Abstract
Prosocial motives such as social equality and efficiency are key to altruistic behaviors. However, predicting the range of altruistic behaviors in varying contexts and individuals proves challenging if we limit ourselves to one or two motives. Here we demonstrate the numerous, interdependent motives in altruistic behaviors and the possibility to disentangle them through behavioral experimental data and computational modeling. In one laboratory experiment (N = 157) and one preregistered online replication (N = 1,258), across 100 different situations, we found that both thirdparty punishment and thirdparty helping behaviors (that is, an unaffected individual punishes the transgressor or helps the victim) aligned best with a model of seven socioeconomic motives, referred to as a motive cocktail. For instance, the inequality discounting motives imply that individuals, when confronted with costly interventions, behave as if the inequality between others barely exists. The motive cocktail model also provides a unified explanation for the differences in intervention willingness between second parties (victims) and third parties, and between punishment and helping.
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Main
Many people voluntarily provide resources such as shelter, food and healthcare to refugees fleeing wartorn regions, while others advocate sanctioning responsible nations, even at personal expense. This altruistic behavior, known as thirdparty punishment (3PP) and helping (3PH), involves sacrificing personal interests to punish transgressors or help victims. Such behaviors have been observed in both laboratory^{1,2,3} and field studies^{4,5}. What, then, motivates these actions?
According to one line of theories, thirdparty intervention serves as a strategic means to obtain future rewards, by signaling one’s trustworthiness to potential cooperators^{3,6} or deterring potential transgressors from harming oneself or valued others^{7}. However, thirdparty intervention in oneshot, anonymous scenarios^{1} aligns more with the strongreciprocity theory^{8}, where individuals may reward cooperation, punish noncooperation or more generally sanction violations of social norms^{9,10}, even without prospect of personal gain. These two lines of theories are not necessarily conflicting; the motives for sanctioning norm violations can be viewed as internalized external motivations. A widely observed norm in human societies is egalitarian distribution. By quantifying inequality—a violation of this norm—as a loss in a utility maximization framework, Fehr and Schmidt^{11} provide a unified explanation for various socioeconomic phenomena, including altruistic punishment and helping behaviors^{1,12,13}. Human representation of inequality is further supported by neuroimaging studies^{12,14,15}.
The power of this normative framework^{1} lies in its potential to integrate different motives into one utility measure to address the complexity of human altruistic behaviors. However, this potential is far from thoroughly explored, because most previous studies only focused on one or two motives (other than selfinterest, SI) and often contrasted models with distinctive motives^{13,16}, as if human behaviors were guided exclusively by one of the alternative motives at each moment. Such practice makes it difficult to unify the knowledge gained from different studies that examine different motives. Furthermore, it limits the power of the normative framework to explain intricate behavioral patterns.
For example, when a victim seeks revenge against the transgressor, a tradeoff between SI and inequality reduction would predict either no punishment or full punishment to restore equality, depending on whether the impact ratio of the punishment is below or above a certain threshold (Supplementary Fig. 1). However, people often choose to punish the transgressor without fully restoring equality^{1}, which some researchers explain by resorting to a separate personal tendency called ‘willingness to punish’^{12}, a factor not motivated by socioeconomic utilities. The hesitation of previous studies to simultaneously test multiple motives may be partly due to limitations in their experimental designs^{17}, where different motives often yield similar predictions^{18}, making them empirically indistinguishable. However, practices from relatively developed modelingreliant fields such as human decisionmaking^{19} and working memory^{20,21} suggest that including multiple motives in one model and empirically teasing them apart are both plausible and valuable for advancing our understanding of human altruistic behaviors.
In this Article we aimed to extend the normative framework of utility maximization to provide a unified explanation for a wider range of phenomena in altruistic behaviors. We constructed a series of computational models assuming that altruistic behaviors are driven jointly by multiple socioeconomic motives. These ‘motive cocktail’ models cover a comprehensive set of socioeconomic motives. Five of the motives are based on established theories from the literature, including two variants of selfcentered inequality (SCI)^{1,13}, victimcentered inequality (VCI)^{13}, efficiency concern (EC)^{14,22} and reversal preference (RP)^{23,24}. While some of the established socioeconomic motives are qualitatively similar, they lead to different quantitative patterns and can thus be distinguished through computational modeling. Furthermore, we also identified two new ‘compound’ motives that are nonlinear combinations of more elementary motives.
To separate the effects of different socioeconomic motives, we need an experimental setup that can systematically vary all the motives in the same context. We thus designed a thirdparty intervention task—the interveneorwatch task (Fig. 1a,b), which enables an unusually rich set of experimental conditions for testing this variety of motives that would otherwise be indistinguishable. In each trial (Fig. 1c,d), participants saw the outcomes from a dictator game, where the dictator (‘transgressor’) allocated more to themselves than to the receiver (‘victim’, for example, 88 versus 12 tokens). As the unaffected third party, participants received 50 tokens in each trial and were offered an opportunity to intervene, such as spending 10 tokens (intervention cost) to reduce the transgressor’s payoff by 15 tokens (impact ratio = 15/10 = 1.5). Participants decided whether to accept this intervention offer or to keep all 50 tokens to themselves. Each participant completed 300 trials in 100 different conditions that varied in the transgressor–victim inequality as well as the scenario (punishment versus helping), the cost and the impacttocost ratio of the intervention offer.
We performed one laboratory experiment (N = 157) and a preregistered online experiment (N = 1,258), with all major findings of the former replicated in the latter. A threeway interaction of inequality × cost × impact ratio found in participants’ intervention decisions suggests utility calculations that go beyond linear combinations of different motives. Indeed, participants’ behavioral patterns were best fit by a motive cocktail model whose utility calculation involves seven socioeconomic motives, including two compound motives. We called the compound motives ‘inequality discounting’ (ID), which refers to people’s tendency to behave as if they are underestimating the inequality between others as the intervention cost increases. Individuals’ cocktail motives fall into three groups: ‘justice warriors’, who have a strong intention to intervene whenever there is inequality, ‘pragmatic helpers’, who are sensitive to the impact of their intervention to help the victim, and ‘rational moralists’, who seek to achieve an acceptable standard of morality at the lowest cost to SI. Our model provides a unified explanation for phenomena beyond 3PP and 3PH, such as why interveners spend more to penalize transgressors when they themselves are victims rather than unaffected third parties^{1,12}.
Results
Each trial was either in a punishment scenario (as in the example above, Fig. 1a,c) or in a helping scenario (to increase the victim’s payoff, Fig. 1b,d). The inequality between the transgressor and the victim (50:50, 60:40, 70:30, 80:20 or 90:10, with ±2 jitters), the intervention cost (10, 20, 30, 40 or 50) and the impact ratio (1.5 or 3.0) were also varied across trials. Each participant completed 300 trials (5 inequality levels × 5 cost levels × 2 impact ratios × 2 scenarios × 3 repetitions) of intervention decisions.
Behavioral patterns in 3PP and 3PH
In experiment 1, there were 157 participants (all students). We first performed a generalized linear mixed model analysis (GLMM1, see Supplementary Table 1) on participants’ decisions (to intervene or not) to assess the effects of each independent variable and their interactions. We found intriguing interaction effects as well as classic 3PP and 3PH behavioral effects.
Preference for helping over punishment
Consistent with most previous studies, participants had a higher probability to help the victim (M = 0.25) than to punish the transgressor (M = 0.18, b of scenario = –1.22, 95% confidence interval (CI) [–1.64, –0.80], P < 0.001; Fig. 1e).
Inequality aversion and rationality
As we would expect from inequality aversion, participants were more willing to intervene when the transgressor–victim inequality was more extreme (b (regression coefficient) = 1.61, 95% CI [1.40, 1.81], P < 0.001; Fig. 1f) and when the impacttocost ratio was higher, that is, when the same cost yielded a greater reduction in inequality (b = 0.82, 95% CI [0.62, 1.01], P < 0.001; Fig. 1g). Meanwhile, participants were also rational decisionmakers who cared about their own interests, being less willing to intervene under a higher cost of intervention (b = –2.12, 95% CI [–2.37, –1.86], P < 0.001; Fig. 1h).
