Introduction

Humans can learn how to navigate through the world by observing the actions of others. For example, individuals can learn complex motor skills by observing and imitating how experts coordinate their movements (Hayes et al., 2008). Observational learning can also transmit important information about social and moral norms, such as reciprocity (Engelmann & Fischbacher, 2009), cooperating with others (van Baar et al., 2019), or context in which punishment is considered appropriate (FeldmanHall et al., 2018). In some cases, an individual learns from others in a straightforward and unambiguous social context, where the tensions endemic to many moral dilemmas—e.g., benefit one-self versus the collective good—are not directly juxtaposed against one another. And yet, the social world is rarely straightforward, often ambiguous, and moral dilemmas that pit self-benefit over the collective good abound (FeldmanHall & Shenhav, 2019; Vives & Feldmanhall, 2018).

Consider the case of inequity for which individuals exhibit a strong distaste: concerns for fairness are well documented in adults (Güth et al., 1982; Sanfey et al., 2003), children (Fehr et al., 2008; McAuliffe & Dunham, 2017), primates (Brosnan & De Waal, 2003, 2014; Van Wolkenten et al., 2007) and even domesticated dogs (Essler et al., 2017). This aversion to inequity manifests perhaps most famously in the Ultimatum Game (UG), in which one player (the Proposer) decides how to split a sum of money with another player (the Receiver), a role typically assumed by the participant (Güth et al., 1982; Sanfey et al., 2003). A Receiver’s acceptance results in both parties receiving the offered money, whereas rejection results in neither party receiving any money—a form of costly punishment. A recurring observation supporting inequity aversion is that people tend to reject disadvantageous offers that unfairly benefit the other party (Brosnan & De Waal, 2014; Fehr & Schmidt, 1999).

At the same time, not all inequity is experienced in the same way. For example, when we stand to receive less than our “fair share”, such disadvantageous inequity (DI) engenders feelings of envy, anger, and/or disappointment (Heffner & FeldmanHall, 2022) which often manifests in punishment of unfair offers in the UG via rejection (McAuliffe et al., 2014, 2017; Pedersen et al., 2013; Pillutla & Murnighan, 1996). In contrast, when we stand to receive a favorable share of resources—albeit one that is unfairly distributed—these advantageous inequitable (AI) offers often engender feelings of guilt or shame (Gao et al., 2018). Despite these negative emotions, Receivers are much less willing to engage in costly punishment of offers that are advantageously inequitable (Civai et al., 2012; Hennig-Schmidt et al., 2008; Luo et al., 2018).In short, AI versus DI engender markedly different punishment preferences.

A growing body of developmental research demonstrates that this difference in punitive responses to AI versus DI manifests early in the developmental trajectory (Amir et al., 2023; Blake et al., 2015; Blake & McAuliffe, 2011; McAuliffe et al., 2017). Indeed, punishing AI offers requires the sacrifice a (larger) personal gain to achieve a fairer outcome—mirroring many moral dilemmas in which self-versus other-regarding interests are at odds—AI aversion likely necessitates complex cognitive abilities. More specifically, because the aversion to AI appears to arise from more abstract concerns about fairness (Tomasello, 2019), AI aversion is thought to impose considerable demands on more sophisticated cognitive processing (Gao et al., 2018). This may explain, in part, why the developmental trajectory of AI-averse preferences comes online much later relative to DI (McAuliffe et al., 2017).

Thus, one open question concerns how people acquire inequity-averse preferences. One influential framework posits that we often adapt our behaviors to people around us through a process of conformity (Cialdini & Goldstein, 2004). Put simply, loyally following the behaviors of another—a social contagion effect—is a powerful motivator of social behavior. Such behavioral contagion effects are observed in diverse decision-making domains such as valuation (Campbell-Meiklejohn et al., 2010), risk-taking (Suzuki et al., 2016), delay of gratification (Garvert et al., 2015), moral preferences (Bandura & Mcdonald, 1963; Vives et al., 2022), and social norms (Hertz, 2021). Recently, we demonstrated that punitive responses to DI can be ‘taught’ to participants in the context of the Ultimatum Game, whereby individuals’ preferences for rejecting disadvantageous unfair offers were strengthened as a result of observing another individual’s (a ‘Teacher’) desire to punish these offers (FeldmanHall et al., 2018).

At the same time, social contagion effects may be far less robust if the behavior demands sacrifice of self-benefit. Since this type of dynamic places behavioral contagion and desire for self-gain in opposition, it remains unclear whether AI aversion can also be acquired ‘vicariously’ through observing another’s preferences. Here, we investigate whether the act of observing the AI-averse preferences of another punitive Receiver enhances an individual’s aversion to AI, even if the rejection of such AI offers requires sacrificing self-benefit. Answering this question not only enriches our understanding of the nature of inequity aversion, but also enable us to better understand the mechanisms underpinning vicarious learning of moral preferences during social interactions.

