Social cohesion and cooperation

May 17, 2017 | Penulis: Jeroen Bruggeman | Kategori: N/A
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Social cohesion and cooperation

Jeroen Bruggeman 1 and Douglas White September 2008 Humans are more cooperative with non kin than any other animal, but how can we comprehend this anomaly of evolution? The long debate on cooperation has been succinctly summarized as follows: “Selfishness beats altruism within groups. Altruistic groups beat selfish groups. Everything else is commentary” (Wilson and Wilson 2007). To contribute to this debate, we should thus help to explain altruism (cooperation) within groups, especially in the longer run with inevitable turnover of group members. Ideally, models of cooperation are as simple as possible, and then still tractable and have analytic solutions. In the simplest models, individuals can either cooperate (C) or defect (D), but cooperation in groups on the basis of simple reciprocity (with options C and D only) can’t be sustained in general (Boyd and Lorberbaum 1987). Among the large variety of human behavior and information transmission in different cultures around the world, researchers came to realize that reputation for cooperative behavior exists in all cultures, and that adding it to games can increase levels of cooperation (Nowak and Sigmund 1998). In the pertaining experiments, all subjects take an equal share in a public good, usually a monetary reward, independently of their contributions to it. To the public good is then added an individual premium, attributed by the other players and paid by the experimenter, for being a good cooperator/contributor. In actual societies, reputation, both positive and negative, diffuses as gossip at negligible cost (Gluckman 1963, Sommerfeld et al 2007). The gossiper affects the subject of gossip indirectly, and the action aspect of reputation is therefore called indirect reciprocity (IR), extending the options C and D in direct reciprocity. Another universal trait in human cultures is punishment (P) (Henrich et al 2005), which is applied in a range of circumstances from socialization of children (Simmel 1908) to restoring solidarity among adults (Durkheim 1895). It has been shown experimentally that punishment of defectors can have a positive effect on cooperation (Fehr and Gächter 2002). When both options of indirect reciprocity (IR) and punishment (P) are available (plus C and D), cooperation is enhanced considerably (Rockenbach and Milinski 2006). An important side result of the latter experiment was that the effect of reputation, i.e. when defectors with a bad reputation don’t receive extra benefits, reduces substantially the need for costly punishment (Rockenbach and Milinski 2006). In later rounds of the experiment, a threat of it sufficed. Punishment, however, invokes a new explanatory problem: why would individuals incur costs to punish defectors? Along with this problem, the positive effect of punishment itself has been criticized. Punishment by anonymous/non-related people may work in experiments in individualistic societies, but is counter productive in collectivist societies, 1

Acknowledgements: Aljaž Ule.

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by entailing revenge on collaborators (Hermann, Thöni and Gächter 2008; they called these societies “traditional” – but are there societies without traditions?). Some researchers argued that punishment is maladaptive altogether, and concluded that “winners do not use costly punishment, whereas losers punish and perish” (Dreber et al. 2008, p.350). Here, the critics missed a crucially important point, namely the network structure of social interactions: C, D, IR and P don’t happen in a social vacuum and generally not in random encounters either, but in a network of social relations that is longer lasting than elementary actions (cf. Granovetter 1985). Our proposal focuses on the network of collaborators.

Network topology and cooperation To see why networks are important, let us look at a dyad, of two people A and B in repeated interactions (Fig.1). There is no network beyond the dyad. Their (possibly asymmetric) network tie is the set of memories and expectations that A and B have towards each other, undoubtedly associated with emotions, and possibly meshed with social norms beyond the dyad, e.g. acquired during childhood socialization (Simmel 1908). Suppose A wants to establish cooperation with B, then B may or may not respond cooperatively, while without further assumptions, A has little means to establish cooperation as normative behavior, or to win over B to cooperate after a defective action. If there is noise in information transmission or in B’s interpretation, B might take A’s contribution as a defection, with adverse consequences. Last but not least, if punishment is added as an option, and A thinks that B violates the cooperative norm and punishes B, then B may deny the existence of the norm and retaliate, like subjects in collectivistic societies did in experiments (Hermann, Thöni and Gächter 2008). In sum, without further network, A and B are in an awkward predicament to establish cooperation in the long run.

