As Smaldino notes, cultural diversity matters because it is one source of a group's ability to generate solutions to challenges. He suggests that the patterns that give rise to group-level cultural traits can also increase individual-level cultural diversity (sect. 4.1, para. 6). Smaldino distinguishes between two dimensions of collaborative interdependence: social differentiation between individuals' characteristics and social organization – the fact that differentiation contributes to individuals playing different roles in collaborative tasks.
Although differentiated social roles in a collaborative process may depend on differences in individuals' characteristics, social roles need not require different characteristics. The same person may play the role of juror in one trial, witness in another, and defendant in a third. Moreover, some social roles, such as serving on a jury, do not require special characteristics. On the other hand, differences in social roles usually result in differences in experience. Thus, social roles may themselves generate diversity in patterns of thought and behavior, as suggested by Smaldino's remarks.
Social organization can encourage or constrain social network structure. To continue the earlier example, the amount and nature of communication between participants in a courtroom depends on their roles in the proceedings. Work within more persistent organizations often creates more persistent patterns of social networks. Social network models provide one way of characterizing certain differences between social roles by capturing differences in the direction, amount, and nature of what is communicated. Managers and employees both talk to each other, but the kinds of things they say may differ, and what each says to employees with different roles differs. This is exactly the kind of difference that can affect cultural transmission at the individual level, as illustrated, for example, by empirical studies of cultural transmission networks (Atran & Medin Reference Atran and Medin2008; Henrich & Broesch Reference Henrich and Broesch2011).
Thus, collaborative interdependence may influence (a) individual cultural diversity and (b) patterns of cultural transmission. Moreover, we can distinguish the causes of these two effects of collaborative interdependence: two organizations might have different social roles but very similar social network structures, or similar social roles but different social structures (juries and managers may have different roles in different kinds of court proceedings or in different companies).
Some patterns of cultural transmission tend to reduce cultural diversity. These patterns include copying of random individuals (Alexander Reference Alexander2007; Abrams Reference Abrams2013), bias toward copying successful or high-status individuals, and bias toward copying high-frequency cultural variants (Boyd & Richerson Reference Boyd and Richerson1985). Models in which individuals' beliefs are weighted averages of others' generally produce consensus, as long as no individuals are isolated from others and degrees of trust are stable (DeGroot Reference DeGroot1974; Grim et al. Reference Grim, Singer, Reade and Fisher2011; Lehrer & Wagner Reference Lehrer and Wagner1981; Zollman, personal communication, cf. Zollman Reference Zollman2013). Some models can maintain diversity, however.
A coordination game models a situation in which it is better for each person to do the same as others, even if one coordinated action might be preferable to another. In one kind of model, each person makes a single choice in simultaneous games with each neighbor on a network with bidirectional, unweighted links. The best response to neighbors' choices depends on the percentage of them who play various options, and the payoffs for coordination with each. Iterating the process can spread a given choice: if enough of my neighbors adopt, say, option A, I will do the same, which may eventually cause a neighbor who has been playing B to switch to A, if her neighbors switch as well. This models cultural transmission in which individuals are influenced both by the number of neighbors adopting a variant and its perceived intrinsic attractiveness.
Morris (Reference Morris2000) showed that distinct cultural variants can be maintained in such a model if some groups have high enough cohesion, also known as cohesiveness (Vega-Redondo Reference Vega-Redondo2007; Young Reference Young1998). The cohesiveness of a group is the minimum of the ratio between the number of intra-group links and the number of all links, in each group member's links. A group with high cohesiveness is one with mainly within-group communication. Members' interactions reinforce their common cultural variants despite attractive alternatives presented by outsiders.
Alexander (Reference Alexander2007) investigated agent-based simulations of various combinations of (a) games and payoffs, (b) network structures, and (c) rules for copying from neighbors. Some combinations of these factors make it difficult or impossible to maintain cultural diversity; others make it easy. Alexander's results appear to show that on the whole, more social interconnections tend to make cultural disagreement less likely, thus apparently broadening Morris's result to a variety of other cases.
Morris's sense of cohesion is related to others (Wasserman & Faust Reference Wasserman and Faust1994) and to measures of community structure (Newman Reference Newman2010). Using a cohesion measure called close-knittedness, Young (Reference Young1998) proves results for stochastic coordination games that support the idea that cohesion allows local reinforcement and global disagreement (at least in the short run). My own experiments with a simple model of cultural transmission that does not use averaging for updating of beliefs (http://modelingcommons.org/browse/one_model/3829) suggest that cultural diversity can easily be maintained by cohesion on reasonable timescales.
Plausibly, the influence of collaborative interdependence on social network structure sometimes generates structures in which groups exhibit cohesion, communicating largely with members of the same group on certain topics of discussion. This is a second way that collaboration can help maintain cultural diversity within a population.
As suggested by some of Durham's (Reference Durham1991; Reference Durham1992) proposed transmission isolating mechanisms mentioned by Smaldino (sect. 6, para. 1), individual resistance to alternative variants or certain kinds of interlocutors can maintain cultural diversity (Axelrod Reference Axelrod1997; Hegselmann & Krause Reference Hegselmann and Krause2002; Mueller et al. Reference Mueller, Simpkins, Rasmussen and Sun2010). Note though that cognitive processes such as inference and emotion can transfer influence from one mental state to another, and people seem to be quite capable of keeping large domains of thought isolated from others. This suggests that resistance to alternatives might be modeled in terms of cohesion-like properties of networks of influence between mental states (cf. Colombo Reference Colombo2013). Then different social roles may encourage “cohesive” cognitive subnetworks, reinforcing particular patterns of thought in individuals who fill similar social roles. Perhaps cohesion mediates both effects of collaborative interdependence on cultural diversity highlighted above.