One can imagine different possible computational mechanisms driving vicarious learning of inequity aversion. One possibility is that observational learning of moral preference is based on simple action-outcome contingencies—on this view, a simple but elegant Reinforcement Learning (RL; Burke et al., 2010; Diaconescu et al., 2020; FeldmanHall et al., 2018; Lindström et al., 2019) model formalizes how individuals adapt their behavior to recently observed outcomes. In its most basic form, RL makes choices on the basis of learned associations between actions and outcomes, and critically, actions are bound to the specific decision context—applied to the UG, the unfairness of the amount offered by the Proposer. However, during social interactions, people might not consider the behaviors of others as resulting from simple action-outcome associations but alternatively, construct and use models of other agents, representing their stable intentions, beliefs, and preferences (Anzellotti & Young, 2020). Accordingly, we also consider the possibility that moral preferences are immutable across contexts (Bail et al., 2018; Fehr & Schmidt, 1999; Taber & Lodge, 2012), which would suggest that moral preferences are not learned merely as associations (i.e. specific responses tied to different unfairness levels), but rather, through a deeper inference process which models the underlying fairness preferences of the observed individual. Here, across two experiments, we leverage a well-characterized vicarious learning paradigm (FeldmanHall et al., 2018; Son et al., 2019; Vives et al., 2022) to examine the conditions under which individuals are able to learn AI-averse preferences on the basis of exposure to another Receiver’s punitive preferences. In addition, to mechanistically probe how punitive preferences come to be valued in DI and AI contexts, we also characterize trial-by-trial acquisition of punitive behavior with computational models of choice.

Experiment 1

In Experiment 1, following the approach of previous experiments (FeldmanHall et al., 2018), we test if the rejection of advantageously unfair offers can be learned on the basis of exposure to the preferences of another individual (the ‘Teacher’) who has AI-averse preferences. In a between subjectdesign with three phases, participants interacted with other individuals in a repeated Ultimatum Games (Figure 1a). We assess contagion effects by measuring participants’ DI and AI aversion both before and after observing (and implementing) the preferences of a Teacher’s who exhibits inequity aversion in both DI and AI contexts (“AI-DI-Averse” condition; N =100) and inequity aversion only in a DI context (“DI-Averse” condition; N =100).

First, to assess participants’ baseline fairness preferences across inequity levels, in the Baseline Phase (Figure 1c) participants acted as a Receiver in several one-shot UGs, responding to offers ranging from extreme DI (e.g., the Proposer keeps 90 cents and offers 10 cents to the Receiver; a 90:10 split) to extreme AI (e.g., the Proposer keeps 10 cents and offers 90 cents to the Receiver; a 10:90 split). On each trial, participants interacted with a different Proposer, and unbeknownst to participants, the offers were pre-determined by the experimenters. Following the typical formulation of the UG (Güth et al., 1982), participants made the choice between accepting versus rejecting each offer, and also rated the fairness of the offer.

Next, in the Learning Phase (Figure 1d), participants played a repeated vicarious UG as a third party, in which they accepted or rejected offers on behalf of another Receiver (termed the Teacher in this phase) such that the participant’s decisions did not impact their own payoff but would impact the payoffs to the Proposer and the Teacher. Critically, after each decision, participants received feedback whether the Teachers would have preferred acceptance versus rejection (i.e., punishment) of the offer. Thus, through trial-by-trial feedback, the Teacher can signal to participants their preference to punish the Proposer for making unfair offers. Critically, in the ‘DI-Averse’ condition, akin to the typical pattern of human preferences observed in the UG (Güth et al., 1982; Sanfey et al., 2003), the Teacher’s preferences exhibited a strong aversion to DI, and thus routinely punishing unfair offers. Specifically, the Teacher was likely to reject DI offers (i.e. 90:10 and 70:30), but not AI offers (i.e. 30:70 and 10:90; see Figure 1b and Table S1). However, in the ‘AI-DI-Averse’ condition, the Teacher was likely to reject any unfair offer, regardless of whether it was DI or AI, manifesting typical DI-averse preferences as well as the less commonly observed aversion to AI (i.e., punishing advantageous offers). Feedback from the Teacher was also accompanied by fairness ratings consistent with their preferences (see Figure 1b and Table S2).

Finally, to examine contagion (or transmission) of the Teacher’s preferences to the participants, we assessed fairness preferences of the participants for a second time in a Transfer Phase (Figure 1a). This third phase was identical to the Baseline Phase and thus allowed us to quantify changes in participants’ fairness preferences before and after the Learning Phase.

Figure 1.

Preferences Across Baseline and Transfer Phases

Mirroring preferences typically observed in Western, Educated, Industrialized, Rich, and Democratic (WEIRD) participant populations (Henrich et al., 2006), punishment choices in the Baseline Phase were DI-averse, but not AI-averse, as we observed similarly high rejections rates during the Baseline Phase for DI offers across the DI-Averse and the AI-DI-Averse conditions (Figure 2, Table S3; all Ps < 0.001). As expected, the rejection rates for AI offers were much lower than DI offers (Figure 2, e.g. 90:10 vs 10:90, all Ps < 0.001, see Table S3 for estimates of rejection rates). Consistent with these Rejection rates, participants rated DI offers as unfair (i.e., lower than the rating scale midpoint of 4, Table S4; all Ps < 0.001) and AI offers were rated as more fair than DI offers (all Ps < 0.001)— despite the fact that the offers in the AI and DI contexts represent the same magnitude of inequity (e.g. 90:10 vs 10: 90 splits).

To examine whether exposure to the Teacher’s punishment preferences in the Learning Phase resulted in changes in participants’ fairness preferences, we examined changes in Rejection rates and Fairness rating between the Baseline and Transfer phases (Figure 2). First, in response to DI offers (90:10 and 70:30 splits), we observed robust increases in punishment rates after observing a Teacher who prefers punishment. That is, after exposure to the Teacher’s punitive preferences in the Learning Phase, participants were more likely to reject offers that unfairly benefitted the Proposer in the Transfer Phase (Figure 2a), conceptually replicating our previous results (FeldmanHall et al., 2018). These increases in punishment rates under DI contexts were statistically significant in both the AI-DI-Averse (Table S5; 90:10 splits: β (SE)=0.14(0.03), p <0.001; 70:30 splits: β (SE)=0.12(0.03), p<0.001) and DI-Averse conditions (Table S5, 90:10 splits: β(SE)=0.18(0.13),p<0.001; 70:30 splits: β(SE)=0.14(0.03), p<0.001). These preference changes were consistent with the stronger DI aversion exhibited by the Teacher (in both conditions) than participants in the Baseline Phase. However, we did not observe consistent fairness rating changes for DI offers, presumably because the fairness ratings given by the Teacher was similar to participants’ baseline fairness ratings (Figure 2b, Table S6) in both conditions.

