loadings of each item for the three factors. (b-c) Factor scores of each participant were entered into linear regression models for advantageous and disadvantageous inequity aversion parameters. Advantageous IA was negatively associated Factors 1 and 2. Disadvantageous IA was only significantly associated with Factor 1. Error bars indicate s.e.m. * p < 0.05, *** p < 0.001

Finally, we explored whether a supportive family environment leads to higher advantageous IA, via the mediating role of the social-affective factors that were predictive of advantageous IA. Family environment was indicated by the scores on the Family Atmosphere (FA) subscale of the Self-reported Family Dynamics Scale (Kang et al., 2001). This subscale reflects the degree to which one’s family is caring and supportive to its members (Cronbach’s α = 0.89). As Table S3 shows, FA score was significantly positively correlated with advantageous IA and significantly more so than with disadvantageous IA. We ran a mediation model where FA score was entered as the independent variable, the scores of Factor 1 and Factor 2 as two parallel mediators, and the advantageous inequity aversion parameter as the dependent variable. An SPSS macro was used to evaluate mediation models (Hayes, 2013). For the mediation analysis, we also included covariates of no interests as stated above (Table 2). We found that Factor 1 and Factor 2 together fully mediated the relationship between FA and advantageous inequity aversion (direct effect: B = -0.19, SE = 0.13, CI = [-0.45, 0.07]). The mediation effects of Factor 1 (B = 0.12, SE = 0.03, CI = [0.06, 0.19]) and Factor 2 (B = 0.34, SE = 0.05, CI = [0.24, 0.45]) were significantly above zero (Fig. 3). The mediation effect of Factor 2 was significantly stronger than that of Factor 1 (mean difference = 0.22, SE = 0.06, CI = [0.09, 0.35]). Note that although both of the mediation effects are positive, they are “inhibitory”, meaning that a positive family environment is negatively associated with the personality dimensions that are themselves “inhibitors” of advantageous inequity aversion, therefore “disinhibit” it.

Figure 3. Results of the mediation analysis. Family atmosphere is positively associated with advantageous inequity aversion. This relationship is fully mediated by the two social-affective trait dimensions (i.e., Factor 1: ‘Emotion Recognition and Regulation’, Factor 2: ‘Compassionate Social Emotions’) that are predictive of low advantageous inequity aversion.

Discussion

Utilizing a computational model, we demonstrated in a sample of incarcerated adolescents the contribution of callous-unemotional traits to advantageous inequity aversion. In a follow-up study with a large-scale college student sample (N = 2,250), we conceptually replicated and extended the association between callousness and advantageous inequity aversion by adopting a dimensional approach to social-affective personality traits. We found that a trait dimension characterized as ‘Compassionate Social Emotions’ was most predictive of advantageous inequity aversion but was unrelated to disadvantageous inequity aversion.

Past research has documented that individuals with high callousness or low guilt and shame proneness are more likely to engage in unethical behaviors (Blair, 2013; Cohen et al., 2012; Frick & Viding, 2009b; Waller et al., 2015). Replicating and extending those previous studies,

17 here we revealed that it was the advantageous inequity aversion underlying the prosocial behavior that was modulated by this social-affective trait dimension. Interestingly, this social- affective trait dimension was not associated with either diminished or heightened disadvantageous IA. This suggests that this social-affective trait dimension, which is primarily concerned with one’s own unethical behaviors, is dissociable from envy and reactive aggression, which is primarily concerned with unfairness and injustice inflicted on oneself (Costa & Babcock, 2008; Meehan et al., 2001; Walker & Jackson, 2017). It is the former that depends on the agent’s sense of shared social commitments and has only been found in older children and adult human beings, but not in younger children or non-human primates (McAuliffe et al., 2015; Tomasello, 2020; Tsoi & McAuliffe, 2020; Ulber et al., 2017). With these correlational analyses, however, we do not intend to overinterpret our results as implying any direction of causality.

The items traditionally included in the sub-scales of the Interpersonal Reactivity Index (i.e., personal distress, empathic concern, and perspective taking) nicely mapped onto different latent factors, suggesting their dissociable roles in motivating prosocial behaviors. Specifically, personal distress strongly and consistently loaded positively on Factor 1, which is associated with lower advantageous inequity aversion. This is consistent with ample empirical evidence that personal distress is self-centered and promotes withdrawal; even when it motivates helping behaviors, the underlying motivation is more to terminate one’s own distress than to benefit the recipient (Batson, 2011; Batson et al., 1981). In contrast, empathic concern loaded negatively on Factor 2, which is associated with advantageous inequity aversion. Previous research has demonstrated that empathic concern, unlike personal distress, is other-regarding and has an approach tendency (Davis et al., 1999; FeldmanHall et al., 2015; Zaki, 2014).