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A

B

D

E

C

Figure 1. Dyad and triad. In a triad (Fig.1), in contrast, the social situation is entirely different, as Georg Simmel (1908) noticed a century ago. For each dyadic interaction, say between D and E, there is a potential mediator, here C, as a third person related to, and possibly also monitoring, both D and E. Let’s suppose D attempts to cooperate with E, and E defects, analogously to A and B in the dyad, respectively. In the triad, E gets a reputation as a defector through D’s gossip to C, or C’s direct observation of the interaction. For the latter case of monitoring, there is supportive empirical evidence that if people feel being observed by someone, they instantly become more pro-social (Milinski and Rockenbach 2007). Monitoring set apart, C now has more options than are available in a dyad, and C might subsequently avoid cooperating with, or bestowing benefits to E, punish E, through indirect reciprocity reward D’s cooperation, gossip to D about how to behave with respect to E, or a combination thereof. Notice again that indirect reciprocity can take several forms, i.e. transferring positive information or positively convincing alters to cooperate with, or to give benefits to a person, and transferring negative information or negatively influencing alters to defect or to punish, just like gossip in actual societies (cf. Gluckman 1963, Sommerfeld et al 2007). Assuming that also C wants to establish cooperation in the group, then the norm is clearly more stable than between A and B, and through C and D’s collective behavior as the (local) majority, they can make it clear to E that cooperation is the norm rather than D’s idiosyncrasy, even without explicitly communicating the norm. In particular in the case of punishment, it is not isolated individual D against whom E can take countermeasures without ramifications beyond the dyad. If E knows that C and D agree on the norm, E might anticipate punishment or negative indirect reciprocity from C as well. According to evolutionary theory, people have a conformist, or frequency dependent, bias, which is one more explanation why E is more likely to accept the norm than B is in the dyad (Boyd and Richerson 1985). 3

If there is noise in the transmission from D to E or in E’s interpretation and E falsely believes that D defects, C may correct E’s interpretation. Finally, in their interactions, none of the individuals in the triad can monopolize all information transfer, which protects everybody to some extent against strategic manipulation by an individual. Consequentially, in social life in general, there is a strong tendency towards transitivity (elaborate & cite, Levine and Kurzban 2006), and trust is easier established between D and E than between A and B (Krackhardt and Handcock 2007). The advantages of triads with respect to dyads can be generalized to larger networks by the notion of k-cohesion, also called k-connectivity, where k denotes the minimum number of node-independent paths (concatenations of social ties connecting nodes) between arbitrary pairs of nodes (White and Harary 2001). Initially, k-cohesion was an explication of solidarity (Durkheim 1893, Ibn Khaldun 1379), at least the relational aspect of it (White and Harary 2001; Moody and White 2003), which is the tendency of people in groups larger than two to develop emotions for and attachment to the collective---group solidarity---as an emergent property over and above the sum total of ties that individuals have in the group. A redundancy of paths (k ≥ 2) makes it possible to correct errors in information transmission through one path by transmission through other paths. Empirical evidence confirms that gossip from multiple sources is regarded by subjects as more convincing than from a single person (Hess and Hagen 2006). Even if people are only aware of their local environment of network neighbors, social norms and gossip can still diffuse through the network from neighbor to neighbor, and redundant paths are amplifiers in this transmission (Moody and White 2003). Redundancy can also foster continuity of norm maintenance in dynamic networks with some turnover of people and ties. As a matter of fact, k-cohesive networks are robust with respect to disruption, and by Menger’s theorem (from 1927, cf. Harary 1969), there is a minimum of k individuals who should be removed from the network to make it fall apart, or to reduce it to a trivial network of one person. The notion of k-cohesion thus establishes an equivalence relation between numbers of nodes and paths, and it links cooperation with group robustness. For empirical data, it can be measured with the open source software R and its igraph package (http://www.r-project.org/). Menger’s theorem implies that any number of less than k people can migrate at a time while the remainder group members stay in (possibly indirect) contact. Furthermore, if persons A and B are in a dispute about cooperation, there are at least k-1 other people directly connected to them who can intervene. If there is consensus upon a cooperative norm, both defector and punisher(s) know the size of the (local) majority, making defector’s retaliation far more unlikely than in experimental groups with random encounters. It also makes punishment less costly for in individual punisher, who now acts as a representative of the entire group. In many cases, representatives like leaders, spokesmen, judges, or police, have resources from the entire community at their disposal, making their personal costs much lower and their interventions more effective than is assumed in most game studies. For parsimony, we won’t have such institutions in our