Examining punishment choices in response to AI (30:70 and 10:90) splits, we observed that participants in the AI-DI-Averse condition increased their rates of rejection to AI offers (Figure 2a). That is, participants exposed to the Teacher’s preferences to punish AI offers during the Learning Phase became significantly more likely, in the Transfer Phase, to reject unequal offers that stood to unfairly reap further monetary benefits for the participants (30:70 splits: β(SE)=0.09(0.03), p=0.002; 10:90 splits: β (SE)=0.12(0.03), p <0.001; Table S5). Importantly, we did not observe transfer of AI-averse preferences in the DI-Averse condition, where the Teacher did not express a desire to punish the AI offers in the Learning phase (30:70 splits: p=0.666; 90:10 splits: p=0.280; Table S5). Mirroring changes in rejection rates, participants’ fairness ratings also shifted towards those of the Teacher (Figure 2b)— specifically, in the AI-DI-Averse condition, participants rated AI offers as more unfair in Transfer compared to Baseline Phase (Table S6, 30:70 splits: β(SE)=-0.54(0.12), p<0.001; 10:90 splits: β(SE)= 0.76(0.12), p<0.001), while in the DI-Averse condition, participants rated AI offers as more fair (Table S6, 30:70 splits: β(SE)=0.32(0.12), p<0.001; 10:90 splits: β(SE)=0.28(0.12), p<0.001). Exposure to the Teacher’s behavior in response to “fair” offers (50:50 splits) did not appear to elicit changes in punishment rates in either the AI-DI-Averse (Table S5, p=0.349) or the DI-Averse (Table S5, p=0.517) condition, which suggests against the possibility that participants in the AI-DI-Averse condition were simply increasing punitive preferences, regardless of context. Finally, in line with the rejection rates results, for fair offers (Table S6, 50:50 splits), we did not observe any change in fairness ratings in the AI-DI-Averse condition (Table S6, p=0.662) and a slight increase in the DI-Averse condition (p=0.041).

Figure 2.

Learning another’s preferences

Having demonstrated that participants’ preferences to reject unfair DI and AI offers were altered on the basis of exposure to the Teacher’s preferences, we next examined the trial-by-trial changes in rejection rates during the Learning phase (Figure 3a). A mixed-effects logistic regression revealed a significant positive effect of trial number on rejection rates of DI Offers for the AI-DI-Averse condition (70:30 splits: β (SE)=0.36(0.09), p <0.001; not significant in 90:10 splits: β (SE)=0.27(0.20), p=0.164; Table S7) and the DI-Averse condition (90:10 splits: β (SE)=0.63(0.20), p=0.001; 70:30 splits: β(SE)=0.31(0.09), p<0.001), indicating an increase of rejection rates during the Learning phase. In contrast, examining responses to AI offers, we only observed a learning effect—that is, a rejection rate increase—in the AI-DI-Averse condition (30:70 splits: β(SE)=0.47(0.12),p<0.001; 10:90 splits: β (SE)=0.77(0.18), p <0.001) where the Teacher imparted AI-averse preferences, but not in DI-Averse condition (30:70 splits: p=0.111; 10:90 splits: p=0.429), where the Teacher did not. In other words, participants by and large appeared to adjust their rejection choices and fairness ratings in accordance with the Teacher’s feedback in an incremental fashion.

Computational Models of Learning Punishment Preferences

Having established that rejection rates increased for both DI offers (in both the DI-Averse and AI-DI-Averse conditions) and AI offers (only in the AI-DI-Averse condition), we then sought to better understand the learning mechanisms underpinning trial-by-trial learning (Figure 3a). We used computational modelling to formalize two different sets of assumptions about how participants learn from Teachers’ feedback. Under one account, a simple Reinforcement Learning (RL) model proposes that decision-makers learn punishment preferences by observing feedback resulting from actions made in response to specific offers. Previously we have found that this ‘naïve’ model provided a reasonable characterization of participants’ trial-by-trial learning of DI-averse preferences (FeldmanHall et al., 2018). However, this model may fail to capture a critical facet of learning: participants’ moral preferences may not be learned merely as associations—the type of response being tied to specific offers—but rather, through a deeper inference process which models the underlying fairness preferences of the Teacher. Accordingly, our alternative model assumes that the participant uses trial-by-trial feedback to infer the Teacher’s underlying preferences concerning inequality, which may shift depending on the context (DI versus AI). Following Fehr-Schmidt’s (1999) simple inequality aversion formalism, in our model—termed the Preference Inference model—the Teacher’s aversion to DI is modeled by an ‘Envy’ parameter, while the ‘Guilt’ parameter captures the Teacher’s aversion to AI (see Methods for model details). Critically, the RL model does not learn the Teacher’s preferences per se, but the value of each action (accept or reject), independently for each offer type. In contrast, the Preference Inference model explicitly represents the extent of the Teacher’s AI- and DI-aversion—i.e., their underlying preferences—by independently updating the envy and guilt parameters using trial-by-trial feedback from the Teacher.

