Communitarian versus Universalistic Norms ∗

The celebration of communitarianism by political philosophers (Sandel, M. 1982 Liberalism and the Limits of Justice. Cambridge: Cambridge University Press) has apparently been extended to strategic analyses of ascriptively attuned norms (Fearon, J. and D. Laitin. 1996. “Explaining Interethnic Cooperation.” American Political Science Review 90: 715–735) — an intriguing development, given game theory’s individualistic premises. We believe, however, that game theory offers little comfort to prescriptive theories of communitarian rules: a hardheaded strategic analysis supports the Enlightenment view that such norms tend to be Pareto inefficient or distributionally unjust. This survey uses a specific criterion— supporting cooperation as a Nash equilibrium — to compare communitarian norms, which turn on people’s ascriptive identities, to universalistic ones, which focus on people’s actions. We show that universalistic rules are better at stabilizing cooperation in a broad class of circumstances.Moreover, communitarian norms hurt minorities the most, and the advantages of universalism become more pronounced the more ascriptively fragmented a society is or the smaller is the minority group. Though they have hadwell-known disagreements,most communitarians andmany identity theorists share a focus on ascriptive characteristics: race, ethnicity, gender, and (especially for communitarians) family. For example, Michael Sandel, one of the best-known communitarians, wrote that for people “bound by a sense of community. . .community describes. . .not a relationship they choose (as in a voluntary association) but an ∗ We would like to thank Russell Hardin, Nannerl Keohane, Robert Keohane, Keisuke Nakao, and an anonymous referee for their helpful comments. MS submitted 22 June 2007; final version received 8 February 2008 ISSN 1554-0626; DOI 10.1561/100.00007028 © 2008 J. Bendor and D. Mookherjee 2 Bendor and Mookherjee attachment they discover” (1982, p. 152) — i.e., Tonnies’ Gemeinschaft (1887). And though some identity theorists (e.g., Young 1990, pp. 232–236) have criticized communitarians for emphasizing certain ascriptive groups— families, villages and other “communities of place” — they celebrate other kinds of ascriptive identities such as gender. Further, both types of scholars criticize the individualism and “abstract universalism” of liberal political theory (Young 1990, p. 228). Some of these criticisms were based on serious misunderstandings of Enlightenment liberalism. In particular, advocates of universalism have never advocated eliminating communities or the tight interpersonal bonds nourished in them. As Stephen Holmes (1994) put it, “the much reviled “Enlightenment project” did not aim impossibly to extirpate particular attachments from the repertoire of human interaction. [Liberals] strove to dilute or relativize group identity just enough to increase the chances for peaceful coexistence and mutually beneficial cooperation. . .Liberals are not blind to loyalty, therefore, but instead assume that loyalty is sometimes good and sometimes bad, depending largely on the way conflicting affliations and affinities are handled politically. While liberals are not anticommunitarian in a militant sense, they reasonably refuse to apotheosize loyalty as the source of all meaning and the highest human good, insisting that a sharp distinction be made between group identifications to be encouraged and factionalisms and xenephobias to be discouraged” (1994, pp. 601–602). Relatedly, some empirically oriented scholars (e.g., Horowitz 1985) continue to stress the dark side of ascriptively defined identities such as ethnicity, with xenophobia and violence leading the list of negative effects. Nevertheless, although Enlightenment universalism has been vigorously defended on both normative (Okin 1989; Hardin 1995; Barry 2001; Benhabib 2002) and empirical grounds, liberal political theory no longer enjoys the overwhelming intellectual dominance it once had. Now, most aspects of the theory are contested. Most social scientists and philosophers recognize that Hobbes’ problem of order does not vanish with the wave of a magic wand labeled “community.” Hence, the revived interest in Gemeinschaft has been complemented bymore attention to how such systems regulate themselves. A major control mechanism in communities is norms: informal rules backed by sanctions.1 Eventually, rational choice theorists began to explore norms (e.g., Calvert 1995); a few even began to examine communitarian rules (e.g., Bendor and Mookherjee 1990; Hardin 1995; Wintrobe 1995; Fearon and Laitin 1996; Bowles and Gintis 2004). Although some of these writers (prominently Hardin) have criticized communitarianism sharply, others seem more positive. For example, both Bendor and Mookherjee (1990) and Fearon and Laitin (1996) can be read as saying that norms with ascriptively based sanctions can effectively regulate interethnic conflict. Bowles and Gintis (2004) argue that informational problems make communitarian codes useful.2 1 This is the standard sociological definition of norms (e.g., Homans 1950, p. 123). 2 However, rational choice modelers who say positive things about communitarian norms usually do so via theories of the second best: given certain real-world constraints, ascriptively based norms may be efficient. (E.g., in Fearon and Laitin’s model intra-ethnic sanctions for inter-ethnic crimes are desirable when A’s cannot ascertain which B cheated their kinsman. Given this informational constraint, the A’s recourse is to punish the B’s collectively; a spiral of interethnic violence could Communitarian versus Universalistic Norms 3 When rational choice theorists, with their natural inclinations toward individualism and associated liberal theories, begin to see benefits of communitarian norms, one wonders whether the celebration has gone too far. Indeed, so we think. In this survey we seek to redress the balance by arguing that the benefits of communitarian norms have been exaggerated.3 We argue that communitarian norms are often normatively deficient, even when the primary part of a communitarian rule prescribes cooperating with Outsiders (people outside one’s group) as well as with Insiders (people in one’s group). In this latter respect they do not differ from the realistic version of universalism, which — as Holmes suggested — also allows for more cooperation within groups than between them. The key difference is the nature of sanctions levied on transgressors of the cooperative norm. Universal norms require punishments to be applied uniformly; the ascriptive features of deviants or victims are considered irrelevant. In contrast, sanctions in communitarian norms do differentiate on such characteristics. (For example, the equilibrium studied by Fearon and Laitin exhibits xenophobic behavior: members of the victim’s group punish a deviator who is an Outsider; members of