Outgroup Homogeneity Bias Causes Ingroup Favoritism
OOutgroup Homogeneity Bias Causes Ingroup Favoritism
Marcel Montrey ([email protected])
Department of Psychology, McGill University2001 McGill College Avenue, Montreal, QC H3A 1G1 Canada
Thomas R. Shultz ([email protected])
Department of Psychology and School of Computer Science, McGill University2001 McGill College Avenue, Montreal, QC H3A 1G1 Canada
Abstract
Ingroup favoritism, the tendency to favor ingroup over out-group, is often explained as a product of intergroup conflict, orcorrelations between group tags and behavior. Such accountsassume that group membership is meaningful, whereas humandata show that ingroup favoritism occurs even when it confersno advantage and groups are transparently arbitrary. Anotherpossibility is that ingroup favoritism arises due to perceptualbiases like outgroup homogeneity, the tendency for humans tohave greater difficulty distinguishing outgroup members thaningroup ones. We present a prisoner’s dilemma model, whereindividuals use Bayesian inference to learn how likely oth-ers are to cooperate, and then act rationally to maximize ex-pected utility. We show that, when such individuals exhibitoutgroup homogeneity bias, ingroup favoritism between arbi-trary groups arises through direct reciprocity. However, thisoutcome may be mitigated by: (1) raising the benefits of coop-eration, (2) increasing population diversity, and (3) imposing amore restrictive social structure.
Keywords: ingroup favoritism; outgroup homogeneity; directreciprocity; Bayesian learning; conditional expected utility
Introduction
Ingroup favoritism is the tendency for people to favormembers of their own group over members of othergroups. It manifests as a bias in how people evaluate oth-ers (Brewer, 1979; Galinsky & Moskowitz, 2000), distributerewards (Tajfel, Billig, Bundy, & Flament, 1971), mete outpunishments (Bernhard, Fischbacher, & Fehr, 2006), and de-cide whether or not to cooperate (Dorrough, Gl¨ockner, Hell-mann, & Ebert, 2015). Though readily elicited in both natu-ral (Rand et al., 2009) and arbitrary groups (Efferson, Lalive,& Fehr, 2008; Galinsky & Moskowitz, 2000), the existenceof ingroup favoritism is puzzling. It often neither improvesthe population’s average outcome, nor maximizes that of theindividual (Nakamura & Masuda, 2012). Disagreement evenexists as to whether ingroup favoritism is better understood asa preference for improving the welfare of ingroup over out-group, or as a product of divergent beliefs about how thesegroups behave (Everett, Faber, & Crockett, 2015). However,empirical work suggests that people generally expect ingroupmembers to act in a cooperative manner (Brewer, 2008; Ya-magishi, Jin, & Kiyonari, 1999), and meta-analysis confirmsthat this expectation is indeed stronger toward ingroup thanoutgroup (Balliet, Wu, & De Dreu, 2014). A promising av-enue for explaining ingroup favoritism therefore seems to beunderstanding how people arrive at these beliefs. In short, why are ingroup members seen as more cooperative than out-group ones?Many theoretical models have addressed this question.One common approach is to assign phenotypic tags to indi-viduals, and then see what is required to elicit ingroup fa-voritism. Such models have shown that ingroup favoritismmay be selected for when tags are not arbitrary, but rather cor-relate with behavioral traits (Jansen & van Baalen, 2006; Ma-suda & Ohtsuki, 2007; Traulsen, 2008). These traits typicallyinclude willingness to cooperate, or suitability as a cooper-ative partner. Ingroup favoritism may thus occur when tagsconvey information useful in guiding the individual’s ownactions. Other models explain ingroup favoritism as a prod-uct of intergroup conflict (Choi & Bowles, 2007; Garc´ıa &van den Bergh, 2011; Konrad & Morath, 2012), where groupmembership may be arbitrarily decided, but remains relevantfrom a competitive point of view. However, a classic em-pirical finding is that humans show ingroup favoritism evenwhen groups are both explicitly arbitrary and functionally ir-relevant (Billig & Tajfel, 1973; Locksley, Ortiz, & Hepburn,1980). So why should ingroup favoritism occur even whengroup membership is meaningless, and such outcomes aremaladaptive?One explanation is that ingroup favoritism may arisethrough cognitive or perceptual limitations (Masuda, 2012).For instance, humans are known to perceive