Interaction effects
Thanks to our factorial experimental design with four dimensions and 100 conditions, we also identified three twoway and one threeway interaction effects that had been seldom documented before. Under a higher impacttocost ratio, the preference for helping over punishment was stronger (scenario × ratio interaction: b = –0.39, 95% CI [–0.47, –0.30], P < 0.001; Fig. 1j), and the probability of intervention changed more markedly with the transgressor–victim inequality (inequality × ratio interaction: b = –0.08, 95% CI [–0.14, –0.02], P = 0.017; Fig. 1k) and with cost (cost × ratio interaction: b = –0.08, 95% CI [–0.14, –0.02], P = 0.015; Fig. 1l). According to the threeway interaction of inequality × cost × ratio (b = –0.21, 95% CI [–0.27, –0.15], P < 0.001), a higher ratio also led to a stronger modulation of the intervention cost with participants’ sensitivity to inequality (Fig. 1i).
Seven socioeconomic motives and their hypothetical effects
What socioeconomic motives may have driven the observed 3PP and 3PH behaviors? Besides SI (the core of classical economic models), we considered five classes of computationally welldefined socioeconomic motives (Fig. 2a), which expand into seven motive terms in utility calculation (see Supplementary Table 2 and 3 for examples in fictitious characters and reallife scenarios). Five of these motives are adapted from the literature, including three variants of inequality aversion^{1,13}, EC^{14,16} and RP^{23,24}. The remaining two motives, under the class of ID, are defined here to capture the interaction between SI and inequality aversion. They are partly motivated by the observed interaction effect that under higher intervention cost the participants’ probability of intervention not only was lower, but also increased more slowly with the transgressor–victim inequality (Fig. 1i). As unfolded below, each motive affects the utility gain from intervention relative to nonintervention (thus the tendency to intervene) in a different way (Fig. 2b).
SCI refers to the payoff difference between self and others^{1}. It can be further divided into disadvantageous inequality (self < other) and advantageous inequality (self > other), controlled by parameters α and β respectively. The parameter α implies stronger aversion to receiving lower payoff than others (for instance, self 50 versus transgressor 88), while β implies a stronger aversion to receiving higher payoff than others (self 50 versus victim 12). Before intervention, participants had lower payoff than the transgressor but higher payoff than the victim. As the result, higher α motivates penalizing the transgressor to reduce disadvantageous inequality, but discourages helping the victim as it increases disadvantageous inequality with the transgressor and may create disadvantageous inequality with the victim (Fig. 2b, row 1 left pair). In contrast, higher β motivates intervention in both the punishment and helping scenarios, unless greater punishment leads to an undesirable advantageous inequality over the transgressor (Fig. 2b, row 2 left pair).
VCI refers to the payoff difference between the transgressor and the victim^{13}. This inequality aversion variant implies that participants dislike the higher payoff of the transgressor over the victim. Participants with larger γ intervene more in most punishment and helping scenarios (Fig. 2b, row 3 left pair), unless the victimcentered disadvantageous inequality is too small (for instance, transgressor 51 versus victim 49) to compensate for intervention costs.
EC, a motive used frequently for modeling economic games^{14,16} but seldom for 3PP or 3PH, assumes that people care about others’ overall welfare, such as the sum of the transgressor’s and the victim’s payoffs in our case. Participants with larger ω are more likely to help the victim to increase the overall welfare, but less likely to penalize the transgressor to avoid reducing the overall welfare, regardless of the inequality between others (Fig. 2b, row 4 left pair).
RP refers to the motive that participants intend to reverse the payoff difference between the transgressor and the victim, rewarded by their payoff difference in the opposite direction (that is, after intervention the victim would be better off than the transgressor). The parameter κ controlling RP can be positive or negative, implying willingness or reluctance to reverse others’ economic status, making the term a generalized form of rank reversal aversion^{23,24}. Individuals with more positive κ are more willing to punish or help when the impact (cost × ratio) is large enough (relative to the inequality) to yield a rank reversal between the transgressor and the victim (Fig. 2b, row 1 right pair).
ID refers to people’s tendency to behave as if they are underestimating the inequality between others as the intervention cost increases. We defined two types of ID motive: inaction ID (controlled by η_{no}) and action ID (controlled by η_{yes}), representing diminished awareness of inequality when choosing not to intervene and when opting to intervene, respectively. ID motives are compounds that are not just the lack of motivation to reduce inequality as characterized by smaller γ (VCI), but capture the modulation of SI on VCI in both directions. Participants are less likely to intervene when they have larger η_{no}, which differs from smaller γ in that it may cause no intervention even when transgressor–victim inequality is high (Fig. 2b, row 2 right pair). Conversely, participants with larger η_{yes} are more likely to intervene, as if they believe inequality is always minimized following a costly intervention (Fig. 2b, row 3 right pair).
Many of these motives would remain unidentifiable in a task involving only two parties, testing exclusively either punishment or helping scenarios, or lacking variation in cost or impact ratio. However, in our interveneorwatch task, the seven motives forecast unique effects on intervention decisions, thus making them distinguishable in behavioral data. Subsequent modeling analysis validated each parameter’s discernibility, even under simultaneous modeling (Methods and Supplementary Fig. 2).
The motive cocktail model best predicts human behaviors
We assessed the seven socioeconomic motives’ contribution to altruistic behavior by incrementally incorporating them into utility calculations, creating a series of increasingly complex computational models. The introduction of different motives follows a descending order depending on how central and established a specific motive is in the literature of 3PP and 3PH. We then compared these models’ predictive power for the behavioral patterns observed in experiment 1. This solutionoriented approach is similar to the idea of ‘quasicomprehensive exploration’ introduced by a recent study on spatial working memory^{20}. Starting from a baseline coinflipping model, which intervened at a fixed probability, and an SI model, we introduced five motive classes as utility terms in the following order: SCI, VCI, EC, RP and ID. This process yielded seven different models (Methods) with different predictions (Fig. 3). We used maximumlikelihood estimation to fit each model to individual participants’ decisions, and the corrected Akaike information criterion (AICc)^{25} to evaluate each model’s relative goodness of fit, accounting for complexity. We also computed the protected exceedance probability (PEP)^{26} to provide a grouplevel measure that a model outperforms others.
The full motive cocktail model that includes all the motives best predicted participants’ decisions (lowest AICc, PEP > 99.99% among the seven models). A model recovery analysis (Methods) further confirmed that the best performance of the full model was real and could not be attributed to model misidentification: among the 700 synthetic datasets generated by the six alternative models, none was misidentified as the full model (Fig. 3a). Integrating each motive class (SI, SCI, VCI, EC, RP and ID) into our models led to considerable improvements in their fits (as indicated by lower AICc values in Fig. 3b).
The full model closely mirrored changes in participants’ intervention probabilities across the 100 experimental conditions (Fig. 3c), successfully predicting the main and interaction effects of different variables (lines in Fig. 1e–l). In contrast, alternative models failed to replicate certain patterns within the data (Fig. 3d–i). A supplementary analysis that compared more model variants further demonstrated the necessity of the ID assumption (the interaction items) in the full model as well as the nonlinear modulation of SI on the VCI (Supplementary Fig. 3) in fitting the behavioral data. The ID term follows the form of a sigmoid function (Supplementary Fig. 4b), which has the desired mathematical property of ensuring that its value is between 0 and 1. To conclude, participants’ thirdparty intervention decisions were jointly driven by SI and the seven socioeconomic motives, including the two ID terms.