We compared the goodness of fit of six different models to participants’ choices in the Learning Phase: the Preference Inference model which learns the ‘guilt’ and ‘envy’ parameters experientially, a Static Preference model which assumes the ‘guilt’ and ‘envy’ are fixed over the course of learning (baseline model 1, see Methods), three variants of the RL model that make different assumptions about how action values are represented, and a baseline or ‘null’ model which assumed a fixed probability of each action (randomly choosing, baseline model 2). We fit each of the six models via maximum likelihood estimation, penalizing for model complexity (see Methods), and found that the Preference Inference model provided the best characterization of learning (Figure 3b, Table S8), suggesting that participants were performing trial-by-trial inference of the Teacher’s underlying inequity preferences, rather than simply learning reinforced associations between experienced offer types and actions. Even the Static Preference model, which does not assume any learning mechanism but rather, assumes fixed preferences with respect to DI and AI, provided a better characterization of learning than any of the three RL models which do assume incremental learning over paired associations.

To examine the learning dynamics underpinning the best-fitting Preference Inference Model, we simulated Learning Phase choice behavior using participants’ estimated parameter values (Figure 3a, see Methods for details). The close correspondence between the simulated and observed learning curves indicates that the Preference Inference model captures the reinforcement-guided variations in punishment in DI-context and, crucially, the marked differences in learning between DI-Averse and AI-DI-Averse conditions in AI-context (30:70 and 10:90 splits). To better understand how the Preference Inference model accounts for these patterns of change in rejection rates, we examined how model-inferred aversion to DI (‘envy’) and AI (‘guilt’)—the two components of the Fehr-Schmidt inequality aversion model (Fehr & Schmidt, 1999) representing the latent structure of the Teachers’ preferences— emerge as a function of exposure to the Teacher’s preferences. In both the DI-Averse and AI-DI-Averse conditions, the model inferred a similarly “envious” Teacher (Figure 3c), while the model only increased its estimate of the Teacher’s ‘guilt’ parameter (Figure 3d), in the AI-DI-Averse condition where the Teachers’ feedback exhibited AI aversion, mirroring the model’s—and participants’—shift in rejection rates over the course of the Learning Phase and further suggesting that the Preference Inference model captured critical aspect of the participants’ vicarious learning behaviors.

Figure 3.

Relationship between Learning and Contagion Effects

We next investigated whether the extent of a participants’ vicarious learning was associated with greater contagion of punishment preferences. To do this, we examined whether participants’ changes in rejection rates between Transfer and Baseline, could be explained by the degree to which they vicariously learned, defined as the change in punishment rates between the first and last 5 trials of the Learning phase. Across offer types (Figure 4), we observed that participants who more strongly adapted their rejection rates to match the Teacher’s preferences in the Learning phase were more likely to adopt the Teachers’ preference while making their own choices in the Transfer phase. Specifically, for DI offers, these predictive relationships were strong in the AI-DI-Averse (90:10 splits: β(SE)=0.22(0.12), p=0.073; 70:30 splits: β (SE)=0.33(0.08), p <0.001; Table S9) and DI-Averse (90:10 splits: β(SE)=0.48(0.09), p<0.001;70:30 offers: β(SE)=0.36(0.08), p<0.001; Table S9) conditions. However, for AI offers, we only observed a relationship in the AI-DI-Averse Condition (30:70 splits: β(SE)=0.26(0.10), p<0.010; 10:90 splits: β(SE)=0.27(0.07), p<0.001; Table S9) but not the DI-Averse condition (a trend in 30:70 splits: β(SE)=0.25(0.13), p=0.058; 10:90 splits: β(SE)=0.12(0.10), p=0.196; Table S9). As expected, we did not observe any predictive relationships between learning and transfer behavior in response to fair (50:50) offers in either condition (AI-DI-Averse: β(SE)=0.10 (0.20), p=0.625; DI-Averse: β(SE)=0.12(0.18), p=0.503; Table S9). Taken together, the relationships between the degree of successful learning of the Teachers’ preferences and the magnitude of change in punishment rates (when participants acted on their own behalf) strongly suggests that participants’ changes in punitive preferences—particularly for AI offers—occurred as a result of exposure to another’s preferences.

Figure 4.

Conceptually replicating our previous findings (FeldmanHall et al., 2018), Experiment 1 provides evidence for behavioral contagion of DI-averse preferences, but extends this work by revealing that AI-averse preferences—which are believed to be less mutable (Luo et al., 2018)—can be similarly shaped by exposure to another individual with manifesting a strong aversion to resource divisions that unfairly benefit them. These results suggest that individuals’ moral preferences can be learned even in cases where these preferences conflict with one’s own self-interest. Computationally, this learning process was best characterized by an account that prescribes that individuals build a representation of others’ moral preferences about DI and AI (akin to the Fehr-Schmidt (1999) model of inequity aversion), rather than by a simple Reinforcement Learning account. This preference inference account predicts that individuals, when exposed to only a fraction of inequity-related punishment preferences, should generalize these inferred preferences to other similar inequity contexts. In Experiment 2, we sought to test this generalization hypothesis more directly, buttressing the idea that the learning and transfer of Inequity-averse preferences observed in Experiment 1 came about as a result of participants modeling the Teachers’ inequality-averse preferences.

Experiment 2

Experiment 2 provides a more stringent test of whether participants model the Teacher’s underlying inequity preferences. Specifically, if individual indeed learn the Teacher’s latent inequity-averse preferences in the Learning phase, we would expect that feedback-driven learning of Teacher’s punishment preferences on specific (moderate inequity) offers (30:70 splits) should generalize to offers in the same context (10:90 splits) without any direct experience of those offer types. Accordingly, to probe for this sort of generalization—a hallmark of the sort of latent structure learning we attribute to the behavior we observed in Experiment 1—we now eliminate feedback for extreme DI (90:10) and AI (10:90) offers from the Learning phase. If participants’ punishment preferences are informed by modeling inferred inequity-averse preferences of the Teacher, we should expect to see these preferences transfer to participants’ own fairness preferences in a similar, generalized manner in the Transfer Phase.