outgroup mem-bers as more similar to one another than ingroup members, abias known as outgroup homogeneity (Judd & Park, 1988).By approximating individuals’ characteristics through a sin-gle group stereotype, this may serve to reduce cognitive bur-den (Masuda, 2012). Masuda (2012) studied the implicationsof such a bias on indirect reciprocity, where cooperation isconditioned on whether or not partners maintain a good repu-tation. In the simplest such scheme, an individual’s reputationimproves when it is observed to cooperate, and suffers whenit is observed to defect; in more complicated schemes, reputa-tion may, for example, also be gained by being observed pun-ishing a defector, or lost by being observed cooperating withone. To simulate outgroup homogeneity, individuals were al-lowed to observe accurate reputation information about in-group members, but only group-level information about out-group members. Ingroup favoritism occurred, but only whenadditional assumptions were invoked, such as individuals us-ing a different rule for attributing reputation to ingroup than a r X i v : . [ ec on . T H ] A ug o outgroup members. A follow-up model by Nakamura andMasuda (2012) eliminated the need for such double stan-dards, and also produced ingroup favoritism through indirectreciprocity. However, this time the result was contingent onreputation information being only shareable within groups,but not between them.Here, we show that complex rules for assigning and shar-ing reputation are not needed to explain ingroup favoritismbetween arbitrary groups. Rather, outgroup homogeneitybias may drive ingroup favoritism through a much simplermechanism: direct reciprocity (learning through personal ex-perience). We create an agent-based computational model,where individuals are assigned arbitrary group tags, and thenplay a prisoner’s dilemma (PD) game. These individuals useBayesian inference to learn how likely others are to cooper-ate or defect, and then act rationally by maximizing their con-ditional expected utility. We show that introducing outgrouphomogeneity bias into this minimal setting is sufficient to pro-duce strong ingroup favoritism, and propose several ways ofmitigating this outcome. Model
Prisoner’s Dilemma
We consider a PD game where pairs of neighboring individ-uals interact by either cooperating (C) or defecting (D). Thegame is parameterized by two values: the benefit of receivingcooperation, b , and the cost of cooperating, c . When both in-dividuals cooperate, both receive the benefit of cooperation,but pay the cost of cooperating, b − c . If one individual de-fects while the other cooperates, then the cooperator pays thecost while receiving no benefit, − c , while the defector paysno cost but receives the full benefit, b . When both individu-als defect, neither receives the benefit nor pays the cost. Thefollowing table summarizes the row player’s payoffs:C DC b − c − c D b b > c >
0, each player’s payoff is always im-proved by defecting, no matter what the other player does.This makes the game a dilemma, because although the bestindividual outcome is unilateral defection, the best averageoutcome is mutual cooperation.
Social Structure
In PD, ingroup favoritism is operationalized as a higherrate of cooperation toward ingroup partners than outgroupones (Dorrough et al., 2015; Fu et al., 2012; Gray et al., 2014;Masuda, 2012). For ingroup favoritism to be possible, coop-eration must also be possible. By constraining which individ-uals interact, we promote repeat interactions, which in turnpromotes cooperation (Szab´o & F´ath, 2007). For each run,we generate a random r -regular graph (Bollob´as, 2001) with1000 vertices, using Steger and Wormald’s (1999) algorithm.Each vertex represents an individual, and each edge repre-sents a connection between neighbors. This graph governs interactions by limiting individuals to playing PD exclusivelywith their neighbors. Group Tags
Individuals are divided into m groups, where group member-ship is represented by a tag visible to all other individuals.By default, m =
2, though it may take other values, as long as m >
1. Otherwise, tags cease to represent group membership,and instead become a universally shared characteristic. Eachindividual is randomly assigned a tag, such that each grouphas the same initial number of members. When replacementoccurs, newcomers are assigned a tag uniformly at random.