the wrong-doer’s group do nothing.) We show that such communitarian norms are generally less effective in upholding cooperation than universalistic ones: in a significant set of circumstances such norms fail to support inter-group cooperation when universalistic rules could work.4 Further, we show that communitarian norms hurt minorities the most: the smaller the minority, the greater the harm caused by these norms. Thus more than Pareto efficiency is at stake: distributive justice is also involved. The survey is organized as follows. Section “THE CONCEPT OFNORMS” briefly examines the fundamental concept of norms. Section “DURKHEIMIAN MECHANICAL SOLIDARITY AND SUPERFLUOUS THIRD-PARTY SANCTIONS” establishes that when interpersonal relations are homogeneous, all norm-like strategies — universalistic or communitarian — are in a significant sense superfluous: for stabilizing an important class of outcomes, these strategies add nothing above and beyond what can be sustained by dyadic ones alone (Theorem 1). Because this result covers all third-party sanction strategies, it identifies conditions under which universalistic norms are no better than communitarian ones. Section “DURKHEIMIAN ORGANIC SOLIDARITY” then establishes our central positive result: given natural heterogeneities in interpersonal relations, universalistic norms sustain cooperation as Nash equilibria more effectively than particularistic ones do (Proposition 1). ensue.) In contrast, many communitarians and identity theorists seem to be saying — though not with this language — that certain ascriptively-attuned rules are part of a first-best system. We side with the game theoretic perspective and, more importantly, with the Enlightenment view that communitarian norms are typically either Pareto deficient or unjust. 3 Henceforth we shall use “communitarian norms” as shorthand for “norms based on membership in ascriptively defined groups.” For the sake of variety we sometimes follow sociological usage and call such norms “particularistic.” (“Communitarian” is more common in political science; “particularistic,” in sociology.) 4 We will show that this conclusion is consistent with the empirical regularity that cooperation within ascriptively defined groups (e.g., ethnicities) is more common and more stable than is cooperation between such groups. 4 Bendor and Mookherjee Section “COMMUNITARIAN NORMS HURT MINORITIES THE MOST” analyzes the impact of communitarian norms on minority groups. Proposition 2 establishes that such norms hurt minorities the most. Further, the advantages of universalism become more pronounced the more lopsided are the sizes of the majority and minority groups (Proposition 3) or the more ascriptively fragmented a society is (Proposition 4). Section “IMPERFECTMONITORING” extends our central result to contexts of fragmentary information and of imperfect monitoring: provided that the error rate is not too great, it still pays to have everyone who has relevant information punish deviants (Proposition 5). Section “CONCLUSIONS” concludes. Because tractability pressures intensify as the analysis proceeds, we impose increasing amounts of structure as we move from section to section. THE CONCEPT OF NORMS Before presenting our formal model, we must unpack a key concept: norms. For a major concept in the social sciences, ordinary language and academic definitions exhibit a surprising degree of consistency: in both, a norm is a rule of action that prescribes or proscribes certain actions.5 Sociological definitions usually add that the rule is informal rather than formal, thus distinguishing norms from laws, and that norms are backed by sanctions.6 We hew to all of these parts of the sociological notion: in this survey, norms are informal social rules backed by sanctions. Under the sociological conception, norms may enhance conformity to a code for three reasons.7 First, humans — even young ones (Kochanska and Thompson 1997) — sometimes internalize norms.8 Internalization produces what Ellickson (1991) calls firstparty control of behavior: the more a decision maker believes that, e.g., the norm of honesty is a legitimate rule, the less likely s/he is to lie. Second, people hurt by the violation of a norm may punish the deviant — Ellickson’s second-party control. Third, norms are usually backed by third-party sanctions: Susan punishes Bill if Bill has cheated Joe, even if Bill cooperated with Susan.9 5 See Gibbs (1981, pp. 7–9) for an extensive review of sociological definitions. 6 For example, in the Webster’s Ninth Collegiate Dictionary’s first definition of “norm” (“a principle of right action binding upon themembers of a group and serving to guide, control or regulate proper and acceptable behavior”), sanctions are implicit in the statement that behavior is controlled and regulated. Homans’ definition makes sanctions explicit. 7 The following is taken from Bendor and Mookherjee (1990). 8 Most developmental psychologists now agree that children do not passively “absorb” parental socialization; they actively reconstruct what adults try to teach them. Nevertheless, specialists also agree that at the end of the day children do often internalize parental values. On both points see Kuczynski and Grusec (1997). 9 Empirically, all three aspects of norms can occur simultaneously, e.g., a person may feel morally compelled to tell the truth, those victimized by a lie may retaliate, and third parties may punish the miscreant. Because ascertaining the strengths of these different controls is difficult, scholars often study the effects of one kind of control in isolation, holding the other two constant experimentally or analytically. Communitarian versus Universalistic Norms 5 Second-party control is a weak indicator of a norm because it does not rely on social ties; it can arise even in situations characterized only by bilateral relationships. In contrast, third party sanctions are a quintessentially social dimension of norms: people who are not parties to an original interaction become involved because social networks connect them to the original players and because community-wide codes of conduct, germane to the original interaction, were violated.10 We use the important distinction between secondand third-party controls in our analysis. Game-theoretically, player i’s strategy is dyadic, or uses bilateral sanctions, if its behavior toward any other player j is based only on the history of play between i and j. The strategy of i is norm-like, or uses third-party sanctions, if at some time i’s conduct toward j is based on j’s behavior toward some third player k. DURKHEIMIANMECHANICAL SOLIDARITY AND SUPERFLUOUS THIRD-PARTY SANCTIONS In this section, we focus on a group where all bilateral relationships are homogeneous in all strategically relevantways: payoffs, information, and frequency of interaction.Ascriptive differences may exist, but if so, they do not affect any payoff-relevant attributes. Consider, for