Initial prejudices create cross-generational intergroup mistrust

The present investigation modeled the emergence and persistence of intergroup bias and discrimination in artificial societies. Initial unfair prejudices held by members of a dominant group elicit confirmatory behavior (diminished cooperation) from members of a subordinate group via a self-fulfilling prophecy. Further, when individual learning is tempered by conformity to peers, inaccurate beliefs about the stigmatized subordinate group persist long-term. Even completely replacing dominant group members with enlightened individuals through generational change is inadequate to break the cycle of intergroup distrust and non-collaboration. The longer the enlightenment of a society is delayed, the more intergroup trust is irretrievably lost.


Introduction
Among the most intractable problems facing human societies across the world is that of group based discrimination and inequality. Social stratification is a human universal [1], and the correlate of the emergence of an elite is the development of subordinate groups characterized by social marginalization and a lack of economic resources [2,3,4]. Members of socially stigmatized and negatively stereotyped ethnic, religious, and cultural groups are chronically overrepresented among the most disadvantaged members of a society [1]. Such group-based inequality persists into comparatively more enlightened times, in which the virulent prejudices of the past, if certainly far from absent, have at least abated significantly [5].
The simplest explanation for the resilience of group-based inequality across generations of many societies is that it constitutes a tragic residue of the blatant discrimination of the past [6,7]. The historical record is replete with cases in which a dominant group brutally oppressed subordinate groups through conquest, colonialism, slavery, and/or forced segregation, leading to savage inequalities in objective resources. Under conditions of inherited wealth, initially disadvantaged groups will continue to suffer deficits in economic resources, educational attainment, and human capital long into the future.
Although objective and persisting gaps in resources are certainly one of the fundamental causes of the problem, the present research highlights the role of subjective, psychological variables in creating patterns of group-based mistrust, marginalization, and inequality. Through a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 the analysis of interactions in artificial societies, we show that prejudice toward members of a subordinate group in the early stages of a society elicits confirmatory behavior (reduced cooperativeness) via a self-fulfilling prophecy, creating a sustained cycle of intergroup mistrust and non-collaboration. The terms prejudice and stigma are used here interchangeably to refer to inaccurate and negative beliefs about a subordinate group's worth as collaborators [8,9,10]. We assume that some prejudice exists at the very beginning of intergroup interactions. Discrimination is used to refer to the behavior of choosing not to collaborate with a member of a subordinate group based on prejudiced beliefs about them. This is of course a simplification of real-world intergroup interactions, which involve multifaceted and in some cases contradictory stereotypes, attitudes, and norms related to other social groups. However, in line with previous work using agent based modeling to examine intergroup processes [11] we use cooperation (vs. defection) and relevant beliefs about the trustworthiness of the counterpart as our operationalizations of intergroup behaviors and attitudes, respectively.
In our simulations, societal prejudices and discrimination give rise to a self-fulfilling prophecy [12,13], as discriminated-against subordinate groups develop response patterns they did not initially possess, learning to mistrust members of the dominant group [14,15]. Distinct from the recent work on the origin of social biases [11,16], our analysis focuses on the destructive consequences of the initial prejudiced treatment of the subordinate group, at the same time pointing to the roots of the troubling persistence of such unfair beliefs. To this effect we demonstrate that despite some changes in the actual cooperativeness of members of the subordinate group in response to initial prejudices against them, beliefs about the subordinate group continue to be harmfully inaccurate long into societies' development, and under some plausible conditions, never converge with actual behaviors. Thus, although unfair discrimination leads stigmatized groups to develop the very lack of cooperativeness they were presupposed to have, they do not become as uncooperative as members of the dominant group believe they are.
Perhaps most dramatically, we find that when initial generations of the dominant group are prejudiced and some degree of conformity to peers exists, even a complete replacement of prejudiced dominant group members with non-prejudiced individuals through generational change fails to end the cycle of intergroup mistrust and non-collaboration [17]. Although ameliorating the effects of past discrimination always poses a challenge, the longer the enlightenment of the dominant group is delayed, the more intergroup relations are irreparably damaged.

Method
We conceive of each individual social interaction as a coordination game, where players have no incentive to cheat but must choose strategies based on their priors about others [18,19,11,20,21]. Each player has two generic strategies: collaborate or not. Consistent with the studied phenomenon, the two existing Nash equilibria are Pareto-ordered and we refer to the superior equilibrium as collaboration or trust, while calling the inferior one noncollaboration or distrust. Fig 1 illustrates the structure of the game. The intuition is that each player gains more if they collaborate and less if they do not. This is consistent with the simple idea that trust is an important determinant of the social welfare [22,23].