As Smaldino notes, cultural diversity matters because it is one source of a group's ability to generate solutions to challenges. He suggests that the patterns that give rise to group-level cultural traits can also increase individual-level cultural diversity (sect. 4.1, para. 6). Smaldino distinguishes between two dimensions of collaborative interdependence: social differentiation between individuals' characteristics and social organization – the fact that differentiation contributes to individuals playing different roles in collaborative tasks.
Although differentiated social roles in a collaborative process may depend on differences in individuals' characteristics, social roles need not require different characteristics. The same person may play the role of juror in one trial, witness in another, and defendant in a third. Moreover, some social roles, such as serving on a jury, do not require special characteristics. On the other hand, differences in social roles usually result in differences in experience. Thus, social roles may themselves generate diversity in patterns of thought and behavior, as suggested by Smaldino's remarks.
Social organization can encourage or constrain social network structure. To continue the earlier example, the amount and nature of communication between participants in a courtroom depends on their roles in the proceedings. Work within more persistent organizations often creates more persistent patterns of social networks. Social network models provide one way of characterizing certain differences between social roles by capturing differences in the direction, amount, and nature of what is communicated. Managers and employees both talk to each other, but the kinds of things they say may differ, and what each says to employees with different roles differs. This is exactly the kind of difference that can affect cultural transmission at the individual level, as illustrated, for example, by empirical studies of cultural transmission networks (Atran & Medin Reference Atran and Medin2008; Henrich & Broesch Reference Henrich and Broesch2011).
Thus, collaborative interdependence may influence (a) individual cultural diversity and (b) patterns of cultural transmission. Moreover, we can distinguish the causes of these two effects of collaborative interdependence: two organizations might have different social roles but very similar social network structures, or similar social roles but different social structures (juries and managers may have different roles in different kinds of court proceedings or in different companies).
Some patterns of cultural transmission tend to reduce cultural diversity. These patterns include copying of random individuals (Alexander Reference Alexander2007; Abrams Reference Abrams2013), bias toward copying successful or high-status individuals, and bias toward copying high-frequency cultural variants (Boyd & Richerson Reference Boyd and Richerson1985). Models in which individuals' beliefs are weighted averages of others' generally produce consensus, as long as no individuals are isolated from others and degrees of trust are stable (DeGroot Reference DeGroot1974; Grim et al. Reference Grim, Singer, Reade and Fisher2011; Lehrer & Wagner Reference Lehrer and Wagner1981; Zollman, personal communication, cf. Zollman Reference Zollman2013). Some models can maintain diversity, however.
A coordination game models a situation in which it is better for each person to do the same as others, even if one coordinated action might be preferable to another. In one kind of model, each person makes a single choice in simultaneous games with each neighbor on a network with bidirectional, unweighted links. The best response to neighbors' choices depends on the percentage of them who play various options, and the payoffs for coordination with each. Iterating the process can spread a given choice: if enough of my neighbors adopt, say, option A, I will do the same, which may eventually cause a neighbor who has been playing B to switch to A, if her neighbors switch as well. This models cultural transmission in which individuals are influenced both by the number of neighbors adopting a variant and its perceived intrinsic attractiveness.
Morris (Reference Morris2000) showed that distinct cultural variants can be maintained in such a model if some groups have high enough cohesion, also known as cohesiveness (Vega-Redondo Reference Vega-Redondo2007; Young Reference Young1998). The cohesiveness of a group is the minimum of the ratio between the number of intra-group links and the number of all links, in each group member's links. A group with high cohesiveness is one with mainly within-group communication. Members' interactions reinforce their common cultural variants despite attractive alternatives presented by outsiders.
Alexander (Reference Alexander2007) investigated agent-based simulations of various combinations of (a) games and payoffs, (b) network structures, and (c) rules for copying from neighbors. Some combinations of these factors make it difficult or impossible to maintain cultural diversity; others make it easy. Alexander's results appear to show that on the whole, more social interconnections tend to make cultural disagreement less likely, thus apparently broadening Morris's result to a variety of other cases.
Morris's sense of cohesion is related to others (Wasserman & Faust Reference Wasserman and Faust1994) and to measures of community structure (Newman Reference Newman2010). Using a cohesion measure called close-knittedness, Young (Reference Young1998) proves results for stochastic coordination games that support the idea that cohesion allows local reinforcement and global disagreement (at least in the short run). My own experiments with a simple model of cultural transmission that does not use averaging for updating of beliefs (http://modelingcommons.org/browse/one_model/3829) suggest that cultural diversity can easily be maintained by cohesion on reasonable timescales.
Plausibly, the influence of collaborative interdependence on social network structure sometimes generates structures in which groups exhibit cohesion, communicating largely with members of the same group on certain topics of discussion. This is a second way that collaboration can help maintain cultural diversity within a population.
As suggested by some of Durham's (Reference Durham1991; Reference Durham1992) proposed transmission isolating mechanisms mentioned by Smaldino (sect. 6, para. 1), individual resistance to alternative variants or certain kinds of interlocutors can maintain cultural diversity (Axelrod Reference Axelrod1997; Hegselmann & Krause Reference Hegselmann and Krause2002; Mueller et al. Reference Mueller, Simpkins, Rasmussen and Sun2010). Note though that cognitive processes such as inference and emotion can transfer influence from one mental state to another, and people seem to be quite capable of keeping large domains of thought isolated from others. This suggests that resistance to alternatives might be modeled in terms of cohesion-like properties of networks of influence between mental states (cf. Colombo Reference Colombo2013). Then different social roles may encourage “cohesive” cognitive subnetworks, reinforcing particular patterns of thought in individuals who fill similar social roles. Perhaps cohesion mediates both effects of collaborative interdependence on cultural diversity highlighted above.