Justice warriors, pragmatic helpers and rational moralists
Our interveneorwatch task, with its 100 factorially designed conditions, yielded a multifaceted profile that captured not only the collective behavioral tendencies but also the nuanced 3PP and 3PH behaviors of individual participants. A clustering analysis of the behavioral patterns of the 157 participants revealed that they were best summarized by three distinct clusters (Methods and Fig. 4a,b). Among them, the justice warriors (35% of participants) had an overall high probability to intervene, especially when the transgressor–victim inequality was high and the cost was relatively low (Fig. 4j). The pragmatic helpers (18%) also had a high probability to intervene, but were insensitive to inequality or cost, and preferred helping over punishment (Fig. 4k). The rational moralists (47%) barely intervened unless their intervention cost was minimal (Fig. 4l). The full motive cocktail model accurately predicted not only the average behavior (Fig. 4i) but also the behavioral patterns specific to each individual cluster (Fig. 4j–l).
These marked individual differences were associated with different combinations of motive parameters (Fig. 4c–e). Kruskal–Wallis tests with Bonferroni correction revealed significant differences across the three clusters for three out of the seven motive parameters (Fig. 4f–h and Supplementary Fig. 5): action ID η_{yes} (H(2) = 22.18, P < 0.001, with H(2) denoting the Χ^{2} statistic with two degrees of freedom), RP κ (H(2) = 15.57, P < 0.001) and inaction ID η_{no} (H(2) = 9.71, P = 0.008). The highest values of η_{yes}, κ and η_{no} respectively occurred for justice warriors, pragmatic helpers and rational moralists. To unravel the relationship of these parameters with the observed individual differences, we carried out a series of correlation analyses between individuals’ parameter values and their sensitivities to different variables at the group level (multiple comparisons corrected for each parameter using false discovery rate; Supplementary Fig. 6), where a participant's sensitivity to a variable was defined as the normalized intervention probability difference after the corresponding variable was dichotomized. The observed behavioral differences across clusters coincide with the correlational effects of these parameters (Fig. 4m–r) and agreed with the insights we obtained through simulation (Fig. 2). For example, higher η_{yes} implies increased tendency to perceive one’s action as effective in reducing inequality, irrespective of the actual impact, when the intervention cost is high. Indeed, individuals with higher η_{yes} were less sensitive to the impact ratio. Justice warriors, those who had the highest η_{yes} among the three clusters, were least sensitive to the impact ratio (Fig. 4n).
Replication in a preregistered, large online experiment
To test whether our findings can be generalized to a large population with different cultural backgrounds, we performed a preregistered, largescale online experiment using the same experimental procedures, with 1,258 participants (all students, sample size predetermined on the basis of a modelbased power analysis, Supplementary Fig. 7) from over 60 countries (or regions, Supplementary Table 4). All major statistical and modeling findings of experiment 1 were replicated in experiment 2 (Fig. 5; see Supplementary Table 5 for the GLMM results).
As in experiment 1, the full motive cocktail model outperformed the other models and accurately captured the behavioral patterns in experiment 2 (Fig. 5a,b; see Supplementary Fig. 8 for model recovery analysis). The behavioral patterns of the 1,258 participants were best captured by six clusters (Supplementary Fig. 9), in which the first three clusters agreed with those in experiment 1—justice warriors (16.60%, Fig. 5c), pragmatic helpers (17.30%, Fig. 5d) and rational moralists (27.00%, Fig. 5e). As in experiment 1, each of these three clusters was best fit by the full motive cocktail model (or its derivatives; Supplementary Fig. 9b). The remaining three clusters of participants (39.10%, Fig. 5f–h) seemed to respond to one single stimulus dimension (for instance, always help but seldom punish) or even purely randomly; these choice behaviors were best described by a simpleresponse model that linearly combines different independent variables (Methods and Supplementary Fig. 9b). These choice patterns likely resulted from these participants’ less engaged participation (lower attention check accuracy than participants in the first three clusters: t(1,256) = –9.78, P < 0.001), which is more common in online settings, rather than representing realworld behavioral patterns.
Upon completion of the experiment, participants were asked to fill out personality questionnaires that assessed their prosocial inclinations in everyday life, including a social value orientation scale (SVO)^{27} to measure selfishness and the Interpersonal Reactivity Index^{28} for empathy concern. We computed the Pearson correlation coefficients (r) between each participant’s model parameters (from the motive cocktail model) and the participant’s personality measures (Supplementary Figs. 10 and 11). In both experiments 1 and 2, we found that stronger selfcentered disadvantageous inequality aversion (α) or inaction ID (η_{no}) was associated with more selfishness. When one of these two parameters was controlled, the correlation between η_{no} and selfishness (experiment 1, partial correlation coefficient ρ = –0.22, P = 0.006; experiment 2, ρ = –0.16, P < 0.001) was still significant, but the correlation between α and selfishness was significant only in experiment 2 (experiment 1, ρ = –0.11, P = 0.16; experiment 2, ρ = –0.12, P < 0.001). We also found that inaction ID (η_{no}) and action ID (η_{yes}) were associated with empathy in opposite directions. When one of these two parameters was controlled, the correlation between η_{no} and empathy was still significant in both experiments (experiment 1, ρ = –0.25, P = 0.002; experiment 2, ρ = –0.12, P < 0.001), but the correlation between η_{yes} and empathy was significant only in experiment 2 (experiment 1, ρ = 0.12, P = 0.13; experiment 2, ρ = 0.12, P < 0.001).
Before the main experiments, we recorded the amounts participants allocated to their receiver in a dictator game. Kruskal–Wallis tests revealed significant differences across the three clusters for both experiment 1 (H(2) = 14.56, P < 0.001) and experiment 2 (H(2) = 46.72, P < 0.001). In both experiments, rational moralists allocated least to their receiver (see Supplementary Fig. 12 for post hoc tests). We also found significant differences between the three clusters of participants in selfishness (Kruskal–Wallis tests: experiment 1, H(2) = 11.70, P = 0.003; experiment 2, H(2) = 74.02, P < 0.001) and empathy concern (experiment 1, H(2) = 4.21, P = 0.122; experiment 2, H(2) = 21.32, P < 0.001). According to the personality questionnaires, the rational moralists were the most selfish and the justice warriors had the highest empathy (see Supplementary Fig. 13 for post hoc tests), which echoes the highest inaction ID (η_{no}) in the former and highest action ID (η_{yes}) in the latter (Fig. 4f,h). We also report some exploratory analyses of cultural differences in Supplementary Section 5.
The motive cocktail quantitatively reproduces more phenomena
To demonstrate that this motive cocktail estimated in participants’ interveneorwatch decisions underlies human responses to inequality in general, we performed an outofsample prediction, using an adapted version of the motive cocktail to simulate behavioral patterns in published studies with different experimental settings^{1,12}. Indeed, we found that the motive cocktail model can predict the behavioral patterns in secondparty punishment (2PP) as well as 3PP and 3PH (Fig. 6).
One robust phenomenon is that interveners spend more to penalize transgressors when they themselves are victims rather than unaffected third parties (that is, 2PP > 3PP). This can be explained by the motive of deterrence^{7}, which is not in conflict with our utility maximization framework. We integrate this by assuming that deterrence motives lead to reduced EC (parameter ω) in secondparty situations. More broadly, ω may decrease with social distance^{29} and intent viciousness^{30}.
In our simulations, we model secondparty interveners as having all the motives of thirdparty interveners except EC (ω = 0, Methods). Using parameters estimated from experiment 1 participants, our model reproduces both the 2PP > 3PP phenomenon and the increase in punishment with increasing inequality observed in previous laboratory experiments^{1,12}. For both experiments, simulations with the justice warriors’ parameters best matched the data.
Stallen et al.^{12} used a scenario where the first party robs the second party. The inequality here was caused by the more vicious intentions of the transgressor, thus triggering stronger 3PP than the same level of inequality caused by a dictator allocator (Supplementary Fig. 14). For this case, we assume that even unaffected third parties have no EC, allowing our model to reproduce the less common 3PP > 3PH phenomenon they observed.