example, an ideal-typical village in which networks are maximally dense — every person encounters everyone else in every period — and all pairs play the same game of bilateral exchanges. Through gossip and observation everybody knows everyone else’s business: what happened in all past interactions is common knowledge to everyone. Clearly, this community is tightly-knit. Nevertheless, in this prototypical village we show below that norms do not matter in an important sense: whenever the strongest such norm can uphold adherence to prescribed symmetric behavior as a Nash equilibrium, so can some dyadic strategy. Equivalently, if no dyadic strategy can ensure that people do what they are supposed to, then neither can any norm. So norms are useless in this tightly knit village.11 To see why these properties hold, consider the interactions among three members of the village, i, j, and k. Suppose that in period t player i is thinking about cheating j. Suppose further that no dyadic strategy packs enough punch to deter i: even if j 10 Although our models do not directly represent internalization, they do lend themselves to such an interpretation. If i sanctions j for cheating k, even though j did not harm i, one can well believe that i, adhering to fair dealing as a code of conduct, is morally outraged by j’s behavior and so punishes j (Fehr and Fischbacher 2004). However, as Ellickson’s categorization makes clear, the standard sociological conception of norms involves multiple, redundant controls. If socialization worked perfectly then the other two controls would be superfluous. However, socialization is never perfect — to believe otherwise is to succumb to the “overly socialized” view of humans (Wrong 1961) — so secondand third-party controls also matter. 11 Because they use third-party sanctions, norm-like strategies are more complex than dyadic ones. So if using more complex strategies imposes a cost or if simpler strategies are lexicographically preferred then normswould be Pareto dominated in our ideal-typical village. To see the implications of taking strategic complexity into account, see, e.g., Banks and Sundaram (1989) or Binmore and Samuelson (1992). 6 Bendor and Mookherjee retaliates by punishing i in all subsequent encounters, cheating j today would still be i’s best move. How would i’s thinking be affected if he knew that he would be punished not only by j but also by a third party, k? Because this doubles the maximal punishment that j alone can unleash, it seems obvious that this norm-like rule would restrain i in some settings in which dyadic sanctions fail. But this reasoning ignores two key related facts. First, it does not analyze i’s optimal deviation in period t. Second, it overlooks the fact that i’s relations to j and to k are identical. Hence, if it is optimal for i to cheat j today, given that only j will retaliate, then it must be best for i to cheat k as well, anticipating k’s bilateral response. But then k, as a third party trying to enforce cooperation between i and j, has nothing with which to threaten i, who is contemplating defecting against k anyway for dyadic reasons. Thus, if bilateral sanctions cannot support cooperation here then neither can any norm-like strategies. (For further details on this example, see Bendor and Mookherjee (1990).) It is well-understood that informalmethods of social control—e.g.,maintaining cooperation in iterated PDs by strategies of conditional cooperation— generally work better when networks are dense andmonitoring is informative. (See Ellickson (1991) for a good summary of this perspective.) One might call these village-attributes. However, many scholars also maintain that one type of informal control, norms, are especially useful in village-like communities (e.g., Ostrom 1990, pp. 88, 89; Ellickson 1991, pp. 167–169, 177–182). These two points are easily confused with each other. As the preceding example suggests, they are logically unrelated. Our first result, Theorem 1, generalizes this example. The next section shows that what enables norms to be more efficacious than dyadic strategies is relational heterogeneities—Durkheim’s organic solidarity — not the village attributes at all.12 The latter strengthens all kinds of informal social controls, including dyadic ones. These ideas generalize considerably. Consider a finite set of players, N = {1, . . . , n}, with n ≥ 3 to allow for third-party sanctions. As in the above example, all pairwise relations in this community are the same. Formally, we say that the (i, j) relation and the (i, k) relation are homogeneous if two conditions hold for all t: (1) i and j meet in period t if and only if i and k also meet in t; (2) i and j play the same game in t as i and k play in t. In addition, we shall assume payoff separability throughout this survey: a player’s total payoff in any period is simply the sum of her payoffs from all her different bilateral relationships. Although the notion of two relations being identical is rather intuitive, formalizing an intuitive idea usually introduces some conceptual nuances. Given that game-theoretic analyses of norms usually assume a conventional setting — the agents are playing a standard repeated game—understandingwhat relational homogeneity does not presume is important. For several reasons it does not presuppose a standard repeated game. First, people may be playing a finite game, with a commonly known ending date. Second, the nature of interactions could change over time. Imagine a cohort of people, all the same 12 “Mechanical solidarity [i.e., where everyone and their ties are alike] does not bind men together with the same strength as does the division of labour” (Durkheim 1997 [1893], p. 123). The division of labor creates relational heterogeneities. Communitarian versus Universalistic Norms 7 age, who together go through childhood, adulthood and old age. All relations are the same at any one date; all change the same way as people age. Finally, relational homogeneity does not require that interaction probabilities are stationary: meetings could be based on a nonstationary calendar. (For example, people meet at the start of the full moon and never otherwise.) Thus the notion of relational homogeneity is not confined to standard repeated games; it can be applied to a much wider set of environments. Whenever players meet they play a game that belongs to a class of oneshot games, G. (The temporal sequence of games is exogenously fixed and is common knowledge.) Because norms include sanctions for deviations,G is defined by the kind of punishments that are available. Throughout this paper we focus on games with simple punishment by requiring that every game in G has an action, ap, with the following properties: it minmaxes the other player and it is a best response to itself.13 Requiring that each game inG has this kind of sanction simplifies our analysis greatly: it implies that irrevocably deploying ap after someone