Rational Bayesian Learning
Learning involves estimating a pair of parameters for eachpartner i that the individual interacts with. The first parameter p i represents the estimated probability that partner i will co-operate with the individual, given that the individual cooper-ates with that partner, Pr ( C i | C ) . The second parameter q i es-timates the probability that partner i will cooperate, given thatthe individual defects against that partner, Pr ( C i | D ) . Becausethe game is simultaneous, actions cannot be conditioned onthose of the partner. However, there is no a priori reasonfor individuals to know this, and indeed repeated interactionscause p i and q i to diverge, as individuals change their be-havior in response to that of their partner. Individuals useBayesian inference to arrive at point estimates for p i and q i .Here, the posterior predictive distribution corresponds to theposterior mean (Griffiths, Kalish, & Lewandowsky, 2008), p i : = n CC + α + n CC + n CD + α + β + q i : = n DC + α + n DC + n DD + α + β + , (1)where n AB counts the number of times the individual took ac-tion A when partner i took action B . Similarly, α and β arepseudocounts (Griffiths et al., 2008) that encode prior knowl-edge or expectations about the frequency of cooperation anddefection, respectively. These take the value α = β = p and q valuesfor each partner i . However, individuals exhibiting outgrouphomogeneity bias do not distinguish between outgroup mem-bers, so they instead track a single pair of values, p j and q j ,for each outgroup j . Outgroup homogeneity thus causes indi-viduals to treat outgroups as if they were a single individual.Individuals act rationally on their Bayesian estimates, so asto maximize their conditional expected utility (Jeffrey, 1990).More formally, an individual cooperates if pb − c > qb , (2)and defects otherwise. To give individuals a chance to sam-ple both actions, we implement a small trembling-hand pa-rameter (Selten, 1975). When an individual selects an action,with a small probability ε = .
01, it takes the opposite actionigure 1: Ingroup and outgroup cooperation rates over time,in the absence of outgroup homogeneity bias. Cooperationrates climb rapidly as individuals learn that defection is metwith defection. Ingroup cooperation rates mirror outgroupcooperation rates, because group membership is irrelevant.instead. Removing this parameter (setting ε =
0) does notqualitatively alter our results.
Simulation
At each time step, individuals interact with their neighborsin random order. Interactions involve selecting an action (Cor D), and then playing PD. After each interaction, individu-als note the outcome of the game, and then update their es-timates p and q . Once everyone has finished playing, indi-viduals are subjected to a 0 .
01 probability of being replaced.Newcomers are assigned a group tag uniformly at random,and have no knowledge of their predecessor’s p and q val-ues. Because there is no selection over genotypes, ingroupfavoritism cannot evolve, but arises through phenotypic plas-ticity (i.e. learning) instead. We run simulations for 1000time steps, by which time cooperation rates have long stabi-lized. All results are averaged across 20 independent runs,and stabilized cooperation rates are further averaged over thelast 100 time steps. In all figures, line width represents 95%confidence intervals. Results
We first consider unbiased individuals, connected to r = b =
3) moderately exceeds the cost of giving it ( c = q . Withunilateral cooperation seeming increasingly unlikely, qb fallsbelow pb − c , and individuals seek out mutual cooperationinstead. As cooperation is met with cooperation, estimates of p increase, and high rates of cooperation ( ∼ m = i is an ingroup member, then the individual revises itsbeliefs about that partner’s willingness to cooperate, and p i declines. Soon, pb − c drops below qb , and the individualceases to cooperate. Once partner i learns that defection doesnot evoke cooperation, its q falls low enough for it to alsoseek mutual cooperation. Any successful instance of mutualcooperation promotes further cooperation, causing p valuesto increase, entrenching that behavior. However, if partner i isan outgroup member, then the individual does not know whoto blame for the partner’s unilateral defection. The individualthus revises its beliefs about the entire group’s willingness tocooperate, and p j declines. This causes the individual to pun-ish not just the defecting partner, but also any others from thatigure 3: Stabilized ingroup and outgroup cooperation ratesfor various benefit-to-cost ( b / c ) ratios. Increasing the b / c ra-tio favors cooperation more broadly by making the temptationto defect less appealing, thus reducing ingroup favoritism.group. Those neighbors then punish the focal individual, aswell as members of its group, for this seemingly unprovokedhostility. Intergroup