It is interesting to compare the effect of the trait dimension represented by Factor 2 and episodic social emotions (e.g., guilt) on inequity aversion. For example, Gao et al. has demonstrated that when episodic guilt state was induced experimentally, individuals exhibited higher advantageous inequity aversion and lower disadvantageous inequity aversion (Gao et al., 2018). This is conceivable because retrospective guilt should not only discourage individuals from engaging in future transgression, but also motivate individuals to make amend for existing transgression and damage (De Hooge, 2019; Kamau et al., 2013; H. Yu et al., 2014). In contrast, many of our

18 social-affective trait measures are anticipatory in nature (Cohen et al., 2012). Our result lends support to a cognitive account of the prosocial function of social affective traits (i.e., compassionate social emotions), namely individuals who anticipate more future social emotions (e.g., guilt, shame) find the prospect of unjustly getting better off than others more aversive (see also (Gong et al., 2019). Future studies are necessary to ascertain the neurobiological links between behavioral tendency (e.g., advantageous IA), episodic social emotions (e.g., guilt), and social-affective traits (e.g., guilt proneness).

Our finding that a positive family environment is associated with social affective traits pertaining to compassionate social emotions provides evidence for the developmental observations that family environment and parental warmth play a key role in the proper development of prosocial emotions such as empathy and guilt (Ferguson & Stegge, 1995; Hinde, 2002; Tangney & Dearing, 2003; Zahn-Waxler & Kochanska, 1990). The novel contribution of our findings is that we revealed possible routes from family environment to prosocial behavioral preference via social-affective traits. However, it should be noted that these results are correlational and should be interpreted with caution. For example, the mediation results cannot rule out the possibility that participants low in social-affective trait have inaccurate and self-motivated perceptions or memories of their family interactions (Klein & Epley, 2016; Tasimi & Johnson, 2015). Rigorous developmental experiments are needed to establish the causal relationship between positive family environment and compassionate social emotions.

To conclude, by combining computational modeling and a dimensional approach to personality measures, this well-powered study offers a cognitive account of how compassionate social emotions as a social-affective trait promotes prosocial behaviors – individuals high on this dimension are more careful not to be unfairly better off than others (i.e., advantageous inequity aversion). Moreover, we highlight the association between a positive family environment and the development of the trait of compassionate social emotions, and provide evidence for an intermediate role of affective trait in the relationship between family environment and advantageous inequity aversion. Together, the results of this study suggest that the trans- diagnostic approach is not only useful in discovering dimensional markers of behavioral anomaly

19 in psychiatry, but is also applicable to ascertaining the specificity of social-affective trait dimension in predicting prosociality.

Acknowledgments

The authors thank Luis Sebastian Contreras-Huerta for his insightful suggestions regarding the factor analysis approach. This work was supported by research grants from the National Natural Science Foundation of China awarded to X.Z. (31630034, 71942001) and a grant from the China Postdoctoral Science Foundation awarded to X.G. (2019M650008).

20 References

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27 Supplementary Material for

Explaining individual differences in advantageous inequity aversion by social-affective trait dimensions and family environment

List of items included in the Supplemental Materials

1. Supplementary Methods a. The original (Chinese) text of Self-rating Scale of Systemic Family Dynamics and English translation (pp. 2 – 4) b. Comprehension questions for the Dictator Game (pp. 5 – 6) c. Participant payment methods (p. 6)

2. Supplementary Results a. Fitting the lapse rate parameter (p. 7) b. Results of Study 2 under different data exclusion criteria (p. 8)

3. Supplementary Figures a. Figure S1. Trial set for the modified Dictator Game (p. 9) b. Figure S2. Distribution of inequity aversion model parameters (p. 10) c. Figure S3-S5. Factor loadings of Factor 1 – Factor 3, under three different data exclusion criteria (pp. 11 – 13) d. Figure S6. Results of regression analysis under three different data exclusion criteria (p. 14) 4. Supplementary Tables a. Table S1. Type and frequency of offences of Study 1 participants (p. 15) b. Table S2. Distribution of inequity aversion model parameters (group-based estimation) (p. 16) c. Table S3. Partial correlations between questionnaire subscale scores and inequity aversion parameters (pp. 17 – 18) d. Table S4. Top loading items on Factor 1 (‘Emotion Recognition and Regulation’) (pp. 19 – 20) e. Table S5. Top loading items on Factor 2 (‘Compassionate Social Emotions’) (pp. 21 – 23) f. Table S6. Top loading items on Factor 3 (‘Expanded Self and Belief of Justice’) (pp. 24 – 25) g. Table S7. Average factor loadings of sub-scales (p. 26) h. Table S8. Regression results under three data exclusion criteria (p. 27)

1 Supplementary Methods

Self-rating Scale of Systemic Family Dynamics

Reversed Subscale Question Items

Members of my family have deep connections with each other. If one member is in trouble, everyone will feel the pain and anxiety. 我们家的⼈互相间感情很深，⼀⼈有⿇烦，⼤家都会感到痛苦，焦虑不安。 My family members are proud to be close with each other. 家庭成员为彼此间的亲密⽽⾃豪。

My family members often quarrel. R 我们家的⼈经常争吵。

My family members can easily express warmth and Family concern for each other. atmosphere 家庭成员之间很容易表达彼此的温暖和关怀。

All of my family members have a say in major family decisions. 全家⼈对重⼤的家庭决策都有发⾔权。 While relaxing during family time, we can speak our minds freely. 我们家的⼈在⼀起时轻松愉快，能畅所欲⾔。 My family is very united with a strong sense of team spirit. 我们感到⼀家⼈很团结，富有协作精神。 The members of my family are aware of each other’s strengths and weaknesses. 家庭成员都能看到相互间的长处和不⾜。 Members of my family are allowed to live their lives in the way that they choose. Individualiz 我们家允许家庭成员按⾃⼰的⽅式⽣活。 ation My parents allow me to freely develop my hobbies.