We think of the game as involving two stages: (i) formation of a pure-strategy belief, and (ii) acting on this belief. Stage (i) is subject to learning and initial biases [14] as agents make their own, idiosyncratic assumptions, seeing either trustworthiness in their counterparts or the lack thereof. Stage (ii) represents the choice of strategy.
From the structure of the game (see Fig 1) it follows that players will opt for a pure strategy that reflects their beliefs about others. In simple terms, our agents trust those they perceive as high quality collaborators and do not invest in interactions with those they see as low quality collaborators. Note that we do not assume any specific payoffs to strategies. Rather we consider only behavioral aspects of a game where players decide to collaborate or not based on their preconceived expectation about the probable choice of the other player. Such a conception of social interactions allows for a clear definition of human bias. If, given some criterion, player i is less likely to see a quality collaborator in player j than the latter in fact tends to be, player i can be said to be biased along this criterion.
Building on the large body of previous formal work with a modified approach designed to capture intergroup dynamics [18,24,25], we assume that players can discriminate between groups rather than just individuals [26]. At any moment in time a member of group I is equally likely to collaborate with (i.e., see a desirable collaborator in) any member of group J. Interactions are selected at random from all possible dyadic interactions, meaning that the probability of interacting with any member of group J (as opposed to any member of group I) is proportional to the relative size of the two groups. Unless otherwise indicated, we assume |I| = 80 and |J| = 20. We present results for alternative relative group sizes (see S8-S12 Figs).
In our model, the individual i's (i 2 I) probability (ρ i:J,t ) to collaborate with any individual j in group J in period t is subject to the following learning process [19,20]: Where s j,t is the strategy chosen by the player from group J in a given interaction, such that s j,t is 1, when she collaborates and 0 otherwise, and α i 2 [0,1] is the learning parameter. Note that in our simulations all dyadic-level interactions are random. In other words, any member of group I is equally likely to interact with any other individual, irrespective of whether this individual belongs to group I or to group J. Further, an agent updates her priors about the entire group. This learning process implicitly captures the concept of indirect reciprocity in that an individual i changes her priors to reciprocate what she experienced in the last interaction with a certain group [25].
We consider two groups, I, dominant and J, subordinate, where initially, the former wrongly sees the latter as low quality collaborators, i.e. 8i 2 I, j 2 J, E(ρ i:J,0 ) < E(ρ j:I,0 ). At the individual level we allow for variation in beliefs [27] so that systematic discrimination occurs only at the group level. Specifically, we consider a population, where ρ j:I,0~U (0,1) and ρ i:J, 0Ũ (0,θ), θ < 1 (our findings are qualitatively robust to a wide spectrum of alternative specifications and distributions of priors, see S1 and S2 Files, S1-S12 Figs). Such asymmetry captures the idea of prejudice and social stigma in that members of the dominant group on average unfairly believe that members of the subordinate group are lower quality collaborators than they actually are.
In sum, our model portrays a society in which people form idiosyncratic beliefs about members of other groups and act on these beliefs in their decision making. At the outset, members of this society differ in their propensity to trust other people and as such vary in their willingness to collaborate. Our agents are also liable to flaws of human judgment. At the group level, some members unjustly see bad qualities in those who differ from them. These beliefs, however, change as individuals interact and learn about each other. With the help of this model we trace transformations in intergroup relations that occur in our society over time.
The random and learnt aspects of the model make formal analysis prohibitively difficult. Accordingly, to analyze social processes that span eras of history we use agent-based modeling [18,24,28,26,29,30]. The code for this model was written in C++ (see S1 File). Below we describe our observations from the modeled social process.

Results and discussion
Interaction and learning drive social mentality. Naturally, when α i is 0 and no learning occurs, initial prejudices persist indefinitely. When, in contrast, α i is constant and greater than 0 any inaccurate belief about the subordinate group disappears in the limit. The flipside of learning is that members of the stigmatized group learn not to naïvely collaborate and gradually suppress their readiness to trust in the face of biased treatment from the dominant group (see Fig  2). Unjust social stigma thus provokes a symmetric behavioral response from the stigmatized, giving rise to a vicious circle of distrust. This creates a self-fulfilling prophecy, as members of the subordinate group who were initially willing to collaborate with dominant group members learn not to invest in collaboration instead. Distrust in turn increases the frequency with which individuals enter inferior equilibrium. For a large class of problems, where mutual trust is a key condition for value creation, this implies a comparative wealth disadvantage for the stigmatized subordinate group.