Mirroring Experiment 1, we employed two conditions governing the Teachers’ preferences in the Learning Phase: the Teacher in the DI-Averse condition only exhibited strong punishment preferences concerning moderate DI offers (30:70 splits), while the Teacher in the AI-DI-Averse condition exhibited strong preferences in response to both moderate DI and moderate AI offers (30:70 and 70:30 splits).

Contagion Effects for Extreme Unfair Offers Suggest Generalization

In Experiment 2, we took the same analysis approach as in Experiment 1, examining changes in rejection rates between the Baseline Phase and the Transfer Phase (after participants experienced feedback with moderately unfair offers). Similar to what we observed in Experiment 1 (Figure 5a), participants increased their rates of rejection of extreme DI (i.e., 90:10) in the Transfer Phase, relative to the Baseline phase (AI-DI-Averse Condition: β (SE)=0.13(0.03), p <0.001; DI-Averse Condition: β (SE)=0.18(0.03), p <0.001; Table S10), suggesting that participants’ learned (and adopted) DI-averse preferences, generalized from one specific offer type (70:30) to an offer types for which they received no Teacher feedback (90:10). Examining generalization across AI offers, we found a trend that participants in the AI-DI-Averse Condition increased their rejection rates of extreme AI offers (10:90) for which they did not receive any Teacher feedback in the Learning Phase (β(SE)=0.06(0.03), p=0.060). Furthermore, we saw decreases in rejection rates of extreme AI offers for participants in the DI-Averse Condition (β (SE)=-0.06(0.03), p=0.035). Mirroring the observed rejection rates (Figure 5b), participant rated these (untrained) extreme unfair DI offers (90:10) as less fair in the Transfer phase in both the AI-DI-Averse (β(SE)=-0.23(0.13), p=0.076; see Table S11) and DI-Averse conditions (β(SE)=0.29(0.13), p=0.023), and rated extreme AI offers (10:90) as less fair only in AI-DI-Averse Condition (β(SE)=- 0.84(0.13), p<0.001).

We further reasoned that if the contagion effects observed for extremely unfair offers (90:10 and 10:90 splits) resulted from the same latent structure learning process driving the observed contagion for moderately unfair offers (30:70 and 70:30 splits), we should expect the magnitude of contagion effects in moderately unfair offers to relate to the magnitude of contagion effects in extremely unfair offers. Examining changes in punishment rates in AI contexts—between the Transfer and Baseline phases—we observed that participants with larger contagion effects for 30:70 offers also exhibited larger contagion effects for 10:90 offers (Figure S2). This was observed both in rejection rate changes (AI-DI-Averse Condition: p<0.001, DI-Averse Condition: p<0.001) and perceived fairness changes (AI-DI-Averse Condition: p<0.001, DI-Averse Condition: p<0.001). In DI contexts, we found that the same relationships between responses to moderately unfair offers (70:30) and extremely unfair offers (90:10), both for changes in rejection rates (AI-DI-Averse Condition: p<0.001; DI-Averse Condition: p=0.003) and perceived fairness rating changes (AI-DI-Averse Condition: p<0.001; DI-Averse Condition: p<0.001).

In short, we find evidence that participants generalized across learning contexts, which in turn shaped their own punitive responses to extreme offers, both in the case of DI and AI offers. In other words, it appears that preferences acquired through contagion extends beyond mere associations between single offers and actions, and instead relies on a mechanism that infers the latent structure of the Teacher’s fairness preferences.

Figure 5

Preference Changes in the Learning Phase Suggest Generalization

A primary goal of Experiment 2 was to demonstrate that learning the Teacher’s preferences with respect to moderately unfair offers generalized to extremely unfair offers, where no feedback from the Teacher was provided. Examining the time course of rejection rates in AI-contexts during the Learning phase (Figure 6) revealed that participants learned over time to punish mildly unfair 30:70 offers, and these punishment preferences generalized to more extreme offers (10:90). We observed a significant increase in rejections rates for 10:90 (AI) offers in the AI-DI-Averse Condition (Figure 6, β (SE)=1.06(0.31), p<0.001; mixed-effects logistic regression, see Table S12), but not in the DI-Averse Condition (β (SE)=-0.54(0.40), p=0.170). We observed significant rejection rate increases for 90:10 (DI) offers in DI-Averse Condition (β (SE)=0.96(0.27), p <0.001) but not in the AI-DI-Averse Condition (β(SE)=0.36(0.26), p=0.116). Finally, we observed significant decreases in fairness ratings over time for 10:90 offers in the AI-DI-Averse Condition (β(SE)=-0.27(0.09), p=0.004; Table S13), again suggesting that participants generalized fairness ratings across offer types on the basis of inferred fairness preferences attributed to the Teacher. We did not observe this sort of generalization for fairness ratings in the DI-Averse condition, nor did we observe significant changes in fairness ratings over time in DI context (ps > 0.131 for all offers; see Table S13), perhaps owing to the smaller difference between the Teacher’s preferences and participants’ default (Baseline) preferences concerning DI offers. Furthermore, we reasoned that participants’ learning in moderately unfair contexts (for which participants received feedback) should predict their learning in extremely unfair contexts (for which no feedback was provided). To test this, we examined individual differences in changes in punishment between the final 5 trials and the first 5 trials of the Learning phase, finding that learning for moderately unfair (30:70 and 70:30) offers predicted changes in punishment rates for extremely unfair (10:90 splits: p < 0.001 and 90:10 splits: p < 0.001) offers. In other words, participants who increased their punishment more in response to (reinforced) moderately unfair offers also exhibited changes in their preferences for (non-reinforced) rejection of extremely unfair offers.