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experiment, though, but find it important to stress this point. (elaborate on trust among group members; collectivist – individualist societies; institutions take a share in solidarity). When scaling up to larger groups, it is a mathematical fact that a given level of kcohesion can be maintained without increasing individual costs in terms of average degree (number of ties per person, White and Harary 2001; White 2008). While cooperation in very large groups is problematic in current theory, this problem can thus be overcome by k-cohesion. Humans’ pro-sociality, mostly locally in their immediate social environment, has the unintended side effect of creating, or at least making possible, larger groups with certain levels of cohesion that – if we are right – resolve the dilemma of cooperation for the entire group. In sum, we hypothesize that higher k-cohesion fosters higher levels of cooperation in establishing collective goods (Bruggeman 2008; White 2008), which has never been studied empirically up to date.

Confounding effects The notion of k-cohesion fleshes out social cohesion with sufficient precision to test it in the lab, and makes it possible to disentangle it from associated confounding network effects on cooperation: network density; social distance; centralization; and the number of people involved. First, since more cohesive groups tend to be denser, network density is often mentioned as a crude approximation to cohesion. However, density glosses over its inhomogeneity over larger networks and their relatively denser sub-communities (Moody and White 2003). We therefore object to alternative but for large networks computationally more efficient measures of social cohesion like k-cores (a set of nodes where each node has at least k-ties in the group), which are also vulnerable to inhomogeneity (although less than density is), contradicting the arguments above; compare Fig.2 to Fig.3 below, which are both 3-cores but with different cohesion. Second, when cohesion increases, average social distance (the number of concatenated ties along the shortest path connecting two nodes) tends to decrease, which may have a positive effect on cohesion of its own. People at smaller social distances better identify with each other, which might increase their mutual pro-sociality (Hoffman, McCabe and Smith 1996; Bohnet and Frey 1999; Akerlof 1997). Third, two k-cohesive groups may at the same time have different levels of centralization, or power inequality. Centralization is measured in terms of the variation of centrality scores of the people involved (Freeman 1979). The simplest centrality measure is degree, which we will adopt for our small and structurally simple experimental groups below. In centralized groups, a small cohesive subgroup of highly central individuals can take initiative in mobilizing collective action in the larger group (Marwell and Oliver 1988), for example by putting pressure on others to act cooperatively, and cooperation in small (sub) groups is often easier established than in large groups (Olson 1965). Leaders, avantgardes, and elites can play a role in cooperation (Khaldoun 1379), especially to get it started, but it’s more parsimonious to explain cooperation without them first.

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Fourth, the size of a k-cohesive group can have an effect of itself, for example as a critical mass to get a protest demonstration started and to make it effective (Granovetter 1978). Since over human history, critical mass effects are less general than cohesion, and networks abstract away from visual and geographic distance, we prefer to side step the possible influence of group size on cooperation. To exclude these four network effects from k-cohesion proper, we compare two groups with different k-cohesion levels, of k = 1 (Fig.2) and k = 3 (Fig.3), which are otherwise equivalent in terms of their density, average path distance, degree centralization, and group size. We conjecture that in the 3-cohesive group cooperation will be higher than in the 1-cohesive group. There is no free partner choice, which if combined with choosiness (a bias in favor of cooperative partners) could explain cooperation by itself (McNamara et al 2008). However, we want to explain cooperation under more difficult circumstances, which better model hunter-gatherer groups as well as modern working conditions, wherein people have to get along with their colleagues whether they like each other or not.

Figure 2. k = 1.

Figure 3. k = 3. 6

Notice that in the public goods game proposed below, the public good is equally shared among everybody. If, in contrast, a smaller subgroup would have a public good exclusively for its own subgroup, e.g. the left part of Fig.2, then only the k-cohesion of that subgroup would matter, not the entire group’s. This is consistent with the literature on critical mass, which in turn is related to the size of the public good and the number of people necessary to achieve it (Oliver and Marwell 2001). Finally, we propose a control group without centralization and with k = 2.

Figure 5. k = 2, and centralization equals zero.