⽗母允许我⾃由发展兴趣爱好。

2 Everyone in my family has the freedom to make their own decisions. 在我们家⾥每个⼈能很⾃由地⾃⼰做决定。 I arrange my own schedule.

我的时间由⾃⼰安排。 Our parents don’t need strict rules to control us.

⽗母不⽤严格的规则来约束我们。 In my family, each person is allowed to have their unique personality and characteristics.

我们家允许每个⼈有⾃⼰的个性或有与别⼈不同的特点。 In my family, we don't like people who don't agree with R us. 我们家不喜欢与我们观点不⼀样的⼈。 When discussing a person or thing, my family members like to use "yes" or "no", and "good" or "bad" to make simple generalizations. R 议论⼀个⼈或⼀件事时，我们家的⼈喜欢⽤“是”或 “⾮”，“好”或“坏”来做简单明了的概括。 When interacting with my family, some people find our Logic of ways of doing things terrible, while some find them excellent. family R systems 我们家待⼈接物时，有的⼈和事被看得糟糕透顶,有的又被认为再好不过。 We believe that good things are good and bad things are bad. There are no exceptions. R 我们家的⼈认为⼀件事情好就是好，不好就是不好,不存在其它情况。 My family members always accept only views that are in R line with ours. 我们家的⼈总是只接受与我们观点相同的看法。 My family members believe that psychological self- regulation can be used to treat mental illness. 我们家的⼈认为⾃我调整⼼理状态可以治疗⼼理疾 Illness 病。 conception My family members believe that some illnesses are the result of interpersonal tension. 我们家的⼈认为，某些疾病与⼈际关系紧张有关。

3 We believe that the occurrence of mental illness is related to the family environment. 我们家的⼈认为，⼼理疾病的发⽣与家庭环境有关。 My family members believe that mental illness is strongly related to lifestyle. 我们家的⼈认为⼼理疾病与个⼈的⽣活⽅式有很⼤关系。

Items are scored on a five-point Likert scale (1-completely disagree, 2-disagree, 3-partially agree, 4- agree, 5-completely agree). Items with “R” are reverse coding items.

4 Comprehension questions for the Dictator Game

Prior to the Dictator Game, the participants answered 8 comprehension questions aiming to test whether they understood the rules of the task and the consequences of their choices. The questions are listed below (English translations):

Please answer the following questions. These questions are aimed to test your understanding of the game.

1. How many players are participating in the game? - 1 - 2 - 3 - Not sure

2. Will the partner paired with you play the same game as you? - Yes - No - Not sure

3. Whose payoff will be impacted by your choice? - Your own - The paired partner’s - Both yours and the paired partner’s

4. If you choose “You: 15, Partner: 10”, and this trial is selected, how many monetary points will you receive? - 15 - 10

5. If you choose “You: 12, Partner: 13”, and this trial is selected, how many monetary points will the paired partner receive? - 12 - 13

6. How will the system determine the outcome? - The system will randomly select one of your choices - The system will randomly select one of the paired partner’s choices - The system will randomly select one of your and the paired partner’s choices

7. How will your payoff be determined? - The monetary points you allocate to yourself in the selected choice - The monetary points the paired partner allocates to you in their selected choice - The sum of the above two

8. How will the paired partner’s payoff be determined? - The monetary points you allocate to them in the selected choice - The monetary points the paired partner allocates to themselves in their selected choice - The sum of the above two

Participant payments

For Study 1, due to the restrictions of the correctional institution, the participants in the incarcerated sample did not receive monetary payment. Nevertheless, in our verbal instructions, we emphasized that the participants need to imagine vividly that they would split the money with another randomly paired participant. For Study 2, the participants were instructed that one of their choices would potentially be picked up randomly and made real after the experiment. The participants were only paid as Dictators. On average, the participants received 25 CNY (about 4 USD).

6 Supplementary Results

Fitting the lapse rate parameter To formally characterize participants’ “decision errors”, we fit the choice data with an additional free parameter, lapse rate (or ε), that closely captures attention lapse, response error, etc. (Crockett et al., 2014). Specifically, the observed probability of choosing the unequal option can be written as

�(��) = (1 − �)� + �(1 − �)

where Ptrue = indicates the true probability of choosing the unequal option. The λ underlying assumption is that the observed probability of choosing the unequal option has two sources – the participant’s true probability of choosing the unequal option (i.e., Ptrue), and response error, where the participant intends to choose the equal option but due to factors other than value difference (such as inattention and erroneous responses) mistakenly choose the unequal option (i.e., 1 – Ptrue). The two sources of contribution to the observed P(unequal) are weighted by the lapse rate ε parameter. Larger ε indicates that more of the participant’s choices are due to irrelevant factors and response errors.