Finally, following Experiment 1, we fit a series of computational models of Learning phase choice behavior, comparing the goodness-of-fit of the four best-fitting models from Experiment 1 (see Methods). As before, we found that the Preference Inference model best characterized participants’ Learning Phase behavior (Figure S1a, Table S14). This is unsurprising, given that this model—by virtue of learning the Teachers’ underlying preferences— assumes the sort of generalization of preferences between offer types that Experiment 2 sought to test directly. We also simulated this model’s Learning Phase behavior using participants’ estimated parameter values and found that the model, mirroring participants’ choices, exhibits clear incremental changes in rejection rates (Figure 6; thick lines), both for offers where the model received explicit feedback (70:30) and for offers where the model received no feedback (90:10). In other words, like participants, the model generalizes the learned inequity-averse preferences to extreme AI offers (90:10), which stems from the model’s trial-by-trial updating of the parameters governing the Teacher’s preferences (see Figures S1b and c).

Figure 6.

Discussion

While people tend to reject proposed resource allocations where they stand to receive less than their peers (so-called disadvantageous inequity; DI), they are markedly less averse to resource allocations where they stand to unfairly gain more than their peers (advantageous inequity or AI; Blake et al., 2015; Luo et al., 2018). Here we considered the possibility that these complex, other-regarding preferences for fairness can be imparted merely by observing (and enacting) the preferences of another person. We investigated, in an Ultimatum Game setting, whether AI-averse preferences can be shaped by learning and the preferences of another individual. We leveraged a well-characterized observational learning paradigm (FeldmanHall et al., 2018), exposing participants to another individual (the Teacher) exhibiting a strong preference for punishment of advantageously unfair offers, and probed whether these punishment preferences in turn transferred to participants making choices on their own. We found that participants’ own AI-averse preferences shifted towards the preferences of the Teacher they just observed, and the strength of these contagion effects related to the degree of behavior change participants exhibited on behalf of the Teachers, suggesting that they internalized, at least somewhat, these inequity preferences.

While we observed apparent adoption of the Teachers’ inequity-averse preferences, in the face of both AI and DI, previous work has outlined a number of important differences with respect to how individuals respond to the two sorts of inequity. Aversion to DI is thought to arise from negative emotions such as spite (McAuliffe et al., 2014; Pillutla & Murnighan, 1996) engendered by consideration of one’s standing relative to others, while AI aversion, in contrast, is thought to stem from concerns about fairness or inequality (McAuliffe et al., 2013). Hence, the expression of AI aversion may signal, and even enforce, egalitarian social norms. Developmental evidence supports this distinction between AI versus DI aversion. While DI aversion emerges at the tender age of 4, AI aversion does not appear to manifest until about 8 years (Blake et al., 2015; Blake & McAuliffe, 2011; McAuliffe et al., 2017). In fact, AI aversion—which entails trading off self-interest against a social norm enforcement— is not even commonly observed in adults (Blake et al., 2015; Hennig-Schmidt et al., 2008; Luo et al., 2018), suggesting that AI aversion is more difficult (and less likely) to be learned than DI aversion. That we found evidence that AI averse-preferences can be learned suggests that observational learning processes are a potent and promising means by which sophisticated fairness preferences can be imparted.

Mechanistically, we found that participants’ feedback-based learning of punishment preferences was best characterized by a computational model that assumes individuals infer the Teacher’s latent and structured preferences for punishment—rather than a simple Reinforcement Learning (RL) account assuming that individuals learn contextually-bound punishment preferences. To support the interpretation that individuals indeed ‘model’ the fairness preferences of others, in a second experiment we direct test whether participants can infer the Teachers’ inequity-averse preferences across contexts. We found that participants generalized the Teacher’s punitive preferences to other contexts that varied in their unfairness, and this occurred in the both AI and DI contexts, suggesting that the discovery of latent structure is instrumental for generalization.

The representation of others’ beliefs in other interpersonal decision-making tasks has been previously formalized, computationally, by a Bayesian account of theory of mind (ToM) in which the hypothetical beliefs were described by a prior distribution, and participants update this distribution using Bayesian updating (Baker, Chris et al., 2009; Jara-ettinger, 2019). This computational framework has been applied to describing behaviors in a group decision making task (Khalvati et al., 2019). In our Preference-inference model, on each trial, the learner makes a guess about the Teacher’s inequity aversion parameters, then the Teacher’s feedback is subsequently used to further constrain the range of parameter values which could conceivably produce the Teacher’s observed feedback. The learner then updates their initial guess range. Conceptually, this learning mechanism is consistent with the sort of Bayesian updating.

One open question concerning the contagion effects is how the identities— and number—of teachers experienced in the Learning phase bear on the strength of the learning and contagion effects observed. For simplicity, our Learning Phase employed only one distinct Teacher, that included no identity information, which contrasts with many social interactions in daily life, which are almost always accompanied by identifying information or attributes concerning the other (Hester & Gray, 2020). In contrast, our interactions with others are profoundly influenced by the identities of others—for example, whether they are conservative versus liberal (Leong et al., 2020), whether they are inversus out-group members (Hein et al., 2010; Vives et al., 2022). At the same time, the strength of social influence often increases with the number (or proportion) of individuals in a group expressing a particular preference (Cialdini & Goldstein, 2004; Son et al., 2019). However, it may also be the case that social contagion effects require repeated interactions with the same individual (Tsvetkova & Macy, 2014), which the contagion observed in the present paradigm corroborates. Accordingly, future work should aim to examine the influence of the teacher’s identity—and its concordance with the learner’s identity—as well as seek to understand the how the relative balance of repeated experience with identical teachers versus the number of distinct teachers modulates the strength of contagion effects in AI/DI punishment preferences.