Discussion
While helping and punishment equally reduce VCI, they differ in their influences on SCI. Inequality aversion alone would predict a preference for punishment over helping, unless participants are more uncomfortable with their advantage over others than the reverse. However, participants in our experiments were more likely to help the victim than to punish the transgressor, a finding consistent with most studies^{5,31,32,33}. The motive cocktail model can naturally explain the preference for helping over punishment, because it includes EC as a utility term: that is, people also care about the overall payoff of the transgressor and the victim. With an additional assumption that the motive of EC is weakened when the participant is the victim or when the transgressor violates social norms in a more aggressive way such as robbing or stealing from the victim^{12,34}, it can also explain why people spend more resources for 2PP than for 3PP^{1,12} and why a reverse preference for punishment rather than helping is found in some studies^{12,34}, as our simulation shows (Fig. 6). Our model thus provides a unified account for 2PP, 3PP and 3PH behaviors.
One motive documented in previous studies, seemingly contradicting inequality aversion, is rank reversal aversion^{23,24}. Our motive cocktail model includes a generalized form of this motive and reveals that participants in our experiment prefer to reverse the initial inequality, giving the victim an advantage over the transgressor, similar to the outcome in Shakespeare’s The Merchant of Venice. This RP motive opposes rank reversal aversion, suggesting that the latter may apply only when the initial inequality is caused by luck^{23,24}, instead of by the intentional choice of the benefited party, as in our task and classic thirdparty intervention tasks^{1,12}.
In line with the joint functioning of multiple motives identified in our modeling analysis, we found a threeway interaction between cost, impact ratio and transgressor–victim inequality. Such an interaction was not reported in previous studies, probably because most studies used cost as a dependent rather than an independent variable, measuring the amount of money participants were willing to spend on the intervention, which would prevent such effects from being detected by usual statistical analysis. In contrast, the cost is manipulated by the experimenter in our task, resembling another type of realworld scenario where individuals are confronted with limited options when it comes to addressing others’ inequalities.
Beyond individual differences in attention to others’ inequality^{35}, we found that, even within the same individual, attention to others’ inequality is modulated by the personal cost of intervening. The two forms of ID—inaction ID and action ID—have distinct psychological implications. The former assumes that people act as if increasingly ignoring the victim’s inequality due to rising intervention costs, leading to reluctance to engage in potentially selfharming altruistic actions. Action ID assumes that people act as if ignoring the remaining inequality faced by the victim after their intervention, resulting in being willing to intervene even when it hardly improves equality. The coexistence of these two types of ID demonstrates motive diversity in altruistic behaviors across various social contexts. These findings have implications for addressing realworld social issues: reducing barriers and costs for reporting injustices can encourage public engagement against inequities, while emphasizing the resolution achieved by intervention can further encourage altruistic behavior.
In both the laboratory and the largescale online experiments, we identified three types of intervener: justice warriors, pragmatic helpers and rational moralists, differing in intervention probability, sensitivity to variables such as cost and inequality, and preference for helping over punishment. The observed behavioral clustering aligns with previous findings that most individuals possess some form of prosocial preference, with few being purely selfinterested^{36}. The motive parameters estimated from the motive cocktail model provide a multifacet measure of such individual differences, raising questions about how personal experiences, cultural background or genetic makeup may influence individuals’ motives.
In sum, the proposed motive cocktail model extends the economic modeling of altruistic behaviors, enabling us to understand the cognitive processes behind human altruistic behaviors, measure individual differences related to psychiatric disorders and developmental trajectories, and more precisely predict behavior, guiding social policymaking to foster prosocial behaviors on a societal scale. By elucidating the cognitive processes underlying prosocial behavior and identifying various motives and individual differences, our model can provide insights into psychiatric disorders characterized by social dysfunction and inform future research on the neural basis of human morality and its disorders^{37}. Our model and task framework can also be used to investigate the developmental trajectories of altruistic motives, guiding efforts to foster prosocial behaviors across life stages^{38}. By capturing the interplay of multiple motives and their impact on behavioral patterns, our model enables more precise predictions of prosocial behavior. Leveraging insights from the motive cocktail model, interventions can be designed to account for individuals’ diverse motivations, experiences and crosscultural backgrounds^{9}, aiming to create a more cohesive and prosocial community. Meanwhile, further research is needed to bridge the gap between our simplified laboratory task and realworld applications.
We used a oneshot anonymous interaction setting, a common practice in previous studies^{1,12,13,32,36,39,40,41,42,43}, to minimize participants’ concern for their own reputations, a motive that is instrumental to the longterm reciprocity in human society^{44}. Consequently, our motive cocktail model, which adequately explained our data, excluded reputation as a motive. However, in realworld scenarios with more interaction opportunities, reputation concern is likely to influence 3PP and 3PH behaviors^{3,6}. The victim’s reputation (for example, once a transgressor or not) also matters, with reputationbased expectancies emerging early in human development^{45}. Similarly, deterrence^{7}, reciprocity^{8} or social norms beyond egalitarian distribution^{10} are other realworld motives not examined in this Article. Integrating these motives into the motive cocktail model will be topics for future research. Whether the three types of intervener relate to the different cooperative types found in public goods games^{46}, thus connecting to a larger picture of human altruistic behaviors, also deserves future research.
Methods
Both experiments 1 (in laboratory) and 2 (online) had been approved by the Ethics Committee of Beijing Normal University (CNL_A_0001_009 and IRB_A_0003_2020001).
Experiment 1
Participants
Experiment 1 was conducted in a laboratory room at Beijing Normal University and 157 university students (59 males, mean age ± s.d. 21.24 ± 2.56) were recruited. No statistical methods were used to predetermine sample size. No participants were excluded from the subsequent analysis. Participants completed the screening form before the task to confirm that they had normal or correctedtonormal vision and no history of psychiatric or neurological illness. All participants provided informed consent. On average, participants were compensated with ¥80 (range ¥60–120).
Experimental procedure
Participants were selfpaced to read the instructions of the task. A quiz followed the completion of each subsection of the instruction. Participants proceeded to the next section of the instruction only if they gave the correct answer to the quiz. Before the formal task, participants underwent several practice trials to ensure that they fully understood the rules of the game. The interveneorwatch task (detailed below) lasted approximately 45 min. After completing the task, participants were asked whether they had any doubts or questions during the task in an openended question. In experiment 1, four participants reported doubts about whether all the players were real people. To examine whether participants who reported doubts used different strategies when compared with those who did not have doubts during the task, we conducted a GLMM similar to GLMM1 but added ‘doubt’ as an additional predictor (a categorical variable) in the model. We found that the predictor doubt could not predict participants’ choice (b = –2.74, 95% CI [–7.19, 2.24], P = 0.304), and concluded that participants who reported doubts did not employ different strategies in the task. Therefore, all participants were included in the following analysis. In the final section, participants were asked to fill out a few personality questionnaires (detailed below), including measures of SVO, the Machiavellianism Scale (MACH–IV) and the Interpersonal Reactivity Index, to assess their prosocial personalities.