Counterintuitively, the time that it takes for this negative intergroup dynamic to stabilize decreases with α i (see S1 Fig). Although a higher rate of learning might be presumed to cause dominant group members to reject negative beliefs about the subordinate group, it actually leads biased beliefs to become self-fulfilling more quickly. As a result, subordinate group members rapidly learn that dominant group members are biased against them and hence really do become reluctant to invest in collaborations.
The speed of learning itself is a product of factors that are largely exogenous to the process of intergroup interaction, with the important exception of social conformity. We model social conformity by allowing the extent to which one learns from experience to vary with the deviation of her belief from those of other ingroup members. Given that members with views different than the norm tend to be more likely to adjust their beliefs in response to new information-an effect demonstrated in the context of U.S. racial attitudes and norms [31,32]-for every individual at any point in time t, learning speed α i,t is set proportional to the deviance of one's belief from the group average. The less representative a given member's beliefs are of those in her group (i.e., the greater the distance between her prior and the group norm), the more likely she is to change her views in response to personal experiences with outgroup members. This characterization captures the idea, supported by experimental research, that behavior is comparatively "sticky" around the group norm and malleable away from it [31,32].
Specifically, at any moment in time, α i,t is the equivalent of |ρ i:J,t − ρ I:J,t |, where ρ I:J,t characterizes the group I's norm of collaboration with members of group J, and ρ i:J,t is individual i's (i is a member of group I) willingness to collaborate with members of group J (similarly  Fig 3 shows the dynamics of the learning speed when individuals are subject to social conformity. Average speed of learning in a group is defined as a simple average of learning rates among all members of this group. Note that the dynamics of the learning rate is key to understanding our analyses. Over time individuals become less and less likely to learn from their experience and increasingly rely on their prior beliefs, which gradually approach the group's norm. The initial difference between α dominant and α subordinate is due to the greater variance in beliefs within the subordinate group (cf. S2 Fig). Members of the dominant group preserve a higher learning rate for longer (recall that the learning rate is a function of an individual belief relative to that of the group; greater variance in beliefs, therefore, corresponds to a higher learning rate), because they are more numerous and therefore their group opinion is less sensitive to individual updating of beliefs.
https://doi.org/10.1371/journal.pone.0194871.g003 defined for j and I). Our analysis relies on a careful definition of the group norm. Drawing on research examining closeness in social networks [33], we measure the norm as a group-wide weighted average willingness to trust, where weights originate from all pairwise comparisons of priors among the members and are inversely proportional to the average deviance of one's belief from those of peers.
Formally, for each individual i, we calculate the total distance d i,t in beliefs from all group members, such that d i;t ¼ X i;k2I jr i:J;t À r k:J;t j. We then weight individual beliefs by our distance measure in calculating the group norm such that: Our main results are qualitatively robust to alternative measures of the group norm where we weight individuals' beliefs by the absolute distance from the arithmetic group mean or median.
In the presence of social conformity α i,t is a decreasing function of accumulated social interactions (see Fig 3). Fig 4 demonstrates that for intergroup collaboration this means that the emergence of a discriminated-against subordinate group is accompanied by a lasting and unjustified stigma against them. Over time, members of the subordinate group become less and less willing to collaborate with the prejudiced dominant group, yet they do not become as unwilling to collaborate as members of the dominant group believe they are. Consider that if α i ! 0, then ρ i:J,t ! ρ i:J,t-1 . That is, over time individuals become gradually less ready to adjust their beliefs about members of other groups. Sadly, this happens before stigma disappears. The reason for this is that learning about other group happens at the individual level (i.e. α i is individual specific) whereas convergence to the belief shared by one's group is in part a group- level phenomenon. Specifically, any cross-group interaction affects the average belief, and therefore α i , but only an interaction that involves a given individual affects his or her subjective probability to collaborate ρ .:.,t . In a stabilized society, therefore, we can expect that alienated subordinate groups coexist with prejudiced dominant groups, who even eras later would still discriminate against those who are not like them.