deviates is the maximal credible punishment (Abreu 1988) in any subgame-perfectNash equilibrium.Hencewe can easily characterize the set of (subgame-perfect) Nash equilibrium outcomes: those that can be sustained by the threat of reverting to this punishment path following any deviation from the prescribed pattern of behavior. We assume that every game in G is symmetric: the same actions are available to both players and reversing actions reverses payoffs. The set of actions in a particular game, say τ, is A(τ); every action-set is finite.14 Let v1τ(ax(τ), ay(τ)) be player 1’s payoff when she does ax(τ) and player 2 uses ay(τ) in game τ. Similarly, v2τ(ax(τ), ay(τ)) is player 2’s payoff from this pair of actions. Because the game is symmetric, v1τ(ax(τ), ax(τ)) = v2τ(ax(τ), ax(τ)) in any game inG, so we suppress players’ subscripts when both players select the same action. Players’ utilities are additive across their pairwise games and over time, and future payoffs are discounted by a common parameter δ ∈ (0, 1). Theorem 1 Suppose that all bilateral relationships are homogeneous and every oneshot game they play belongs to G. Then any sequence of symmetric outcomes can be supported by a subgame perfect Nash equilibrium by any norm-like strategy if and only if it can be supported by some dyadic strategy.15 Theorem 1 is not confined to standard repeated games or to stationary norms. (A natural example of a nonstationary norm: one kind of behavior is prescribed for the young and another for the old.) But to get a sense for the result’s content let us focus briefly on stationary norms used in a conventional repeated game. People in this context can adhere 13 Thus G includes the prisoners’ dilemma-type games, but many others as well, e.g., Stag Hunt, in which mutual cooperation is a Nash equilibrium in the oneshot game. Such coordination games can represent interactions in cohesive communities inwhich altruism or norm-internalization transform objective, PD-like payoffs into Stag Hunt-like utilities. 14 Although most of our results extend to games with compact action sets, such an extension provides little insight. 15 Note the restriction to symmetric outcomes, where both members of a given bilateral relationship choose the same action. See Bendor and Mookherjee (1990) and Section “DURKHEIMIAN ORGANIC SOLIDARITY” for further discussion of this restriction. 8 Bendor and Mookherjee to a stationary social rule with a very simple structure. For instance, by coding members of a community as being in either Good or Bad Standing (a sociologically intuitive notion), a Grim Trigger-type norm could be defined as follows. (1) In every period every player must be categorized as being either in Good or Bad Standing. (2) Everyone is in Good Standing initially. (3) A player is in Good Standing in t + 1 if and only if in t she was in Good Standing and played the socially prescribed action, a , with every partner who was in Good Standing at that time. (4) Play the punishment action, ap, toward any partner who is in Bad Standing.16 Thus, this norm-like strategy requires that everyone in the community keep track of each other’s social standing. Given a person’s standing, the prescribed action follows immediately. In this world, reputation, in the colloquial sense, is everything. Note that the prescribed outcome of (a , a ) need not be Pareto optimal. (Consider rat races in organizations in which working long hours is inefficient but normatively prescribed.) Of course, if the payoff to the prescribed outcome is less than that of mutual punishment, then that a cannot be supported as a Nash equilibrium. Even then, however, bilateral and norm-like strategies are equivalent: neither works if v(a , a ) < v(ap, ap). Although the example that opened this section presumed dense interaction— people encounter each other in every period — Theorem 1 does not require this temporal density or any particular interaction rate at all. Thus, it shows that what is central is not the cohesiveness of the community, as reflected by, e.g., interaction rates, but the homogeneity of ties. Suppose, for example, that interaction is not stationary; instead, people are more likely to meet on weekdays than weekends. The result still holds because whenever i meets j — no matter how irregular the calendar of interaction — she also meets all other players. Theorem 1 identifies circumstances in which universalistic rules are not superior to particularistic ones: they are equally useless. This property extends to some settings where bilateral relationships are not homogeneous. Suppose there are two ascriptive groups, A and B. All pairs play repeated games. Intragroup and intergroup pairs play different games: specifically, (A,B) pairs play a Prisoner’s Dilemma, while intragroup pairs play a Stag Hunt.17 Between-group relations — all (A,B) pairs — are homogeneous. Then the following properties can be established. (1) Some norms are useful in supporting intergroup cooperation: they can support cooperation with Outsiders as a subgame-perfect Nash equilibrium when the former cannot. For instance, Insiders can punish someone who cheats an Outsider. The difference between inter-group and intra-group ties can allow players to want to deviate in the latter but not in the former. 16 Whereas evolutionary stability requires that norms have a complete metanorm structure (Bendor and Swistak 2001), subgame perfection and the existence of a punishment action that is a best reply to itself do not entail this type of structure. If k knows that j is going to punish him forever with ap, k’s best response is to do likewise, i.e., mutual punishment is a subgame-perfect Nash equilibrium. Hence enforcement is credible on a bilateral basis; metanorms — i sanction j if j does not punish the deviant k— are unnecessary. 17 Stag Hunt’s key property is that mutual cooperation (as well as mutual defection) is a Nash equilibrium in the one-shot game. Communitarian versus Universalistic Norms 9 The sanction imposed by one’s own group can thus effectively deter the cheating of Outsiders. (2) The best communitarian norm is just as effective as the best universalistic rule in supporting intergroup cooperation. In this example, only the threat of sanctions imposed by comrades can credibly inter-group transgressions; Outsiders’ sanctions are impotent because one does not cooperate with people from other groups in the first place. Relational homogeneity of all inter-group matches is driving property (2). If Ai is thinking about cheating Bj then optimal deviation entails cheating all other B’s as well, since their ties to Ai are the same as his relation to Bj . Hence a within-group norm — only Ai ’s kin punish him for his misconduct — is maximally effective; the sanctions of Bj ’s kin add nothing. Hence, no universalistic rule is better than the best particularistic one. A key pattern is emerging: third-party sanctions matter when they do not suffer from correlated