The interveneorwatch task and experimental design
The interveneorwatch task was a paradigm adapted from the 3PP task^{1}. In the task, participants played the role of an unaffected third party who watched an anonymous dictator (transgressor) allocate amounts between himself/herself and an anonymous receiver (victim), and then decided whether to intervene. The stimuli were presented using the EPrime 2.0 software (Psychology Software Tools). In each trial, the transgressor allocated the 100 game tokens between himself/herself and the victim, while the victim had to accept the offer without any other options. Participants were told that all offers between a transgressor and a victim were made by other real participants, and that their decisions would affect their own payoffs as well as those of the victims and the transgressors. In reality, the offers between the transgressors and the victims were generated by a custom code and were designed to disentangle different hypotheses. To give the participants a more realistic experience and to familiarize them with the roles in the game, they were instructed to play two trials of the dictator game, in which they played the role of transgressor and victim respectively. In the interveneorwatch task, participants had 50 game tokens in each trial which could be used to reduce the payoff of the transgressor in the punishment scenario or increase the payoff of the victim in the helping scenario. To avoid serial or accumulative effects, participants were instructed that their payoff was independent across trials and would not be accumulated through the task. They were also informed that 10% of the trials would be randomly selected and implemented at the end of the study to determine the payoffs of all players (or roles). Specifically, participants’ actual payment was calculated by adding a base payment to the average remaining tokens from these randomly selected trials, with each token being exchanged for ¥1. Additionally, participants were explicitly informed that the roles of the transgressor and the victim were played by different participants in each trial, hence encouraging them to make decisions based solely on the current situation. We are aware that our experimental setting included deception, in the sense that participants’ intervention to the players in the dictator game was not really implemented. Nevertheless, all of the offers we used in the interveneorwatch task were ones that real human players might make in the dictator game^{47,48}. Such use of deception has been a common practice of previous studies^{12,32}. Furthermore, participants’ payoff was actually determined by the randomly selected 10% of their decisions, akin to a random lottery design^{49}, which did not involve deception.
Since all players in the task were anonymous, no reputation concern was involved in this task. The players also had no opportunities for interaction; thus, reciprocity could be excluded. Therefore, participants’ decisions to help and to punish in the interveneorwatch task were altruistic.
Each trial (Fig. 1c,d) began with a fixation cross (600–800 ms), followed by an inequality window (1,500 ms) displaying the allocation between the transgressor and the victim, and an intervention offer window (1,500 ms) showing the intervention cost for the participant and the consequence of the intervention (impact ratio × intervention cost) to the transgressor or victim. Subsequently, in the decision window, participants were asked whether they would like to accept the intervention offer: yes (to intervene) or no (not to intervene). The intervention would only be implemented if participants chose yes. For example, if the intervention offer window displays an intervention cost of x in a trial, a decision of intervention would result in the transgressor losing (or the victim gaining) 1.5x or 3.0x in the punishment (or helping) scenario. There was no time limit for the decision. A visual feedback window after the decision highlighted the selected choice in red. Four independent variables were varied across trials: scenario (punishment and helping), inequality (transgressor versus victim, 50:50, 60:40, 70:30, 80:20, 90:10, jitter ±2), cost (10, 20, 30, 40, 50) and impact ratio (1.5 and 3.0). This led to 100 unique conditions, with each condition repeated three times for each participant. The scenario variable varied between blocks and the other three variables were randomly interleaved within blocks. Before each block, participants were told whether the following section was the ‘increase’ condition (the helping scenario) or the ‘reduce’ condition (the punishment scenario). In total, each participant completed 300 trials in six blocks, with three blocks each for the punishment and helping scenarios. The main experiment of the interveneorwatch task lasted 30.86 ± 3.25 min for experiment 1 and 33.97 ± 7.59 min for experiment 2. The main experiment included six blocks, with each block lasting around 5 min, followed by a 30 s rest between blocks.
Personality questionnaires
Following the interveneorwatch task, participants completed several personality questionnaires that allowed us to access their prosocial tendencies in daily life. Specifically, SVO^{27} was used to measure individual preference about how to allocate financial resources between themselves and others. A higher score on the SVO scale reflects a greater degree of concern for others’ payoffs and, therefore, indicates a more prosocial personality. MACH–IV^{50} was used to assess an individual’s level of Machiavellianism, related to manipulative, exploitative, deceitful and distrustful attitudes. Higher scores on the MACH–IV scale are indicative of a more pronounced degree of Machiavellian traits. The Interpersonal Reactivity Index^{28} was used to measure the multidimensional assessment of empathy, including (1) perspectivetaking, assessing an individual’s tendency to consider a situation from another’s perspective; (2) fantasy, evaluating an individual’s inclination to identify with the situation and emotions of characters in books, movies or theatrical performances; (3) empathy concern, measuring an individual’s inclination to care about the feelings and needs of others; (4) personal distress, assessing an individual’s tendency to experience distress and discomfort in challenging social situations.
Modelfree analysis
Figures were generated using MATLAB R2020b (MathWorks) and R 4.2.1. All statistical analyses were conducted in R 4.2.1^{51} and MATLAB R2020b. GLMMs assuming binomial distributed responses were used to model the probability of intervention, given various predictors (for instance, scenario, inequality) and their interactions. The GLMMs were implemented using the lme4 (v.1.1.30) package^{52}, with the fixedeffect coefficients output from the binomial GLMM on the logit scale and the significance of each coefficient determined by the Z statistics. For significant main effects in GLMMs, twotailed paired ttests were used for pairwise comparisons for two adjacent conditions with Bonferroni correction. The standard linear mixedeffect models (LMMs), which assume that the error term is normally distributed, were estimated using the afex (v.1.2.1) package to model participants’ decision times. For the estimation of marginal effects and the post hoc analysis, the emmeans (v.1.8.0) package was used^{53}. Interaction contrasts were performed for significant interactions and, when higherorder interactions were not significant, pairwise or sequential contrasts were performed for significant main effects. The null hypothesis testing reported in the main text (Kruskal–Wallis test and paired ttest) and in the Supplementary Information (Mann–Whitney test) were implemented in MATLAB R2020b using the Statistics and Machine Learning Toolbox.
GLMM1: participants’ choices in all trials in experiment 1 are the dependent variable; fixed effects include an intercept, the main effects of the scenario, inequality, cost, ratio, trial number and all possible interaction effects of the independent variables; random effects include correlated random slopes of scenario, inequality, cost, ratio and trial number within participants and random intercept for participants. The scenario is a category variable. Trial number, inequality, cost and ratio are continuous variables that were normalized to Z score before model estimation. The inclusion of trial number controls for timerelated confounds, such as potential fatigue or practice effects. See Supplementary Table 1 for the statistical results of GLMM1.
GLMM2: participants’ choices in all trials in experiment 2 are the dependent variable. The fixed and random effects remain the same as for GLMM1. See Supplementary Table 5 for the statistical results of GLMM2. Both the main and interaction effects of the independent variables on intervention decisions of experiment 1 (as in Fig. 1e–l) were replicated in experiment 2 (Supplementary Fig. 15a–m).
LMM1: participants’ decision times for all trials in experiment 1 are the dependent variable. In addition to the fixed and random effects included in GLMM1, participants’ intervention decisions (choice) are added as well. See Supplementary Table 6 and Supplementary Fig. 16 for the statistical results of LMM1.
We found an inverted Ushaped relationship between the intervention probability (P(yes)) and decision time (Supplementary Fig. 16j), which implies that participants made decisions with more difficulty when the decision uncertainty (or entropy) was higher. This result is in line with previous research demonstrating an inverted Ushaped relationship between confidence levels and decision times^{54}.
LMM2: participants’ decision times for all trials in experiment 2 are the dependent variable. The fixed and random effects remain the same as for LMM1. See Supplementary Table 7 for the statistical results of LMM2. The inverted Ushaped relationship between the probability of intervention (P(yes)) and decision time was replicated in experiment 2 (Supplementary Fig. 17).
Sensitivity analysis to different variables
We measured participants’ intervention sensitivity to different variables, which was defined as the normalized intervention probability difference after the corresponding variable was dichotomized (Fig. 4n–r and Supplementary Fig. 18). Specifically, participants’ sensitivity to the main effects, including scenario, ratio, cost and inequality, was calculated as the intervention probability difference in the helping trials when compared with the punishment trials, the highimpactratio trials (3.0) compared with the lowimpactratio trials (1.5), the lowcost trials (cost ≤ 20) compared with highcost trials (cost > 20) and the highinequality trials (that is, the inequality level between the transgressor and the victim is 80:20 and 90:10) compared with the lowinequality trials (70:30, 60:40 and 50:50), divided by their overall P(yes), respectively. For the interaction effects, the sensitivity (that is, the normalized intervention probability difference) was calculated in a similar way as the main effect, that is, marginalizing over the other variables.