We fitted this model at the individual participant level for the college student sample (Study 2), the incarcerated sample (Study 1), and another college student sample reported in Gao et al. (2018). The lapse rate parameter was significantly larger for the incarcerated sample (0.11 ± 0.09) than for the college student sample in Study 2 (0.06 ± 0.08; Mann-Whitney U test, Z = - 4.52, p < 0.001) and in Gao et al. (2018) (0.06 ± 0.05; Mann-Whitney U test, Z = -6.54, p < 0.001). These analyses indicate that the choice behaviors of the incarcerated sample are significantly noisier than the college student samples. Estimating model parameters based on the limited number of trials of each incarcerated participant would be a suboptimal practice, as long as the reliability of the model parameters is concerned. We therefore adopted the group-based parameter estimation approach that has been used to estimate computational model parameters based limited and noisier choices of brain lesion patients (Zhu et al., 2014).

Results of Study 2 under different data exclusion criteria To test whether the results we reported in the paper are robust to data exclusion criteria, we analyzed the data of Study 2 under three exclusion criteria: 1) including the entire sample (i.e., no exclusion; N = 4,888); 2) excluding only based on the comprehension check questions in the Dictator Game task and the attention checks in the personality questionnaires, and not excluding participants based on their choices in the catch trials (N = 2,250); 3) including only the participants who passed all the attention check questions and catch trials (N = 1,727). As can be seen from Supplementary Figures 3 through 6, the results of the factor analysis (i.e., number of factors and factor loadings) and of the regression analysis with inequity aversion parameters and factor scores are almost identical under the three different exclusion criteria, indicating that these analyses are robust and replicable.

We reported the results based on the second exclusion criterion in the main text, due to the following considerations. First, we can reasonably assume that the participants who got all the comprehension check questions correct understood the rules of the game and the consequences of their choices to themselves and the recipient. Because each comprehension check question has 3 options, the probability of getting all the 8 questions correct by choosing at random is less than 0.1 ‰, which is negligible given our sample size. Second, the attention check questions embedded in the personality questionnaires are obvious and objective; they all have the format of “This question is to make sure you are paying attention. Please choose ‘2’.” If a participant failed in any of these attention check questions, we can reasonably assume that they were not paying attention. Third, we dropped the criterion that the participants have to choose the more profitable option in the two “catch trials” in the DG task due to the consideration that relative to the above two criteria, this one was more subjective and the participants who chose otherwise may have preferences that we are not aware of. As long as they understood the rules of the DG task (by passing the comprehension check questions) and maintained sufficient attention to the survey (by getting all the attention check questions correct), we should allow the existence of individual differences in the preference with regard to their decisions in the DG task. That said, as the results show, excluding the participants who chose at least one less profitable option from data analysis did not change the pattern of our results (Figs. S3 – S6)

8 Supplementary Figures

Figure S1. Trial set for the modified Dictator Game. The combination of Ms and Mo for each trial is indicated as a dot in the figure.

Figure S2. Distribution of inequity aversion model parameters. There is substantial overlap in the highest density credible interval (HDI) of the advantageous inequity aversion parameter and the inverse temperature parameter between the Low CU group and the college student group. No such overlap is observed between the High CU group and the college student group. For the High CU and the Low CU groups, there is substantial overlap in the HDI of the disadvantageous inequity aversion parameter, but not the other two parameters. Note that because the college student sample is much larger, the parameter distributions are more focused than the incarcerated sample.

Figure S3. Factor loadings of Factor 1, calculated based on the entire participant sample (a), a sample where participants who failed any of the 8 comprehension questions in the Dictator Game task and attention check questions in the personality questionnaires were excluded (b), and a sample where, on the basis of the sample in (b), we further excluded participants who chose the less profitable option in either of the catch trials in the Dictator Game task (c).

Figure S4. Factor loadings of Factor 2, calculated based on the entire participant sample (a), a sample where participants who failed any of the 8 comprehension questions in the Dictator Game task and attention check questions in the personality questionnaires were excluded (b), and a sample where, on the basis of the sample in (b), we further excluded participants who chose the wrong option in either of the catch trials in the Dictator Game task (c).

Figure S5. Factor loadings of Factor 3, calculated based on the entire participant sample (a), a sample where participants who failed any of the 8 comprehension questions in the Dictator Game task and attention check questions in the personality questionnaires were excluded (b), and a sample where, on the basis of the sample in (b), we further excluded participants who chose the wrong option in either of the catch trials in the Dictator Game task (c).

Figure S6. Results of regression analysis. Regression coefficients of the individual factor scores for advantageous inequity aversion parameters (a-c) and for disadvantageous inequity aversion parameters (d-f). Results were based on the entire participant sample (a, d), a sample where participants who failed any of the 8 comprehension questions in the Dictator Game task and attention check questions in the personality questionnaires were excluded (b, e), and a sample where, on the basis of the sample in (b) and (e), we further excluded participants who chose the wrong option in either of the catch trials in the Dictator Game task (c, f). Across all the 3 exclusion criteria and samples, Factor 2 remains to be the strongest predictor of the advantageous inequity aversion parameter and consistently exhibits a significantly stronger predictive power for the advantageous inequity aversion parameter than for the disadvantageous inequity aversion parameter. Error bars indicate s.e.m.