failure.Ai ’s cheatingBj is not linked to his cheating otherA’s, but it is perfectly correlated with his hurting other B’s. So Ai ’s ties to other A’s are useful strategic backups to the (Ai ,Bj) pair, but his ties to the other B’s are not. This suggests that in a fully differentiated community — all ties are heteogeneous and do not suffer from correlated failure — universalistic norms will out-perform communitarian ones. We examine this idea next. DURKHEIMIAN ORGANIC SOLIDARITY We now examine a community where relationships are differentiated in two ways. The first arises from a difference in matching patterns: every pair does not meet in every period. Instead, any given players meets exactly one other in any given period. The exact pairing is decided by a random draw. We shall assume that any given pair of players can meet with postive probability in every period, independently and identically across periods. We also assume that a given pair play the same stage-game whenever they meet. Having completed play in period t, the probability that the populationwill be re-matched and play in period t + 1 is a fixed probability δ ∈ (0, 1). With the complementary probability of 1 − δ play ends. Following common usage, we call this social matching, as distinct from the round-robin play examined in the previous section. With social matching, relationships are differentiated ex post even if they are identical ex ante: only some of these relationships result in an actual meeting in any given period, while others do not. As will become evident shortly, this kind of heterogeneity suffices to nullify the result of Theorem 1. Cooperation is harder to sustain by the threat of bilateral sanctions alone: with these, the deviant may not expect to re-encounter the victim soon after the infraction. In contrast, with third party sanctions the wrong-doer could be punished by everyone she meets in all subsequent dates. We also allow a second source of differentiation: the population is broken up into ascriptively defined groups. Relations with Outsiders and with Insiders can differ ex ante as well as ex post: they may involve different pairwise games and different matchingprobabilities.There arem (1 < m ≤ n) ascriptively defined groups, labeled {A1, . . . ,Am}. 10 Bendor and Mookherjee (For convenience, if there are only two groups then they are labeledA andB.)We assume that the groups partition the society: each person belongs to exactly one group.18 Hence ∑m r=1 nr = n, where nr is the number of people in groupAr . If there are only two groups then Bj denotes player j and indicates that he belongs to group B, and analogously for Ai .19 We have defined homogeneous ties in an ideal-typical way. Hence, heterogeneity is a residual category: relations that are not homogeneous must be heterogeneous. Hence, once we have stepped off the well-defined island of homogeneity we are in a more complicated world. Accordingly, we imposemore structure on (1) how players encounter each other and (2) the games they play. We assume that a given pair whenever matched with one another at any date play the same stage-game. It would be simpler to assume that all intergroup pairs are the same in all respects (i.e., payoff and frequency of interaction), and all intragroup relationships are the same. But as this is inessential for the results of this section, we do not make this assumption here. What is essential is that the model represent intergroup cooperation as problematic in some fundamental way. We describe this in more detail below. Regarding the stage games, we restrict attention to two nested subsets ofG. Intragroup pairs play stage games that belong to G′. In addition to the simple punishment feature shared by all games in G, games in G′ have a uniquely efficient cooperative action ac, distinct from ap, such that 2v(ac, ac) ≥ v(ax, ay) + v(ay, ax) for all x, y, with equality holding if and only if x = y = c. Hence, in these games the meaning of “cooperating” is clear: it means playing ac. (Anything other than (ac, ac) we call a noncooperative outcome.) Cooperation may or may not be a Nash equilibrium of the one-shot game: we impose no restriction in this regard. Intergroup pairs play stage games that belong to a subset of G′, called G′′, where cooperation is not aNash equilibrium.Thus, in addition to the twoproperties definingG′, games inG′′ add a third: there is a unique best response to ac, but that response, called ad for “defection”, is not ac. Thus intergroup pairs meet each other in situations where cooperation is collectively valuable but strategically problematic. In contrast, intragroup stage games need not belong to G′′: ascriptive groups might be so cohesive — due 18 We do notmodel group-formation or how different ascriptive labels are activated. (Hence we take no stand on the primordialism-versus-constructivism debate. For a lucid discussion of this controversy, see Laitin (1998), Chapter 1.) However, we do examine the effects of an exogenous change in the number of politically active ascriptive groups. 19 Group membership need not involve any objective differences other than the observable feature (e.g., skin color) that enables ascriptive labeling. Game theorists have known for some time that ascriptively-oriented strategies can be based on such purely nominal differences. See Axelrod (1984, p. 147) for an early analysis. 20 If this condition did not hold then the socially optimal pattern could be to alternate, as in the Battle of the Sexes or in PDs in which 2R < T +S. As is well-known, ascriptive labels can be normatively desirable in such situations: they can aid coordination. 21 The punishment action ap need not be the best response to ac. It is the best response in the ordinary PD, where “punishment” and “defection” are the same, but in some games in G′′ they are distinct actions. Communitarian versus Universalistic Norms 11 perhaps to altruism or because norms prescribing cooperation with Insiders are wellinternalized — that intragroup cooperation could be a Nash equilibrium in one-shot encounters (e.g., the Stag Hunt game).22 Thus, any game in G′′ exhibits a gap between collective optimality and individual rationality: the socially optimal outcome of (ac, ac) does not constitute aNash equilibrium outcome in intergroup relations. However, the feasibility of punishment — using ap via either dyadic or norm-like sanctions — creates the possibility that cooperation can be stabilized by stick-and-carrot strategies of conditional cooperation. We focus on the sustainability of cooperation in across-group relationships. The presumption is that cooperation within groups can be sustained via either altruism or the high frequency of interactions; the essential question concerns the effectiveness of different kinds of norms for sustaining cooperation between groups. For conveniencewe use the payoff notation from the standard binary-choice Prisoner’s Dilemma to label intergroup payoffs