Behavioral modeling
We assumed that participants would make decisions on each trial by calculating the utility of the two options (yes and no) and choosing the option with the higher utility. In the interveneorwatch task, participants were given the context regarding inequality between a transgressor and a victim as well as other related variables (for instance, cost, impact ratio) from the perspective of a third party and afterwards made a decision between two alternatives, yes (to intervene) and no (not to intervene). In general, participants calculated the utilities of the choices by estimating the reduction in inequality for others through their intervention and considering the associated cost to themselves. Specifically, if they chose ‘yes’ (decide to intervene), they could reduce the inequality between the transgressor and the victim to some extent but at a cost. In contrast, by choosing ‘no’ (decide not to intervene), they could retain the inequality between the transgressor and the victim without incurring any cost. To investigate how individuals make decisions in the interveneorwatch task, we constructed a series of computational models with different utility calculation hypotheses (that is, combinations of multiple socioeconomic motives) and compared their goodnesses of fit.
Participants’ choices were then modeled using the Softmax function^{55}, with the utilities of no intervention (U_{no}) and intervention (U_{yes}) from different models as the inputs:
where the inverse temperature, parameter λ ∈ [0, 10], controls the stochasticity of participants’ choices, with a larger λ corresponding to less noisy choices.
In the following descriptions, we will use x_{1}, x_{2} and x_{3} to denote the payoffs of the transgressor, the victim and the third party (participant) if the third party does not intervene (chooses ‘no’), and use x_{1}′, x_{2}′ and x_{3}′ to denote the counterpart payoffs if the third party intervenes (chooses ‘yes’). In particular, x_{3}′ is equal to x_{3} − cost in both scenarios. In the punishment scenario x_{1}′ = x_{1} − impact ratio × cost and x_{2}′ = x_{2}, while in the helping scenario x_{1}′ = x_{1} and x_{2}′ = x_{2} + impact ratio × cost.
Model 1. The baseline model
We modeled each participant’s choices of intervention in each trial (whether to choose the yes option) as outcomes from a Bernoulli distribution, where the intervention probability is controlled by a parameter q ∈ [0, 1]. For each participant, the probabilities of choosing the intervention (P(yes)) and not choosing the intervention (P(no)) are denoted as follows:
Model 2. Selfinterest model (SI)
The models based on socioeconomic motives started with SI, where participants only consider SI when making decisions, thus always leading to a reduced utility of the intervention. Participants’ choices were then modeled using the Softmax function (equation 1).
where x_{3} denotes the payoff of the third party when choosing no (without intervention), which is always 50 tokens in each trial. x_{3}′ denotes the payoff of the third party after choosing yes (with intervention), which is equal to 50 − cost.
Building upon the SI model, the following hypothetical socioeconomic components were progressively introduced into the utility calculation and participants’ choices were modeled using the Softmax function. The necessity of each component to explain participants’ decisions was determined through model comparisons.
Model 3. SI and selfcentered inequality aversion aversion model (SI + SCI)
On the basis of the SI model, we added a selfcentered inequality aversion (SCI) aversion component, which assumes that participants are averse to the inequality between themselves and others in both directions^{11}. The selfcentered disadvantageous Inequality aversion denotes that participants are averse to others having more payoffs than themselves, while the selfcentered advantageous Inequality aversion denotes that participants are averse to themselves having more payoffs than others. The contributions of selfcentered disadvantageous and advantageous inequality^{11} are controlled separately by the parameters α (α ∈ [0, 10]) and β (β ∈ [0, 10]) and are subtracted from the SI. Under the assumption of the SI + SCI model, participants are motivated to maximize their SI and meanwhile minimize the inequality between themselves and others, and then make a choice between no intervention and intervention on the basis of their respective utilities:
where j denotes the index of the transgressor and victim; x_{1} and x_{2} represent the payoffs of the transgressor and the victim when the participant (third party) chooses no; x_{1}′ and x_{2}′ represent the payoffs of the transgressor and the victim after the intervention of the third party.
Model 4. SI + SCI and victimcentered disadvantageous inequality aversion model (SI + SCI + VCI)
On the basis of the SI + SCI model, we introduced another previously proposed inequality component, the victimcentered disadvantageous inequality aversion (VCI). The VCI assumes that participants are averse to the transgressor having more payoff than the victim^{13}, with its contribution to the utility calculation determined by a parameter γ (γ ∈ [0, 10]). Participants with larger γ will be more willing to intervene in almost all punishment and helping scenarios. Within this model, participants were motivated to maximize SI and simultaneously minimize the two kinds of inequality aversion (SCI and VCI):
Model 5. SI + SCI + VCI and efficiency concern model (SI + SCI + VCI + EC)
On the basis of the SI + SCI + VCI model, an efficiency concern (EC)^{16} component was added to the model. EC assumes that participants are motivated to maximize the total payoff of others, which is weighted by parameter ω (ω ∈ [0, 10]). Participants with larger ω will be more likely to intervene in the helping scenario, but not in the punishment scenario:
Model 6. SI + SCI + VCI + EC and reversal preference for victimcentered advantageous inequality model (SI + SCI + VCI + EC + RP)
On the basis of the SI + SCI + VCI + EC model, we introduced another component, the reversal preference for victimcentered advantageous inequality (RP), into the model. RP is mutually exclusive to VCI and assumes that participants prefer to reverse the economic status of the victim. That is, RP motivates participants to make the victim have more payoff than the transgressor by punishing the transgressor or helping the victim. The reversal preference is controlled by the parameter κ (κ ∈ [−10, 10]). A positive value of κ indicates that participants are in favor of the victim having more money than the transgressor, while a negative value indicates that they are averse to such reverse inequality. Participants with larger κ will be more likely to intervene when the initial victimcentered disadvantageous inequality is small enough or the impact is large enough to guarantee an inequality reversal:
Model 7. SI + SCI + VCI + EC + RP and inequality discounting model (the motive cocktail model, SI + SCI + VCI + EC + RP + ID)
On the basis of the SI + SCI + VCI + EC + RP model, we also included the inequality discounting (ID) component that we proposed. Thus, the motive cocktail model includes seven socioeconomic motives. ID is derived from the rational framework of economic decisions and is implemented to capture the interaction between SI and VCI. Specifically, ID assumes that people will systematically disregard the victimcentered disadvantageous inequality as costs increase. We proposed two types of ID: inaction ID (controlled by parameter η_{no}) and action ID (controlled by η_{yes}), which are respectively blind to the initial and residual disadvantageous inequalities between the transgressor and the victim under no intervention and intervention with rising costs, respectively. In the model fitting, the range of parameters η_{no} and η_{yes} is restricted to between 0 and 20.
Participants with larger η_{no} would have a lower probability of intervening. The effect differs from victimcentered disadvantageous inequality aversion (small γ) in that at large η_{no} the tendency to intervene would barely increase with inequality. Conversely, participants with larger η_{yes}, who subjectively exaggerate the reduction of inequality by intervention, would have a higher probability of intervening. Those with large η_{yes} will have similarly high probability of intervening regardless of the impact ratio, as if they optimistically believe that the inequality would be minimized by any of their interventions:
Redundancy checks on the parameter space
In the estimated parameters, we observed three highly correlated pairs in the parameter space of the motive cocktail model: the values of parameter β (selfcentered advantageous inequality aversion) and γ (victimcentered disadvantageous inequality aversion), α (selfcentered disadvantageous inequality aversion) and ω (efficiency concern), γ and η_{no} (inequality inaction inattention). To exclude the possibility that the correlation was due to parameter redundancy in the model, we performed redundancy checks as follows. We first randomly shuffled participants’ labels for different parameters to eliminate correlations in the shuffled parameters. On the basis of these shuffled parameters, we generated 157 synthetic datasets and used them to estimate the model parameters. We found little correlation between the parameters estimated from these synthetic datasets, which indicates that the high correlations found in the data reflect the behavioral characteristics of human participants rather than redundancy in the model itself (Supplementary Fig. 19).