14 Supplementary Tables

Table S1. Type and frequency of offences

Type of offense High CU group Low CU group χ2

N (%) N (%)

Burglary 26 (81) 24 (68) 0.83

Rape 4 (13) 6 (17) 0.04

Assault 6 (19) 5 (14) 0.03

Murder 2 (6) 3 (9) < 0.01

Theft 2 (6) 0 (0) 0.61

Note: the percentage of different types of offence in a column does not add up to 100% because some individuals have multiple charges.

15 Table S2. Distribution of inequity aversion model parameters (group-based estimation)

Group Advantageous IA Disadvantageous IA Inverse temperature

Mean [HDI] Mean [HDI] Mean [HDI]

High CU 0.75 [0.66, 0.86] 0.52 [0.34, 0.66] 0.13 [0.12, 0.17]

Low CU 1.14 [1.01, 1.25] 0.59 [0.42, 0.77] 0.10 [0.08, 0.12]

College student 1.15 [1.13, 1.16] 0.72 [0.70, 0.74] 0.10 [0.10, 0.10]

HDI: highest density interval

16 Table S3. Partial correlations between questionnaire subscale scores and inequity aversion parameters Measure Inverse Advantageous Disadvantageous t-value temperature IA IA GASP

Negative behavioral evaluation (guilt -0.06** 0.16*** 0.05* 5.75 proneness)a Repair 0.02 0.13*** 0.03 5.32

Negative self evaluation (shame 0.03 0.03 0.01 1.13 proneness)b Withdraw -0.01 -0.04 0.02 -2.90

IRI

Perspective taking -0.05* 0.11*** 0.03 3.70

Empathic concern -0.06** 0.11*** 0.03 4.01

Personal distress 0.00 -0.06** -0.03 -1.54

Psychopathy

Callous affect 0.06** -0.16*** -0.06** -4.97

Interpersonal manipulation 0.13*** -0.22*** -0.08*** -7.34

Erratic lifestyle 0.06** -0.11*** -0.08*** -1.59

Alexithymia

Difficulty Identifying Feelings -0.00 -0.08*** -0.02 -2.92

Difficulty Describing Feelings 0.02 -0.07*** -0.05 -1.38

Externally Oriented Thinking -0.05* -0.04* 0.02 -3.07

Self Compassion

Self-Kindness 0.04 0.03 -0.04* 3.49

Self-Judgment 0.06** -0.09*** -0.07*** -1.03

Isolation -0.02 -0.08*** -0.03 -2.77

17 Common Humanity -0.00 0.03 -0.00 1.48

Mindfulness -0.01 0.04 0.01 1.69

Over-Identification 0.04 -0.10*** -0.03 -3.86

General Belief in a Just World

Personal 0.04* 0.06** -0.06** 6.19

General -0.06** 0.13*** 0.01 5.84

Family Dynamics

Family Atmosphere -0.05* 0.07*** 0.03 1.95

Individualization -0.01 0.04* -0.01 2.66

Illness Conception 0.02 0.00 -0.04* 2.25

Logic of Family Systems 0.01 -0.07*** -0.01 -4.11

Note: When computing the correlation between subscale scores and the inequity aversion parameters, participants’ sex assigned at birth, age, perceived socioeconomic status, parents’ highest education, single-child status, where the participants spent most of their pre-college life (urban vs. rural) were controlled as covariates (‘ppcor’ package in R; (Kim, 2015)). a: when computing the correlation between guilt proneness and inequity aversion parameters, shame proneness was also controlled for to produce a measure of ‘shame-free guilt’. b: when computing the correlation between shame proneness and inequity aversion parameters, guilt proneness was also controlled for to produce a measure of ‘guilt-free shame’. t-value: comparison between the correlation coefficients of advantageous and disadvantageous inequity aversion (using the ‘paired.r’ function in the R package ‘psych’ (Revelle & Revelle, 2015). *: p < 0.05; **: p < 0.01; ***: p < 0.001.

Table S4. Top loading items on Factor 1 (‘Emotion Perception and Regulation’)