associated with cooperation and defection. Thus let v(ac, ac) ≡ R, v(ad , ac) ≡ T , v(ac, ad ) ≡ S, and v(ap, ap) ≡ P. The above assumptions imply that T > R > max (P,S) and 2R > T + S for any intergroup game. A player’s ex ante payoffs for the entire game is the discounted sum of her expected pairwise payoffs. We also continue to assume that monitoring of intergroup breaches is perfect. Section “IMPERFECTMONITORING” shows that our results are robust against monitoring imperfections, as long as they are not too big. The result in this section, Proposition 1, establishes sufficient conditions for the superiority of universalistic over particularistic norms in supporting intergroup cooperation.23 Any number of ascriptive groups is allowed; the groups may be of arbitrary sizes. Further, no significant sociometric assumptions are imposed. For example, the proposition allows for cliques: part of a group could encounter each other more often than they meet anyone outside the clique. Or there could be brokers who interact often with people in many groups. More importantly, Proposition 1 holds even when intragroup dyadic ties are stronger than intergroup ones and hence within-group policing is better than between-group policing at sustaining intergroup cooperation. (We do not mention these parametric advantages of intragroup ties in the proposition itself, as we prefer to state it in greater generality. The discussion after the result, however, will make clear that it does indeed hold when intragroup ties are stronger than intergroup ones.) A universalisticnorm is defined as one inwhich sanctions do not condition on ascriptive features: any deviation by any player in any intergroup relationship invites the same response fromall other players, regardless of groupmembership. In the best universalistic norm, any deviation is followed by perpetual reversion to minmax actions thereafter, by every other player in the game. In communitarian norms, sanctions are ascriptively 22 Quite a few scholars have argued that hominid preferences evolved so that intragroup cooperation was a Nash equilibrium even in finite encounters. See Fehr and Fischbacher (2003) for an overview of the argument and a literature survey. 23 The appendix actually proves a stronger result: universalistic norms are always at least as good as communitarian ones in supporting cooperation in both intergroup and intragroup pairs. Since this survey concentrates on the former, the proposition in the survey confines itself to that subset. 12 Bendor and Mookherjee differentiated: the sanctions of people in one’s own group differ (in terms of their payoff consequences for the sanctioned players) from those of other groups. This implies that communitarian norms punish intergroup deviations less vigorously than does the best universalistic norm: some other player, either from one’s own group or some other, will respond with a lighter sanction. An example of such a norm is where only members of the victim’s group sanction the deviator; the latter’s compatriots are passive. Proposition 1 Suppose the game involves social matching and m(1 Rb but the other payoffs are the same, the temptation to cheat an Outsider, T − Rb, exceeds the temptation to cheat an Insider, T − Rw. 26 For example, a trigger strategy’s threat is to substitute a punishment phase for mutual cooperation. Because mutual cooperation is more valuable within groups than between them, ending it hurts more, so the intragroup per period penalty, Rw − P, exceeds that of between-group pairs, Rb − P. 27 The empirical regularity of more cooperation within than between groups is consistent with the survey’s discussion: if stage-game payoffs and social networks make the former easier to support, we should observe more within-group cooperation than between-group. Thus, for certain ranges of δ cooperation across groups cannot be sustained by any norm, while some norms will support it within groups. (E.g., suppose a community has evolved within-group norms but not universalistic ones. Given the advantages of within-group cooperation, δ has a range where only within-group cooperation is a Nash equilibrium outcome.) 14 Bendor and Mookherjee interesting, for there we get discriminating predictions about the effects of different norms. Specifically, if δ is intermediate for any intergroup pair, then the best symmetric equilibrium supported by universalistic norms Pareto dominates all symmetric equilibria supported by communitarian norms. COMMUNITARIAN NORMS HURTMINORITIES THEMOST The previous section showed that for intermediate values of the discount factor, universalism Pareto-dominates communitarian norms. In this section, we examine distributive implications. We argue that failing to use universalistic norms hurts small groups the most. So the consequences of communitarian norms are inequitable as well as inefficient. The next result focuses onwhat can be achieved by the best strategy— those involving the strongest feasible punishments — in two empirically important classes of particularistic norms: within-group punishments (the cheater’s kin punish the miscreant) and between-group punishments (the victim’s kin punish).We restrict attention to outcomes based on symmetric actions within each bilateral intergroup relationship.28 Because the analysis in this section ismore complicated, we employ several simplifying assumptions on stage games and intergroup matching probabilities. A1: All between-group games are identical and all within-group games are identical. A2: All between-group pairings are equally likely to form, in every period. Even with these simplifying assumptions, we can represent the substantively significant situation of cohesive intragroup behavior and problematic intergroup relations, e.g., between-group pairs form less often than intragroup matches. (A2 puts no restrictions on network patterns within groups.) We label the groups in descending order of size: n1 ≥ · · · ≥ nm. In what follows, a within-group norm (resp. between-group norm) is one in which a deviation with someone from a different group is sanctioned by all members of one’s own group (resp. by all members of the victim’s group). Recall that the best withinor between-group norm deploys a maximal sanction — perpetual reversion to the minmax action thereafter. To examine how much cooperation can be sustained by such norms, we can restrict attention to the best version of either norm. 28 Despite its natural appeal as a fair outcome of a symmetric relationship, this restriction is significant in terms of payoffs that can be achieved. Bendor and Mookherjee (1990) showed that allowing asymmetric levels of cooperation in intergroup relationships would generally Pareto-dominate the maximal supportable symmetric payoff. However, because incentives for cooperative behavior are harder to provide tominoritymembers, in these equilibriamembers ofmajority groups providemore cooperation to minority members than