In summary, our study provides an initial demonstration that despite the desire for self-gain, we observe that people can swiftly and readily acquire another’s preferences for advantageous inequity, even when it comes at a monetary cost to the self. Computationally, we find that this contagion of inequity averse-preferences occurs through representing the underlying structure of another’s preferences, rather than a Reinforcement Learning-like process of learning simple context-action associations. Importantly, these inferred preferences are sufficient to induce individuals to change their preferences for punishing advantageous inequity, suggesting that social influence may be one promising route through which social norm enforcement—which is particularly uncommon in the case of AI—can be promoted.

Methods

Participants

We recruited US-based participants from Amazon Mechanical Turk (Crump et al., 2013) for both Experiment 1 (N=200, M age = 37.53 (SD=10.88), 75 females) and Experiment 2 (N=200, M age=37.16 (SD=11.79) years old, 80 females). These sample sizes are based on our previous work employing the same per-condition sample sizes (FeldmanHall et al., 2018)in a punishment-learning task. Participants provided informed consent in accordance with the McGill University Research Ethics Board. Participants were randomly assigned to either the AI-DI-Averse (N = 100) or the DI-Averse (N = 100) condition. As we replicated all key reported results when excluding participants who evidenced some disbelief that the Teacher (see below for procedural details), suggesting that these results are robust to potential disbelief about the task structure as described to them. In Experiment 2, we excluded the data of participants who failed to meet the requirements of each analysis due to missed trials (3 in AI-DI-Averse and 3 in DI-Averse Condition were removed in Contagion effects analysis; 2 in AI-DI-Averse , 5 in DI-Averse Condition were removed for the generalization analysis).

Punishment Learning Paradigm

We used a modified version of the Ultimatum Game (Güth et al., 1982) to probe participants’ fairness preference, In this task, the proposer, offer an allocation of a total amount (e.g. $1 out of $10). Then, another player, the Receiver, chooses to reject or accept the proposed allocation. If the Receiver accepts, both players receive the proposed amount, if they reject, both player receive nothing. Following our past work examining contagion effects (FeldmanHall et al., 2018), our task consisted of 3 phases: Baseline, Learning and Transfer (see Figure 1).

In the Baseline and Transfer phases, participants responded to unfair offers as a receiver in multiple rounds of ultimatum game, and participants were informed that the Proposer on each trial is a different, randomly chosen individual with a unique (fictitious) participant ID (Figure 1c), which permitted us to measure participants’ preferences and beliefs about fairness irrespective of any particular Proposer. We considered 5 unique offer levels (90:10, 70:30, 50:50, 30:70, 10:90) ranging from extreme DI to extreme AI, including ‘fair’ offers (50:50), which allowed us to measure participants’ baseline rejection tendency. We instructed participants that these Proposers were concurrently participating in this task and these were “real time” offers. Critically, participants were responding to offers made by fictitious players with predetermined offers to ensure that we could observed rejection preferences for each offer level. On 3/5 of Baseline and Transfer Phase trials, participants also rated the fairness of the offer on a 1-7 scale (1 being ‘Strongly unfair’; 7 being ‘Strongly fair’) after making an accept/reject choice. Participants experienced 5 trials of each offer type in both the Baseline and Transfer Phase.

In the Learning phase, participants played an Ultimatum Game, acting as a third party deciding to accept or reject Proposers’ offers for another receiver (the Teacher) receiving offers from Proposers (see Figure 1d). After the participant chose to accept or reject the offer, the option the Teacher would have preferred was revealed. In the AI-DI-Averse condition, the Teacher indicated preference for rejection of fair (50:50) and AI offers, and uniformly rated these AI offers as unfair (see Figure 1b). In the DI-Averse condition, the Teacher accepted all fair and AI offers and rated these offers as uniformly fair. In both the DI-Averse and AI-DI-Averse, DI offers were rejected and rated as unfair. The Teachers’ rejection rates and ratings in response to each offer type are provided in Tables S1 and S2.

Again, on 3/5 of trials, participants rated the fairness of each offer, and on these trials participants also saw the Teachers’ fairness rating of the offer. Like the Baseline and Transfer phases, participants saw a unique, randomly chosen Proposer on every trial, but were informed that there was a single, unvarying Teacher over the entire Learning Phase. In Experiment 1, participants experienced 20 trials for each of the 5 offer types considered (90:10, 70:30, 50:50, 30:70, 10:90). To generate each offer, we further added a uniformly distributed noise in the range of (-10 ,10) to each offer type.

Experiment 2 followed the same procedure as Experiment 1 except for the following changes. First, and most importantly, in the Learning Phase participants did not experience feedback on extreme AI offers (10:90 splits). Second, we added to the Learning Phase 25 more trials each for offer type (70:30 and 30:70 splits), to afford greater opportunity to observe the Teacher’s preferences. Third, participants were instructed that Proposers’ offers (which were predetermined) were generated by previous participants in previous similar experiment. Finally, in all task phases, participants were required to respond within a 3-second deadline when making choices, and a 4-second deadline when providing fairness ratings.

Data Analysis

We used mixed-effects regression, implemented in the ‘lmer’ package for R (Bates et al., 2015) to estimate the effect of offer level and punishment condition upon contagion rates— the rejection rate change between the Baseline and Transfer phases. To do this the rejection rate change were modeled by interactions between Offer types (factors of five levels: 90:10, 70:30, 50:50, 30:70, 10:90, encoded as 5 columns) and Condition (AI-DI-Averse vs. DI-Averse, encoded as 2 columns), with random intercepts taken over participants (see Table S7 for full coefficient estimates).