Questionnaire Item Loading Self Compassion When I fail at something important to me, I become consumed by 0.618 feelings of inadequacy. Self Compassion When I think about my inadequacies, it tends to make me feel more 0.598 separate and cut off from the rest of the world. Alexithymia I am often puzzled by sensations in my body. 0.585 Alexithymia I have feelings that I can't quite identify. 0.580 IRI I sometimes feel helpless when I am in the middle of a very emotional 0.574 situation. Self Compassion When something painful happens, I tend to blow the incident out of 0.571 proportion. Self Compassion When I see aspects of myself that I don't like, I get down on myself. 0.569 Alexithymia I am often confused about what emotion I am feeling. 0.564 Self Compassion When I'm feeling down, I tend to obsess and fixate on everything that's 0.561 wrong. Alexithymia When I am upset, I don't know if I am sad, frightened, or angry. 0.556 Alexithymia It is difficult for me to find the right words for my feelings. 0.552 IRI I tend to lose control during emergencies. 0.544 Self Compassion When I fail at something that's important to me, I tend to feel alone in 0.544 my failure. Self Compassion When something upsets me I get carried away with my feelings. 0.543 IRI Being in a tense emotional situation scares me 0.542 Self Compassion When I'm really struggling, I tend to feel like other people must be 0.540 having an easier time of it. Psychopathy / 0.534 Self Compassion When I'm feeling down, I tend to feel like most other people are probably 0.525 happier than I am. Alexithymia I have physical sensations that even doctors don't understand. 0.509 Psychopathy / 0.473 Alexithymia I prefer to just let things happen rather than to understand why they 0.459 turned out that way. Alexithymia I often don't know why I am angry. 0.458 IRI In emergency situations, I feel apprehensive and ill-at-ease. 0.453 GASP You give a bad presentation at work. Afterwards your boss tells your 0.441 coworkers it was your fault that your company lost the contract. What is the likelihood that you would feel incompetent? IRI When I see someone who badly needs help in an emergency, I go to 0.438 pieces. Alexithymia I find it hard to describe how I feel about people. 0.435 Self Compassion I'm intolerant and impatient towards those aspects of my personality I 0.406 don't like. Psychopathy / 0.387 Self Compassion I can be a bit cold-hearted towards myself when I'm experiencing 0.372 suffering.

19 Alexithymia (-)I am able to describe my feelings easily. 0.372 Alexithymia I don't know what's going on inside me. 0.358 Psychopathy / 0.340 Alexithymia It is difficult for me to reveal my innermost feelings, even to close 0.333 friends. Psychopathy / 0.330 Psychopathy / 0.324 Self Compassion When times are really difficult, I tend to be tough on myself. 0.319 Self Compassion I'm disapproving and judgmental about my own flaws and inadequacies. 0.308 Psychopathy / 0.308 Psychopathy / 0.303 IRI I would describe myself as a pretty soft-hearted person. 0.302 IRI I am often quite touched by things that I see happen. 0.292 Psychopathy / 0.291 IRI I sometimes find it difficult to see things from the "other guy's" point of 0.284 view. GASP A friend tells you that you boast a great deal. What is the likelihood that 0.263 you would stop spending time with that friend? GASP You make a mistake at work and find out a coworker is blamed for the 0.260 error. Later, your coworker confronts you about your mistake. What is the likelihood that you would feel like a coward? GASP After making a big mistake on an important project at work in which 0.256 people were depending on you, your boss criticizes you in front of your coworkers. What is the likelihood that you would feign sickness and leave work? Alexithymia People tell me to describe my feelings more. 0.254 IRI (-)I am usually pretty effective in dealing with emergencies. 0.254

Note: Summary of item loadings onto ‘Difficulty in Emotion Recognition and Regulation’ factor. The top loading items from each questionnaire (|loading| > 0.25) are displayed in descending order. Items from the psychopath questionnaires were not displayed due to copyright issue. The mark "(-)" before the item indicates that the item's original loading is negative. Items with red loadings numbers are reverse-coded. IRI = Interpersonal Reactivity Index, GASP = Guilt and Shame Proneness Scale.

20 Table S5. Top loading items on Factor 2 (‘Compassionate Social Emotions’) Questionnaire Item Loading GASP (-)You successfully exaggerate your damages in a lawsuit. Months 0.517 later, your lies are discovered and you are charged with perjury. What is the likelihood that you would think you are a despicable human being? GASP (-)You lie to people but they never find out about it. What is the 0.514 likelihood that you would feel terrible about the lies you told? Psychopathy / 0.513 Psychopathy (-)/ 0.487 Psychopathy / 0.480 Psychopathy / 0.477 IRI When I see someone get hurt, I tend to remain calm. 0.466 Psychopathy / 0.460 IRI When I see someone being treated unfairly, I sometimes don't feel very 0.453 much pity for them. Psychopathy / 0.451 Psychopathy / 0.450 Psychopathy / 0.448 Psychopathy / 0.444 GBJWS (-)I am confident that justice always prevails over injustice. 0.432 Psychopathy / 0.430 Psychopathy (-)/ 0.414 Psychopathy / 0.412 GASP (-)At a coworker's housewarming party, you spill red wine on their new 0.411 cream-colored carpet. You cover the stain with a chair so that nobody notices your mess. What is the likelihood that you would feel that the way you acted was pathetic? GASP (-)You secretly commit a felony. What is the likelihood that you would 0.405 feel remorse about breaking the law? IRI Sometimes I don't feel very sorry for other people when they are having 0.402 problems. Psychopathy / 0.399 GASP (-)You rip an article out of a journal in the library and take it with you. 0.383 Your teacher discovers what you did and tells the librarian and your entire class. What is the likelihood that this would make you would feel like a bad person? Psychopathy (-)/ 0.378 GBJWS (-)I believe that most of the things that happen in my life are fair. 0.371 Psychopathy / 0.368 Psychopathy / 0.367 IRI (-)I would describe myself as a pretty soft-hearted person. 0.367 Psychopathy / 0.360 Psychopathy / 0.356