vice versa. Such patterns of cooperation are rarely observed, presumably because they conflict with notions of fair exchange. For instance, in the standard 2× 2 Prisoners Dilemma, a big-group player would allow, as equilibrium behavior, a small-group partner to sucker him repeatedly. This reverse communitarianism may be enlightened but it is probably uncommon (Brown 1991). Communitarian versus Universalistic Norms 15 Proposition 2 Suppose A1, A2 and the hypotheses of Proposition 1 hold; further, m ≥ 3 and n2 > nm. Then there exist thresholds δ and δ, with 0 < δ < δ < 1, such that the following hold. (i) For any fixed δ ∈ (δ, δ), in any symmetric equilibrium of either the best within-group or the best between-group norm the groups are partitioned into two subsets: one contains the k biggest groups (1 < k < m); the other, the m−k smallest ones. People in the big groups cooperate with each other but those in small groups do not cooperate with any Outsiders. (ii) Under the best withinor between-group norm, the number of groups that can sustain between-group cooperation is weakly increasing in δ ∈ (δ, δ), and strictly so if δ rises sufficiently. (iii) The best universalistic norm can support cooperation between people in all groups for any δ in (δ, δ). Thus, for intermediate values of δ, universalism allows intergroup cooperation to flourish generally, while under communitarian norms members of small groups can cooperate onlywith their peers: trappedwithin their groups, their exchanges are confined to small networks. This is harmful, given the following weak restriction on payoffs. Corollary 1 Suppose the hypotheses of Proposition 2 hold; further, within-group cooperation delivers higher payoffs than does any symmetric noncooperative between-group outcome. If δ ∈ (δ, δ) then the following properties hold in the symmetric equilibrium with cooperation under either the best within-group or the best between-group norm: (i) The expected payoffs of everyone in the large groups (A1 through Ak) exceed those of anyone in the small ones. (ii) The expected payoffs of people in the small groups are strictly increasing in the size of their groups. Thus for intermediate ranges of δ small groups are hurt the most by particularistic codes. Under the conditions of Corollary 1, members of these groups have the most to gain from a transition from communitarianism to universalism. Changes in Group Composition Nowwe examine how changes in group size affect the viability of intergroup cooperation and the ensuing welfare impacts on minorities. First, we continue the analysis of size asymmetries. Proposition 2 and its corollary showed that given a fixed set of ascriptively defined groups, the smaller groups can support less cooperation and suffer accordingly. We now study how changes in size asymmetries affect cooperation and welfare. To keep the comparative statics clean, the number of groups and the total population are held constant. Proposition 3 and its corollary will show that as the size distribution of groups becomes increasingly lopsided, the problems that communitarian norms impose on minorities intensify. To keep the analysis simple we consider a society with two groups, A and B, with A the bigger of the two. Further, we continue to presume A1 and A2. However, these 16 Bendor and Mookherjee assumptions as stated are not adapted to comparative static analysis: they are silent on whether exogenous changes can affect the stage game or matching probabilities. Hence, we introduce extensions of A1 and A2 that address this issue. The extension of the stagegame assumption is simple, but because interaction probabilities are interdependent — they must sum to one — this extension is a bit more complex.29 A1′: All between-group stage games are identical and all within-group games are identical. Further, neither type of game is affected by any parametric change. A2′: (a) Before a parametric change all between-group pairings are equally likely; after the change all such matches are equally likely. (b) A parametric change may affect the probability of such encounters, subject to the constraint that the chance that a player meets an Outsider is increasing in the number of Outsiders. A2(b) implies, e.g., that aB is more likely to run into anA after the parametric change, when there are more A’s, than before — a rather weak constraint. Proposition 3 Assume that A1′, A2′, and the hypotheses of Proposition 1 hold, with nA > nB. Suppose there is an exogenous shift in group-composition: some people shift from minority group B to the majority group A. Then the critical δ-thresholds of the best withinand betweengroup norms rise monotonically, equaling their dyadic values when nB equals one. The explanation is straightforward. If policing is only by one’s own group and constant cooperation is required, then the smaller group’s size is the binding constraint on the viability of cooperation. Hence eventually the intragroup communitarian norm can no longer uphold intergroup cooperation because there are too few B’s to force themselves to cooperate with A’s. The between-group norm experiences the same effect for the opposite reason: once there are enough A’s, they will start cheating B’s because there are too few of the latter to deter the A’s. As usual, the universalistic norm is unaffected. Now consider the welfare effect of this change in identity demographics. If the majority group grows, there is one obvious negative effect on minority member payoffs since there are fewer people in their group with whom to cooperate. This results whenever cooperating withmembers of one’s own group generates higher payoffs than cooperating with Outsiders. The next result shows that minority players can be hurt (and never benefit) as group-sizes becomemore lopsided even when withinand between-group cooperation are equally valuable. In the statement of the results,A’s include people who kept this identity throughout as well as individuals who changed fromB toA. Similarly,B’s include people whomaintain this identity throughout as well as anyone who changed from A to B. (Proposition 3 and its corollary allows for the possibility that no majority group members start passing as minority; the welfare results show why few people would want to make such transitions.) 