Model fitting and model comparison
The behavioral modeling was implemented in MATLAB R2020b using custom codes. For each participant, we fit each model to their intervention decisions across all trials using maximumlikelihood estimates. The likelihood function derived from the binomial distribution was used to describe the relationship between participants’ choice and the model’s prediction. The function fmincon in MATLAB was used to search for the parameters that minimized negative loglikelihood. To increase the probability of finding the global minimum, we repeated the search process 500 times with different starting points. We compared the goodness of fit of each model on the basis of two metrics: the Akaike information criterion with a correction for sample size (AICc)^{25} and the PEP of grouplevel Bayesian model selection^{26}. The spm_BMS function of the SPM12 toolbox was used to perform the grouplevel Bayesian model selection. We chose to use the AICc as the metric of goodness of fit for model comparison for the following statistical reasons. First, the Bayesian information criterion is derived on the basis of the assumption that the ‘true model’ must be one of the models in the limited model set compared^{56,57}, which is unrealistic in our case. In contrast, AIC does not rely on this unrealistic true model assumption and instead selects out the model that has the highest predictive power in the model set^{58}. Second, AIC is also more robust than the Bayesian information criterion for finite sample size^{59}.
Model identifiability and parameter recovery analyses
We further performed a model identifiability analysis to rule out the possibility of model misidentification in model comparisons. For each model, the parameters estimated from the data of all participants were used to generate a synthetic dataset of 157 participants. Each synthetic dataset regarding a specific model was then used to fit each of the seven alternative models and identify the bestfitting model by model comparison. We repeated the above procedure 100 times to calculate the percentage at which each model was identified as the best model on the basis of all synthetic datasets from a specific generating model. The highest percentage assigned to the same fitting model as the generating model suggests that the model is identifiable. To assess parameter recovery in the motive cocktail model (model 7: SI + SCI + VCI + EC + RP + ID), we computed the Pearson correlation between the parameters estimated from the 100 synthetic datasets (recovered parameters) and the parameters used to generate the synthetic datasets. A larger correlation coefficient between the recovered parameter and the estimated parameter indicates a nonredundancy in parameter space.
Clustering analysis
To gain further insight into whether the motive cocktail model (model 7: SI + SCI + VCI + EC + RP + ID) could explain the varying behavioral patterns of individuals, we classified participants’ intervention decisions using kmeans clustering and then investigated the distributions of the estimated parameters across participants as well their unique contributions to behavioral patterns within each cluster. kmeans clustering is an unsupervised machine learning algorithm relying on the Euclidean distance to classify each participant into a specific cluster with the nearest mean^{60}. The clustering evaluation criterion was based on silhouette value, which denotes how well each participant was matched to its own cluster when compared with other clusters, with a higher silhouette value indicating that the clustering solution is more appropriate^{61}. The optimal cluster solution for 157 participants in experiment 1 is 3 (Fig. 4b).
Correlation analysis for parameters and personality measures
To further validate the psychological basis of the hypothetical socioeconomic motives in the motive cocktail model, we calculated the Pearson correlation between the estimated parameters and the scores on the personality measurements. A similar correlation analysis between individuals’ motive parameters and their sensitivity to different variables was carried out to unravel the contributions of the parameters to behavioral differences. Partial correlation was conducted when multiple parameters correlated with the same measurement to ensure that the observed relationships were not confounded by the potential influence of other variables. ρ, ranging between –1 and 1, quantifies the strength and direction of linear links between parameters and measured variables. For multiple comparisons, the false discovery rate was employed.
Simulations to quantitatively reproduce previous phenomena
We made slight modifications to the motive cocktail model and applied it to explain the intervention patterns in 2PP, 3PP and 3PH models in the following two studies. The adapted model could also be used to explain a broader range of phenomena in previous studies.
In a substudy conducted by Fehr and Fischbacher^{1}, participants attended a dictator game, which contains both 2PP condition and 3PP condition. At the beginning of the experiments, participants were randomly assigned either the role of the transgressor (player A) or the victim (player B). In the 2PP condition, the victim also acted as an intervener, who could punish the transgressor after observing the transfer from the transgressor accordingly. In the 3PP condition, the victim could only punish the dictator in another group (player A′ and player B′), in which he/she served as an unaffected third party. A strategy method was implemented in the 3PP condition: the third party (player B) had to indicate how much she/he would punish the outgroup player A′ for every possible transfer of A′ to player B′. The results showed that the intervener as the victim exerted more punishment than the intervener as the third party for all transfer levels below 50 (2PP > 3PP), while the punishment was generally low and similar across transfer levels above 50 (Fig. 6a top left). In the study conducted by Stallen et al.^{12}, participants played three conditions of a justice game. In the 2PP games, the participants played the role of the partner (the victim), in which the taker (the transgressor) had the opportunity to take or steal chips (or payoff) from the victim, and afterward the victim was given the option of punishing the transgressor by spending chips of their own. In 3PP and 3PH games, participants played the role of an observer (the third party) to watch whether the transgressor stole chips from the victim and then decided whether to intervene to punish the transgressor or to compensate the victim, at their own cost. Every time participants needed to make a choice, all intervention costs ranging from 0 to 100 with a step of 10 were displayed on the screen. The results indicated that the intervener in the 2PP condition punished the transgressor more than in the 3PP condition (2PP > 3PP). In addition, the third party was more likely to punish than to compensate (3PP > 3PH, Fig. 6b top left).
For both studies, we simulated participants’ choices by calculating the utility of selecting yes and no for each inequality level using equations (14)–(17). We assume that a secondparty intervener, who is also the victim, is less concerned about overall welfare than is the third party. As the result, the secondparty intervener has all the motives a thirdparty intervener would have except for EC. To implement this assumption, we replaced x_{3} in equations (14)–(17) with x_{2}, and set the EC ω to 0 in the 2PP condition. The same lackofefficiencyconcern assumption (ω = 0) was implemented during the simulation of thirdparty punishment and compensation games in ref. ^{12}. That is, we assume that the unaffected third party would ignore others’ welfare in a robbery situation.
Experiment 2
To further verify our findings and model specifications, we conducted experiment 2 using the same experimental paradigm as experiment 1 on an online participant platform (Prolific, https://www.prolific.co/) by recruiting a larger population with diverse cultural backgrounds.
Preregistration
Experiment 2 was preregistered on OSF (https://osf.io/gcsqp) on 29 September 2022. All methods and analyses followed the design and analysis plan in the preregistration, except that two additional models were tested: a model with lapse rate parameters and a simpleresponse model. This was due to more behavioral patterns being observed from the online experiment. Building on the results of the modelfree analysis in experiment 1, we hypothesized that the main effect of inequality, intervention cost, impact ratio and the interaction of inequality × cost × ratio would be statistically significant, and that participants’ intervention decisions would follow the patterns we observed in experiment 1. For the modelbased analysis, we hypothesized that participants’ decisions would be best described by the full motive cocktail model.
Participants
The criteria for participant recruitment were matched between experiments 2 and 1, including the age ranges (18–30 years old), student status and the degree of education. In addition, the study was only accessible to participants with an approval rate of over 90% in Prolific. We received 1,365 participants’ submissions overall. One hundred and seven of them had an accuracy rate below 75% on the attention check task (see details below) and thus were rejected for further analysis. The final valid samples were 1,258 (621 male, 631 female, 6 genders unknown, aged 23.30 ± 2.89). No participants met the exclusion criterion of average decision time exceeding 2.5 s.d. from the mean decision time of all participants. All participants provided informed consent before the task to confirm that they took part in the study voluntarily, had normal or correctedtonormal vision, and did not have a history of psychiatric or neurological illness. On average, participants were compensated with £9 (range £7–12).