21 GASP (-)You make a mistake at work and find out a coworker is blamed for 0.353 the error. Later, your coworker confronts you about your mistake. What is the likelihood that you would feel like a coward? IRI (-)I am often quite touched by things that I see happen. 0.351 Psychopathy / 0.350 Psychopathy / 0.345 GBJWS (-)I firmly believe that injustices in all areas of life(e.g., professional, 0.344 family, politics) are the exception rather than the rule. GBJWS (-)I think basically the world is a just place. 0.341 GBJWS (-)In my life injustice is the exception rather than the rule. 0.339 GBJWS (-)I am convinced that in the long run people will be compensated for 0.338 injustices. GASP (-)You reveal a friend's secret, though your friend never finds out. What 0.336 is the likelihood that your failure to keep the secret would lead you to exert extra effort to keep secrets in the future? IRI (-)When I see someone being taken advantage of, I feel kind of 0.334 protective towards them. GBJWS (-)I think that important decisions that are made concerning me are 0.323 usually just. GASP (-)You are privately informed that you are the only one in your group 0.321 that did not make the honor society because you skipped too many days of school. What is the likelihood that this would lead you to become more responsible about attending school? IRI (-)I often have tender, concerned feelings for people less fortunate than 0.314 me. GASP (-)After realizing you have received too much change at a store, you 0.304 decide to keep it because the salesclerk doesn't notice. What is the likelihood that you would feel uncomfortable about keeping the money? GASP (-)You give a bad presentation at work. Afterwards your boss tells your 0.301 coworkers it was your fault that your company lost the contract. What is the likelihood that you would feel incompetent? Psychopathy (-)/ 0.298 Psychopathy / 0.297 Psychopathy / 0.286 GBJWS (-)I think people try to be fair when making important decisions. 0.284 Alexithymia People tell me to describe my feelings more. 0.282 Alexithymia It is difficult for me to reveal my innermost feelings, even to close 0.281 friends. GBJWS (-)I believe that, by and large, people get what they deserve. 0.274 GBJWS (-)Overall, events in my life are just. 0.272 GASP (-)You strongly defend a point of view in a discussion, and though 0.264 nobody was aware of it, you realize that you were wrong. What is the likelihood that this would make you think more carefully before you speak? Self Compassion When times are really difficult, I tend to be tough on myself. 0.263 GBJWS (-)I am usually treated fairly. 0.255 IRI (-)In emergency situations, I feel apprehensive and ill-at-ease. 0.250

22 Note: Summary of item loadings onto ‘Lack of Compassionate Social Emotions’ factor. The top loading items from each questionnaire (|loading| > 0.25) are displayed in descending order. Items from the psychopath questionnaires were not displayed due to copyright issue. The mark "(-)" before the item indicates that the item's original loading is negative. Items with red loadings numbers are reverse-coded. IRI = Interpersonal Reactivity Index, GBJWS = General Belief in a Just World Scale, GASP = Guilt and Shame Proneness Scale.

23 Table S6. Top loading items on Factor 3 (‘Expanded Self and Belief in Justice’)

Questionnaire Item Loading Self Compassion When something painful happens, I try to take a balanced view of the 0.611 situation. Self Compassion When I'm going through a very hard time, I give myself the caring 0.584 and tenderness I need. Self Compassion When I'm feeling down, I try to approach my feelings with curiosity 0.582 and openness. Self Compassion I try to see my failings as part of the human condition. 0.573 Self Compassion When I'm down and out, I remind myself that there are lots of other 0.569 people in the world feeling like I am. Self Compassion When I feel inadequate in some way, I try to remind myself that 0.529 feelings of inadequacy are shared by most people. Self Compassion I try to be loving towards myself when I'm feeling emotional pain. 0.522 Self Compassion I'm kind to myself when I'm experiencing suffering. 0.521 Self Compassion When things are going badly for me, I see the difficulties as part of 0.504 life that everyone goes through. Self Compassion I try to be understanding and patient towards those aspects of my 0.477 personality I don't like. Self Compassion When something upsets me I try to keep my emotions in balance. 0.455 IRI I sometimes try to understand my friends better by imagining how 0.419 things look from their perspective. IRI I believe that there are two sides to every question and try to look at 0.411 them both. Psychopathy 0.386 SC When I fail at something important to me I try to keep things in 0.385 perspective. Alexithymia I find examination of my feelings useful in solving personal problems. 0.372 GBJWS I am usually treated fairly. 0.371 IRI When I'm upset at someone, I usually try to "put myself in his shoes" 0.362 for a while. GBJWS Overall, events in my life are just. 0.352 IRI Before criticizing somebody, I try to imagine how I would feel if I 0.346 were in their place. GBJWS I believe that most of the things that happen in my life are fair. 0.335 Alexithymia Being in touch with emotions is essential. 0.330 IRI I am usually pretty effective in dealing with emergencies. 0.330 Self Compassion I'm tolerant of my own flaws and inadequacies. 0.327 GBJWS I think that important decisions that are made concerning me are 0.320 usually just. GBJWS I think basically the world is a just place. 0.318 GBJWS In my life injustice is the exception rather than the rule. 0.316 GBJWS I believe that I usually get what I deserve. 0.315 Psychopathy 0.314 GBJWS I firmly believe that injustices in all areas of life(e.g., professional, 0.313 family, politics) are the exception rather than the rule.