29 More specifically, whereas we assume that the parametric shift does not affect stage games, this cannot hold for matching probabilities. Some of these must change as identities change: since the number of A’s rises, if intergroup pairings occur with the same probability as before then B’s must become less likely to encounter peers. Communitarian versus Universalistic Norms 17 Corollary 2 Suppose the hypotheses of Proposition 3 hold, with nA > nB > 1. Further, within-group cooperation is more valuable than is any symmetric noncooperative betweengroup outcome. If there are still some B’s left after the identity-shifts have occurred, then for either the best within-group norm or the best between-group norm the following conclusions hold. (i) Increased lopsidedness never makes B’s (old or new) better off. (ii) If δ is in (δ, δ), where 0 < δ < δ < 1, then the parametric change makes B’s worse off. (iii) The change never yields a Pareto-improvement: if it benefits any A, old or new, then it harms the B’s. Under the above assumptions, the infeasibility of intergroup cooperation hurts the minority more than themajority because the former necessarily have fewer peers. Hence, the smaller the minority the more damaging is the absence of intergroup cooperation. And since by Proposition 3 this collapse occurs for bigger ranges of δ as the groups becomes more lopsided, for the minority everything goes bad at the same time as their group shrinks: supporting cooperation via either communitarian regime becomes more difficult and the collapse has more dire effects. Thus Proposition 3 and its corollary are normatively significant: they tell us that the minority group has more to gain from a transition from particularistic to universalistic codes, and the smaller it is the more it has to gain. Further, if identity were endogenous — e.g., people could sometimes, perhaps at a cost, change their identity — then in certain parametric environments the minority group will disappear in equilibrium.30 Ascriptive Fragmentation With the rise of identity politics in the seventies, some social commentators remarked that the United States was becoming more ascriptively fragmented. In this subsection we will argue that a society’s degree of ascriptive fragmentation differentially affects the abilities of universalistic and communitarian norms to sustain cooperation: as the number of (active) ascriptive groups increases, the bigger the gap between the effectiveness of these types of norms. By “the number of (active) ascriptive groups” we mean a specific, though empirically important, type of identity-change: those which cause every citizen to lose some peers and not gain any new ones. (Hence i’s peers ex post are a proper subset of her ex ante ones, for all i.) For example, suppose that initially a society is divided into blacks and whites. Then gender is politically activated in addition, dividing the society into white females, white males and so on. In this parametric change, everyone loses peers. In order to focus on the joint effects of increased fragmentation and particularistic norms, we abstract from other impacts that are probably correlated with changes in 30 See Laitin (1998) for a related analysis of an “assimilation equilibrium”. On the choice-theoretic foundations of identity more generally, see Calvert (2002). 18 Bendor and Mookherjee identity: we assume that the rise in the number of active ascriptive groups affects neither the chance that any two specificplayersmeet nor the stage game theyplay.Thus, the result shows that increased ascriptive fragmentation impairs cooperation even when this change does not make pairwise relationships less valuable. Hence, the effects that Proposition 4 uncovers must be due to the isolated causal mechanism: how communitarian norms implement more fragmented ascriptive identities. The result allows for completely heterogeneous matching probabilities and stage games. Proposition 4 Suppose the hypotheses of Proposition 1 hold. Initially there are at least two groups; the smallest group has at least three members. Let the society become more ascriptively fragmented in the sense stipulated above; this change affects neither stage games nor matching probabilities. Then the following hold, for either the best withinor between-group norm. (i) For any two players i and j who are in different groups ex ante, there exist threshold discount factors δij , δij such that if δ is in (δij , δij) then cooperation between i and j is a subgame-perfect Nash equilibrium outcome ex ante but not ex post. (ii) Suppose in addition that no ex post group is a singleton, intragroup stage games belong to G′′ and within-group cooperation is regulated by the best within-group communitarian norm. Then part (i)’s conclusion holds for every pair of players. Thus, under part (ii)’s mild restriction on the parametric change, increased ascriptive fragmentation makes all pairwise cooperation, with Insiders as well as Outsiders, more difficult. This happens because greater ascriptive fragmentation, mediated by the best particularistic norms, makes social networks sparser, de facto; hence, deviants encounter punishment less often.31 Therefore, insisting on being punished only by one’s own kind is probably inconsistent with stable intergroup cooperation in pluralistic societies.32 In contrast, fragmentation has no effect on the universalistic norm, since it ignores ascriptive characteristics. Consequently, the more ascriptively fragmented the society, the bigger is the difference in the effectiveness of universalistic versus the above communitarian regimes. The increased fragility of the best particularistic norms in the face of greater ascriptive fragmentation has sharp welfare effects. 31 As the formulation of the proposition suggests, this argument’s validity depends on comparing the best communitarian norms to themselves, before and after the parametric change. It need not hold for suboptimal communitarian norms. Consider, e.g., a community initially divided into racial groups. Within-group norms regulate interracial cooperation. Suppose, however, the prevailing norm says that a deviator should be punished only by someone of his or her own gender (which is clearly suboptimal). Then, if groups become finer, so that white females are in one group and white males another, cooperation is unaffected. 32 There is an ascriptively-based norm that does not suffer from this effect: if i cheats an Outsider then everyone from uninvolved tribes punish i. An increase inm helps this norm, and at the limit (m = n) it converges to universalism. This might also reflect ideas of impartiality, for it is a particularistic and decentralized version of a specialized universalistic institution (police and courts): instead of an impartial judicial system, A1’s are supposed to be impartial about A2’s cheating A3’s and so on. Communitarian versus Universalistic Norms 19 Corollary 3 If all the hypotheses of Proposition 4 hold then the following conclusions obtain for either kind of communitarian norm. (i) Increased ascriptive fragmentation never makes anyone better off. (ii) It makes some people worse off if δ is intermediate for at least one pair. The criterion of δ-intermediacy identified in part (ii) is very weak: we only need one pair, say i and j, for whom δ is intermediate. That is, δ is high enough so that before the parametric change i and j can cooperate but low enough so that after the change they cannot. If there are many pairs playing different stage games then the union of these intermediate δ-intervals will be large, whence the condition is easily satisfied.