Determination of sample size
The sample size for experiment 2 was predetermined using a parametric simulation method^{62}, derived from the motive cocktail model (the bestfitting model in experiment 1). The effect we focused on is the threeway interaction of inequality × cost × ratio (Fig. 1i). As compensation for the higher randomness of online participants’ decisions, we added another two parameters, P_{min} and P_{max} (lapse rates), in the motive cocktail model to capture participants’ minimal and maximal (1 − P_{max}) intervention probabilities. An online pilot study based on 32 participants showed that the motive cocktail model with lapse rates (see model 8 for more details) fit participants’ behavior better. We therefore used model 8 to generate synthetic datasets to determine the sample size for experiment 2. Parameters α, β, γ, ω, η_{no}, η_{yes}, λ were sampled from the gamma distribution, κ was sampled from the normal distribution and P_{min} and P_{max} were sampled from the beta distribution. The generated intervention decisions of virtual participants were then exported to GLMM1 to obtain the effect size for each variable and their interactions. The power was defined as the percentage at which the threeway interaction effect reaches significance over a specific sample size. We tested different sample sizes ranging from 100 to 1,500 virtual participants, with increments of 100. Within each sample size, we repeated the synthetic data generation and power calculation procedure 500 times. The power of the threeway interaction effect increased monotonically with sample size and achieved a power of 80% with at least 1,200 participants (Supplementary Fig. 7). Our final valid sample size was 1,258 participants from 66 countries (Supplementary Table 4).
Experimental procedure
The procedure of experiment 2 was the same as that of experiment 1, except that it was conducted on the Prolific platform, with the experimental paradigm coded using PsychoPy (v.2021.1.3) and PsychoJS (v.2021.1.3). Participants were informed that their base payment was £7 per hour, and 10% of trials would be randomly selected to determine their bonus after the experiment. The game tokens accumulated from these randomly selected trials would be exchanged for pennies at a 5:1 exchange rate. After the task, participants were asked “Did you think the experimenter had deceived you in any way at any point during the experiment?”, with a binary choice of yes or no. Seventyfour participants answered yes, while the remaining 1,184 participants answered no. To investigate whether participants who had doubts (answered yes) employed different strategies when compared with those who did not have doubts (answered no) during the task, we conducted a GLMM (like GLMM2) and included doubt as a predictor (categorical variable) in the model. We found that the effect of doubt (b = 0.15, 95% CI [–0.09, 0.41], P = 0.221) was not statistically significant to predict participants’ choices, suggesting that participants who reported doubts did not employ different strategies in the task. Therefore, all participants were included in the subsequent analysis.
Attention check
We used the same interveneorwatch task in experiment 2 and included several attention checks during the task to ensure that participants remained constantly attentive to the current task. The attention checks consisted of 12 questions, with two questions interspersed in each block. For each block, the questions appeared randomly without telling the participants, and participants were asked to answer the questions with binary options about their last decision. Specifically, the questions were either “In the last trial, your decision was: yes/no?” or “The last trial was in the increase/reduce scenario?” in each block. Those (107 participants) who gave less than 75% accuracy in the attention checks (incorrect answers on more than three questions) were excluded from further analyses.
Modelfree analysis
All 1,258 participants in experiment 2 were included in the modelfree analysis (Supplementary Table 5). Among them, 492 (39.10%) out of 1,258 participants were best described by a simpleresponse model and were therefore excluded from the analyses in relation to the motive cocktail model. Specifically, only the remaining 60.90% of participants whose intervention patterns could be categorized as justice warriors, pragmatic helpers and rational moralists were included in the following analyses: data versus model prediction (Fig. 5), Kruskal–Wallis tests on the parameters η_{yes}, κ, η_{no} (Supplementary Fig. 5), correlations between the parameters estimated from the motive cocktail model and the intervention sensitivities (Supplementary Fig. 18) as well as the personality measurements (Supplementary Fig. 11).
Behavioral modeling
Model space
We constructed two additional models (models 8 and 9) in experiment 2 to capture the behavioral patterns that online participants would make random choices in a certain amount of trials. Model 8 was constructed on the basis of the motive cocktail model. Model 9 is a simpleresponse model to capture the behavioral patterns of a proportion of participants in the online experiment 2 (39.10%) who only responded to some of the manipulated variables and seemed to entirely ignore the others.
Model 8. The motive cocktail model with two lapse rate parameters
The model assumes that participants make an intervention decision by considering both SI and all socioeconomic motives assumed in the motive cocktail model. However, participants’ minimal and maximal intervention probabilities are bounded by two free parameters. Specifically, participants are willing to randomly intervene with a probability of P_{min} (P_{min} ∈ [0, 0.5]). Meanwhile, they constrain their maximum intervention probability below 1 − P_{max} (P_{max} ∈ [0, 0.5]). The utility calculations and choice mapping remain the same as equations (14)–(17) and equation 1, respectively.
where P(yes) represents the choice probability based on the motive cocktail model.
Model 9. Simpleresponse model
Some of these online participants were sensitive to only a few of the manipulated variables and seemed to use simpleresponse rules for responses. Thus, we also included a simpleresponse model that linearly combines different manipulated variables (scenario, inequality, cost and ratio) to describe participants’ behavior:
Reporting summary
Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.
Data availability
Source data for Figs. 1–6 and most Supplementary Figures and Tables as well as all the raw data produced in this study are available at https://doi.org/10.17605/OSF.IO/6G293 ref. ^{63}.
Code availability
All codes from this study are available at https://doi.org/10.17605/OSF.IO/6G293 ref. ^{63}.
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Acknowledgements
We thank E. Fehr, C. C. Ruff, F. Cushman and J. Gross for discussions, G. Chen for helping to program experiment 2 and H. Lu for statistical and visualization consultation. This study was partly supported by the Scientific and Technological Innovation (STl) 2030—Major Projects 2021ZD020050 (to C.L.), the National Natural Science Foundation of China (32171095 to H.Z., and 32271092, 32130045 to C.L.), funding from Peking–Tsinghua Center for Life Sciences (to H.Z.), the Major Project of National Social Science Foundation 19ZDA363 (to C.L.) and the Beijing Municipal Science and Technology Commission Z151100003915122 (to C.L.).
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Conceptualization: X.W., X.R., C.L., H.Z. Investigation: X.W. Data curation: X.W., X.R. Formal analysis: X.W., X.R. Methodology—development and design of methodology: X.W., X.R., C.L., H.Z. Methodology—creation of models: X.W., X.R., H.Z. Software: X.W. Visualization: X.W. Writing—original draft: .X.W, X.R. Writing—review & editing: X.W., X.R., H.Z., C.L. Funding acquisition: C.L., H.Z. Supervision: C.L., H.Z.
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Nature Computational Science thanks Scott Claessens and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Fernando Chirigati, in collaboration with the Nature Computational Science team.
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Supplementary Sections 1–5, Tables 1–11 and Figs. 1–21.
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Source Data Fig. 1
Excel file containing raw data across all trials for 157 participants in experiment 1 and the data immediately behind Fig. 1e–l.
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Excel file containing all the data used to reproduce the heatmaps in Fig. 2b.
Source Data Fig. 3
Excel file containing all of the data used to generate the model recovery, model comparisons and model predictions in Fig. 3.
Source Data Fig. 4
Excel file containing all of the data for clustering analysis in Fig. 4.
Source Data Fig. 5
Excel file containing all of the data from experiment 2 for the model comparison/prediction and clustering analysis in Fig. 5.
Source Data Fig. 6
Excel file containing all of the data used for the outofsample predictions in Fig. 6.
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Wu, X., Ren, X., Liu, C. et al. The motive cocktail in altruistic behaviors. Nat Comput Sci 4, 659–676 (2024). https://doi.org/10.1038/s43588024006856
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DOI: https://doi.org/10.1038/s43588024006856
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