24 GBJWS I believe that, by and large, I deserve what happens to me. 0.313 GBJWS I think people try to be fair when making important decisions. 0.311 GBJWS I am convinced that in the long run people will be compensated for 0.307 injustices. Alexithymia I prefer to analyze problems rather than just describe them. 0.305 GBJWS I believe that, by and large, people get what they deserve. 0.303 Alexithymia I can feel close to someone, even in moments of silence. 0.286

Note: Summary of item loadings onto ‘Expanded Self and Belief of Justice’ factor. The top loading items from each questionnaire (|loading| > 0.25) are displayed in descending order. Items from the psychopath questionnaires were not displayed due to copyright issue. The mark "(-)" before the item indicates that the item's original loading is negative. Items with red loadings numbers are reverse-coded. IRI = Interpersonal Reactivity Index, GBJWS = General Belief in a Just World Scale.

25 Table S7. Average factor loadings of sub-scales

Scales Factor 1 Factor 2 Factor 3 M (s.d.) M (s.d.) M (s.d.) Interpersonal reactivity index Empathic concern 0.10 (0.18) -0.31 (0.17) 0.12 (0.12) Personal distress 0.40 (0.19) -0.20 (0.14) -0.09 (0.11) Perspective taking -0.09 (0.11) -0.13 (0.08) 0.28 (0.16) Psychopath Interpersonal manipulation 0.24 (0.08) 0.43 (0.06) 0.07 (0.04) Callous affect 0.04 (0.19) 0.34 (0.11) 0.02 (0.15) Erratic lifestyle 0.29 (0.16) 0.29 (0.15) 0.04 (0.07) Guilt and shame proneness scale Guilt negative behavior evaluation 0.06 (0.03) -0.40 (0.09) 0.08 (0.03) Shame negative self evaluation 0.25 (0.14) -0.39 (0.09) 0.00 (0.07) Guilt repair 0.05 (0.05) -0.29 (0.05) 0.17 (0.06) Shame withdraw 0.16 (0.11) 0.05 (0.14) -0.08 (0.02) Self-compassion Common humanity 0.01 (0.10) 0.00 (0.03) 0.54 (0.03) Mindfulness -0.15 (0.04) 0.06 (0.02) 0.51 (0.11) Over-identification 0.57 (0.03) 0.01 (0.06) -0.11 (0.05) Isolation 0.55 (0.03) 0.02 (0.04) -0.14 (0.08) Self-judgment 0.39 (0.11) 0.06 (0.18) 0.02 (0.10) Self-kindness -0.12 (0.09) 0.02 (0.06) 0.49 (0.10) Belief in a just world Personal belief in a just world -0.02 (0.07) -0.25 (0.12) 0.33 (0.02) General belief in a just world 0.01 (0.04) -0.34 (0.06) 0.30 (0.03) Toronto alexithymia scale Difficulty describing feelings 0.39 (0.11) 0.17 (0.11) 0.02 (0.10) Externally oriented thinking 0.10 (0.22) 0.04 (0.11) -0.16 (0.19) Difficulty identifying feelings 0.52 (0.08) 0.12 (0.04) -0.02 (0.06)

Table S8. Regression results under three data exclusion criteria

Advantageous IA Disadvantageous IA Inverse temperature Group B [95% CI] B [95% CI] B [95% CI]

No exclusion (N = 4,888) Factor 1 -0.28 [-0.38, -0.15]*** -0.18 [-0.32, -0.04]* 0.00 [-0.01, 0.02]

Factor 2 -0.49 [-0.60, -0.37]*** -0.09 [-0.24, 0.05] 0.01 [0.00, 0.02]*

Factor 3 0.00 [-0.11, 0.12] -0.15 [-0.30, -0.01]* 0.00 [-0.01, 0.01]

Pass personality checks (N = 2,250) Factor 1 -0.28 [-0.42, -0.133]*** -0.23 [-0.42, -0.04]* 0.03 [0.00, 0.05]*

Factor 2 -0.52 [-0.66, -0.38]*** -0.16 [-0.35, 0.03] 0.05 [0.03, 0.08]***

Factor 3 -0.02 [-0.17, 0.12] -0.12 [-0.32, 0.07] 0.01 [-0.01, 0.04]

Pass all checks (N = 1,727) Factor 1 -0.11 [-0.18, -0.04]** -0.05 [-0.13, 0.03] 0.04 [0.00, 0.08]*

Factor 2 -0.29 [-0.36, -0.23]*** -0.08 [-0.16, 0.00] 0.10 [0.05, 0.13]***

Factor 3 -0.04 [-0.10, 0.03] -0.09 [-0.17, -0.01]* 0.04 [-0.00, 0.08]

Note: *p < 0.05, **p < 0.01, ***p < 0.001.