We estimated changes in punishment rates in the Learning Phase using mixed-effects logistic regressions in Learning. Specifically, rejection choices were predicted as a function of trial number, offer type, condition, and their resultant interactions, taking the 2-way interactions between Trial number and offer type (random slope) as random effects over participants. To estimate changes in fairness ratings, we estimated a linear mixed-effects model with the same terms.

Computational Models of Learning Phase Behavior

We considered 6 computational models of Learning Phase choice behavior, which we fit to individual participants’ observed sequences of choices and Teacher feedback via Maximum Likelihood Estimation. Importantly, Models 1 (Random choosing) and 2 (Static preference) are baseline models which assume that rejection probabilities are fixed over time, while all other models allow for learning of rejection rates over time in accordance with Teacher feedback.

Model 1 (Random Choosing).

This model assumes that participants reject offers with a fixed probability governed by the parameter p_offertype (one for each offer type; 5 free parameters in total).

Model 2 (Static preference):

This model that when choosing for others, the utility of accepting an offer, relative to rejection of the offer, is governed by the Fehr-Schmidt (FS) inequity aversion(Fehr & Schmidt, 1999; Luo et al., 2018) function:

In this function, offer represents the share the Proposer give to the Receiver, α parameterizes the Teacher’s disutility for accepting disadvantageous unfair offers (DI aversion), and β captures Teacher’s disutility for accepting advantageous offers (AI aversion), which can each range from 0-1.

These action utilities were then transformed to choice probabilities using the softmax choice rule:

where the inverse temperature (τ) parameter captures decision noise, where a larger τ corresponds to a higher probability of choosing the action with higher utility, and as γ approaches 0, the two options are chosen with equal probability. In total, this model has 3 free parameters.

Model 3 (Basic RL):

Model 3 is a simple RL model following that used by FeldmanHall et al. (2018) only one learning rate, which represents and updates values of the two actions separately for each offer type, using a delta updating rule:

where actiont_t is the action the participant chose (accept or reject) on the t-th trial, R_t is the reward on the t-th trial, which is defined as 1 (reward obtained) when the action taken was the same as the action the Teacher would have preferred, and 0 (no reward) otherwise. The softmax choice rule was used to translate these action values to predicted choice probabilities. This model has 2 free parameters.

Model 4 (Offer-Sensitive RL):

This RL model is a more complex variant of Model 3, and assumes a separate learning rate for each offer type (as in Model 3). In total, this model has 6 free parameters.

Model 5 (Offer-Sensitive RL with Separate Initial Values):

This RL model extends Model 3, assuming different initial action values for each offer type. Formally, this model treats Q₀(reject, offertype), (offertype ∈ 90:10, 70: 30, 50: 50, 30: 70,10: 90) as free parameters with values between 0 and 1., resulting in 7 free parameters.

Model 6 (Preference Inference):

Model 6 posits that the participant infers the Fehr-Schmidt utility function (Equation 2) governing the Teacher’s preferences, and updates their modeled ‘guilt’ (α) and ‘envy’ (β) parameters incrementally from feedback, under the assumption that the Teacher’s indicated choices are made in accordance with each offer’s Fehr-Schmidt utility (more formally, the Teacher rejects the offer when U_accept(offer) < 0). As α and β govern the disutility of unfair offers, the model infers the minimal value of α (or β) would lead to rejection of DI (or AI) offers, and similarly, the maximum values of α (or β) would lead to acceptance of DI (or AI) offers.

Accordingly, after observing that the Teacher prefers rejection in response to a DI offer, Equation 2 can be transformed to the following inequality:

where the model can infer a lower bound of a, that would lead to the offer’s rejection by solving (6):

The right side of (7) can be denoted as α_lb , and then that trial’s estimate of α (denoted α_t) is updated as follows:

The parameter η governs the rate at which the learner’s estimate of the Teacher’s α value is updated, and is constrained to the range [0, 5].

The updating procedure is similar when Teacher indicates acceptance of a DI offer, which implies that U_accept(offer)>0, and the following inequality:

which yields a upper bound the for the envy parameter α

This upper bound, α_ub, is in turn used to update α_t:

In the case of AI offers, the model employs the identical procedure to update the ‘guilt’ parameter β, and α is updated only in DI offers, while β is only updated in AI offers. Following Luo et al. (2018), α and β were restricted to the range of [0, 10]. The initial value of α and β are taken as free parameters in the range of [0, 10], resulting in a model with a total of 4 free parameters.

All models were fit via Maximum Likelihood Estimation, employing a nonlinear optimization procedure using 100 random start points in the parameter space in order to find the best-fitting parameter values for each participant. We then computed the Akaike Information Criterion (AIC; (Akaike, 1974) to select the best-fitting models of Learning phase choice behavior, penalizing each model’s goodness-fit-score by its complexity (i.e., number of free parameters). See Table S8 and S14 for parameter estimates and goodness-of-fit metrics.

Acknowledgements

This work was funded by the European Union (ERC Starting Grant, NEUROGROUP, 101041799) and by an NSERC Discovery Grant, a New Researchers Startup Grant from the Fonds de Recherche du Québec - Nature et Technologies, and an infrastructure award from the Canadian Foundation for Innovation. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.

Supplementary Information

Figure S1.

Figure S2.

Table S1.

Table S2.

Table S3.

Table S4.

Table S5.

Table S6.

Table S7.

Table S8.

Table S9.

Table S10.

Table S11.

Table S12.

Table S13.

Table S14.