Experiment We propose a public goods network game over multiple rounds, wherein, along with contributions to the public good as usual, there are possibilities for punishment and indirect reciprocity. The asymmetry of ties we leave to the behavior of the players, and we make no assumptions about it. Realistically, information that players receive should be severely limited by social (i.e. path) distance, in our case limited to neighbors’ actions. Also possibilities for punishment and indirect reciprocity should be limited to neighbors, according to the preset network structure. As possibilities for indirect reciprocity, a player (i) may send to his/her neighbor (j) a proposal about punishments or benefits for neighbors’ alters (p), if p is a neighbor of both i and j; as usual, i may also propose to the experimenter a benefit for j. In each round, players can choose to contribute to the public good, punish, or to reciprocate indirectly in one of multiple ways; cooperation and defection are gradual, depending on the contributions to the public good. To test the effect of robustness of the networks, after a number of rounds, we propose to substitute 7

two new players for two incumbents (the central and another player), and we hypothesize that in the more cohesive group, cooperation is sooner recovered. To preclude effects of gender, age, beauty, and other attributes that bring noise to kcohesion, subjects should not be able to have visual contact, and be unaware of the true identity of their neighbors other than what they read and see on their computer screen. The drawback of anonymity and non-visual contact, however, is the removal of an important aspect of social life, namely the effect of being monitored visually. We might add this aspect to the experiments, and to preclude side effects, we would like to present visual contacts only on the computer screens, not in the experimental room, such that all players are in fact watching the same three faces (or six for the central player). Of course the players should not be aware that they all watch the same faces. The faces presented are of people sitting in front of computer screens, and show neither what they can see on their screens, nor their facial expressions in too much detail. When new players are introduced to the game, they should get the same neighbors as their predecessors, and their neighbors should indeed see a new face (or two) on their screens. None of the subjects should know exactly the total number of participants beyond his neighbors, as in actual large social groups people may have estimates but rarely have exact figures. Discussion Recent work has taken other effects of network topology on cooperation into account, starting out with (much) larger networks than we have, with power law degree distributions (Santos and Pacheco 2005), or with numerous groups to which people belong (Santos, Santos and Pacheco 2008). But large networks must have initially started small, and we, instead, move one step closer to the “big bang” of pro-sociality, by dealing with cooperation in small groups first, before scaling up. (Doug, what does your social circles network model predict about this?) We acknowledge that with increasingly larger groups, and keeping k-cohesion at the same level, social distance increases too, even though our world is small (Dodds, Muhamad and Watts 2003). For very large modern societies, however, it seems unlikely that solidarity can be achieved without radio, television, and other media. In teams in organizations, shorter path distances are strongly related to improved coordination and shorter task completion time (Kearns, Suri, and Montfort 2006). In modern societies, there is yet the thorny issue of decreasing reciprocity and trust associated with increasing social inequality, which may have a disruptive effect on solidarity (Wilkinson 2000), and would further complicate the picture. Since this effect is not entirely clear, we abstain from further discussing it here. We also want to conjecture that in groups much larger than in our experiments, the effect of increasing cohesion on individual fitness is probably non-monotonic, as at high levels of cohesion, individuals will suffer an overload of information and social pressure (Durkheim 1897) beyond their abilities to enhance their contributions. Actual societies are locally clustered (because of assortativeness & transitivity) into (hierarchically nested) communities (Ravasz and Barabási 2003), making society modular (Onnela et al 2007; Simon 1962; Newman 2006). This modular structure buffers individuals to some degree against the information overload they would suffer in a “full world” of everybody

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connected to (nearly) everybody else, and insulates communities against failures of cooperation and invention in other communities. However, highly cohesive communities also insulate individuals against good ideas from the outside (Burt 2004), and without sufficient external ties, cohesive communities are resistant to social innovation and change. Furthermore, people in highly cohesive societies who lack external contacts are vulnerable to socially constructed false information (prejudice) about outsiders, which is then not corrected by feedback (Elias and Scotson 1965). High cohesion is no panacea for social problems, and for actual communities, intermediate levels of cohesion seem optimal, if combined with plenty of ties to various other communities. Returning to the question we started out with, social animals like dolphins may live in kcohesive groups (Lusseau and Newman 2004), but they are not nearly as cooperative as humans are. Although (as we hope to show) k-cohesion is conductive to cooperation, it’s the conjunction of network topology and humans’ large social brain (Dunbar and Schultz 2007) that does it. A large brain is clearly costly, but once humans had this brain they could to keep track of, and engage in, many cooperative contacts at relatively low additional costs, but with high benefits. Humans’ special position in evolution is not for any grand or fundamental reason, e.g. because they master fire, or have sophisticated culture and technology, as some scholars argued, but because they have a very simple trait that all other animals lack: in their k-cohesive groups they gossip. [perhaps elaborate on theoretical consequences and practical (policy?) implications]

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