While there is no direct mapping of model time on to real-world time, two aspects of our analyses allow us to conclude that the reported effects persist in the long run. First, the observed time interval. Consider that in our simulated populations we have 100 individuals and 10 7 interactions. If every individual has one interaction involving the choice to collaborate or defect with a random person per day, i.e. a total of 50 interactions in the population per day, our modeled time interval translates into over 500 years. Greater frequency of interactions naturally results in a more compressed correspondence with real-world time intervals.
An important property of these regularities is that even a trivial bias in initial beliefs on the part of the dominant group can result in a lasting social stigma against the subordinate group. Fig 5 shows that the emergence and persistence of a stigmatized subgroup is robust to different degrees of the asymmetry in trust at the onset of cross-group interaction. The effects also hold for larger populations, as seen in Fig 6 for a population of 1000 individuals. We next ask the question of whether it is possible to break the cycle of intergroup mistrust and non-collaboration by changing the prejudiced beliefs of the dominant group. When conformity to normative beliefs diminishes the ability to learn from individual experiences with outgroup members (α i,t ) the time to reverse the negative consequences of initial stigma and discrimination for the behavior of members of the subordinate group is, if not infinite, dramatically larger than the time required for such negative behavioral consequences to emerge.
Indeed, Fig 7 shows that even if all members of the dominant group are repeatedly replaced with enlightened individuals, who do not discriminate between groups, i.e. 8i,t ρ i:J,t = ρ i:I,t , members of the subordinate group will continue to distrust members of the dominant group and exhibit an unwillingness to collaborate with them. The mechanism behind this is the same as that underlying persistence of stigma: over time the learning rate declines (see Fig 3), which causes the members of subordinate group to preserve their beliefs despite the increased collaboration from the members of the dominant group. Consequently, intergroup mistrust and non-collaboration persists. Note that Fig 7 shows an extreme case of instantaneous generational change one would never observe in a real society. If we assume a more realistic process of generational replacement, where members of the prejudiced dominant group are gradually replaced with enlightened individuals, the negative behavioral effects of initial stigmatization are even more resistant to change (see S3 Fig).
Despite the difficulty of alleviating the negative effects of initial prejudices, however, we find that delaying efforts to do so entails further costs for society. Fig 8 shows that if society delays enlightenment, the amount of unrecoverable trust on the part of mistreated subordinate group members becomes even greater. Another neglectful generation, therefore, may cost the society additional losses in terms of intergroup collaboration.

Simulating societies
Although agent-based models are of course artificial in nature, they have the benefit of examining how well-documented experimental effects play out over time, in populations of varying composition and with relevant parameters systematically manipulated in a manner that would be impossible in a real world experimental setting. The simple assumptions in our simulations are supported by copious experimental and field evidence [1,12,15]. Thus, albeit artificial, the models can inform our understanding of how known effects evolve over time in interaction with one another. The basic pattern of our results holds across a wide range of assumptionswe manipulate variables such as absolute and relative group size, high vs. low trust environment, distribution of initial beliefs, strength of initial beliefs, and speed of generational replacement, and show the key findings to be robust to these parameters (see S1 and S2 Files, S1-S12 Figs).
As in related prior work [11,26], the comparisons to contemporary real societies are conceptual rather than literal, reproducing broad social patterns seen around the world rather than corresponding to empirical data on trust levels or income gaps in a single specific society. This follows on earlier work by [34], who shows that a few simple principles can reproduce the generally observed pattern of residential segregation across societies, without arguing this corresponds precisely to residential patterns in the United States, Malaysia, Russia, or Belgium.
A strength of the agent-based modeling is to show that a given set of select factors can be sufficient (albeit not necessary) to produce an outcome of interest. A core principle is therefore to include as few focal variables in the model as possible [35]. There are, however, numerous other psychological biases that could be considered in future research when modeling intergroup dynamics, such as generalization of prejudices from one social outgroup to another [8], the rationalization of prejudice via dissonance or self-perception [36], and discrepancies between perceived and actual norms [37,38], among many others.

Conclusion
Two subjective psychological factors, specifically 1) initial prejudice against a subordinate group among early members of a society's dominant group and 2) the presence of some degree   do not discriminate. The main observation is that even perfect enlightenment, when put into action at such a late stage in societal development, cannot revive intergroup trust (cf. Fig 5).