defections thus bring about not just pun-ishment of the offending individual, but also a cascade of re-tributive defections. Outgroup cooperation is prohibitivelydifficult to establish and maintain under such conditions, re-sulting in strong ingroup favoritism.We next consider various parameters that may mitigate thisoutcome. For example, increasing the trembling-hand param-eter ε reduces ingroup favoritism, albeit in a somewhat trivialmanner. The more errors individuals commit in taking theirdesired action, the more this increases (unwanted) outgroupcooperation and decreases (desirable) ingroup cooperation.Such effects offer relatively little additional insight, however,because ingroup favoritism is merely harder to enact, ratherthan less sought after.Of greater theoretical interest is the effect of increasing thebenefit-to-cost ratio of cooperation. Doing so raises both in-group and outgroup cooperation, which in turn reduces in-group favoritism (Figure 3). Higher b / c ratios represent morecooperative games, where mutual cooperation is more re-warding, and the temptation to defect is reduced (i.e. Inequal-ity 2 becomes primarily driven by p and q values, rather than c ). Whereas the ingroup cooperation rate rapidly approachesa ceiling, the outgroup cooperation rate has more room togrow.Another parameter of interest is the number of groups, m .This may be regarded as a measure of the population’s diver-sity. Increasing the number of groups does not affect ingroupcooperation, but increases outgroup cooperation, thus reduc-ing ingroup favoritism (Figure 4). Intuitively, if an individ-ual’s neighbors all belong to different groups, then trackingthese groups’ aggregate behavior is equivalent to tracking in- Figure 4: Stabilized ingroup and outgroup cooperation ratesfor various numbers of groups ( m ). Increasing population di-versity reduces ingroup favoritism, because fewer neighborsshare the same outgroup. This limits the scope of breakdownsin cooperation caused by outgroup homogeneity bias.dividual behavior. The more diverse the population, the lessmeaningful outgroup homogeneity is as an approximation.More practically, when fewer neighbors share group member-ship, breakdowns in cooperation result in smaller cascades ofretributive defections.Finally, the number of neighbors that individuals interactwith, r , is also relevant. If there are relatively many groupsin the population (e.g. m = m = r = Discussion
We have presented an agent-based computational model of aPD game, where outgroup homogeneity causes ingroup fa-voritism between arbitrary groups. Previous models have re-lied on indirect reciprocity (observing others’ interactions) toproduce such an outcome. However, these only producedingroup favoritism if they invoked additional factors. Forinstance, Masuda (2012) found that reputation assignmentrules had to differ for ingroup and outgroup members, whileNakamura and Masuda (2012) found that the flow of rep-utation information had to be severed between groups. Bycontrast, our model’s results are driven by direct reciprocity(learning from personal experience), which obviates the needfor additional assumptions about how others’ interactions areevaluated, or how that information is shared. The individu-als we model leverage a minimal set of cognitive capacities.igure 5: Stabilized ingroup and outgroup cooperation ratesfor various neighborhood sizes ( r ). If there are many groupsin the population (here m = b / c ratio thus minimizes thesecompetitive aspects, and emphasizes the cooperative ones in-stead. Reducing the temptation to defect, relative to the ben-efits of mutual cooperation, causes individuals to take morerisks to establish mutual cooperation, and to recover it morereadily when it breaks down.Finally, our model also predicts that ingroup favoritismmay be reduced by increasing population diversity. Whenfewer neighbors belong to the same group, this limits thecascades of defection caused by outgroup homogeneity bias.This is also why lowering the number of neighbors can beeffective. In both cases, the chances of being punished foran ingroup member’s actions are reduced. However, this rea-soning only applies if group membership is indeed arbitrary.The role of diversity in ingroup favoritism is typically studiedthrough the lens of group differences, which add considerablecomplexity (Everett et al., 2015). Similarly, if conflicts existalong group lines, increased diversity may not necessarily re-duce ingroup favoritism (Hewstone et al., 2014). No doubt,a great deal of real-world ingroup favoritism is intertwinedwith such pragmatic concerns. However, because ingroup fa-voritism occurs even when such concerns are irrelevant, un-derstanding such social factors could offer promising ways ofaddressing it. Acknowledgments
We thank an anonymous reviewer for their helpful comments.
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