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Structural power and the evolution of collective fairness in social networks

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ABSTRACT

Mug: From work contracts and group buying platforms to political coalitions and international climate and economical summits, often individuals assemble in groups that must collectively reach decisions that may favor each part unequally. Here we quantify to which extent our network ties promote the evolution of collective fairness in group interactions, modeled by means of Multiplayer Ultimatum Games (). We show that a single topological feature of social networks—which we call structural power—has a profound impact on the tendency of individuals to take decisions that favor each part equally. Increased fair outcomes are attained whenever structural power is high, such that the networks that tie individuals allow them to meet the same partners in different groups, thus providing the opportunity to strongly influence each other. On the other hand, the absence of such close peer-influence relationships dismisses any positive effect created by the network. Interestingly, we show that increasing the structural power of a network leads to the appearance of well-defined modules—as found in human social networks that often exhibit community structure—providing an interaction environment that maximizes collective fairness.

No MeSH data available.


Examples of group formation.We represent all the groups where a focal individual, positioned in the blue node, participates. In both (a) and (b), the focal individual has a connectivity of 3 (blue links) thereby playing in 4 different groups: one centered on herself (represented by a grey circle) and the 3 others centered on her (numbered) neighbors (represented by yellow ellipses). For instance, the groups represented by the ellipses iv contain all neighbors of individuals with number 4 (including the focal individual). The motifs presented in (a) and (b) differ in the overlap of the groups where the blue nodes take part, and consequently, the influence that those neighbors exert and are subject to. In (a), none of the 1st neighbors of the focal individual are 1st neighbors of each other; thus, the focal individual only meets each of her/his neighbors in two groups. In (b), all 1st neighbors of the focal individual are directly connected, which means that individuals 2, 3 and 4 take part in all the groups where the focal individual also takes part. Thus, they influence each-other more in (b) than in (a). The structural power (SP, defined in Methods and based on the prevalence of one individual in the interaction groups of another), provides a quantitative measure of the influence capacity of any node onto another (see Methods where we show that the influence extends to second neighbors). When applied to the entire network, the SP is thus higher in (b) than in (a).
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pone.0175687.g001: Examples of group formation.We represent all the groups where a focal individual, positioned in the blue node, participates. In both (a) and (b), the focal individual has a connectivity of 3 (blue links) thereby playing in 4 different groups: one centered on herself (represented by a grey circle) and the 3 others centered on her (numbered) neighbors (represented by yellow ellipses). For instance, the groups represented by the ellipses iv contain all neighbors of individuals with number 4 (including the focal individual). The motifs presented in (a) and (b) differ in the overlap of the groups where the blue nodes take part, and consequently, the influence that those neighbors exert and are subject to. In (a), none of the 1st neighbors of the focal individual are 1st neighbors of each other; thus, the focal individual only meets each of her/his neighbors in two groups. In (b), all 1st neighbors of the focal individual are directly connected, which means that individuals 2, 3 and 4 take part in all the groups where the focal individual also takes part. Thus, they influence each-other more in (b) than in (a). The structural power (SP, defined in Methods and based on the prevalence of one individual in the interaction groups of another), provides a quantitative measure of the influence capacity of any node onto another (see Methods where we show that the influence extends to second neighbors). When applied to the entire network, the SP is thus higher in (b) than in (a).

Mentions: As detailed in Methods, we start from a population of size Z, much larger than the group size N, and equip individuals with values of p and q drawn from a discretized uniform probability distribution in the interval [0,1] containing 101 values (discretized to the closer multiple of 0.01). As already mentioned, to model the interplay between different interaction group assortments, we assume that individuals in the population are arranged in a graph (or network). In line with previous studies [25–27], each neighborhood defines a group, whereas the fitness Fi of an individual i of degree k is determined by the payoffs resulting from the game instances occurring in k+1 groups: one centered on her neighborhood plus k others centered on each of her k neighbors. In other words, each node with degree k defines a group with size N = k+1, including that node (focal) and the neighbors. Fig 1 provides pictorial representations of this group formation process. In homogeneous populations, every individual participates in the same number of groups (and MUG instances), all with the same size. Often, however, individuals face different numbers of collective dilemmas (depending, e.g., on their social position) that may also have different sizes. Such a dimension of social diversity is introduced here (Fig 4) by considering heterogeneous networks [30].


Structural power and the evolution of collective fairness in social networks
Examples of group formation.We represent all the groups where a focal individual, positioned in the blue node, participates. In both (a) and (b), the focal individual has a connectivity of 3 (blue links) thereby playing in 4 different groups: one centered on herself (represented by a grey circle) and the 3 others centered on her (numbered) neighbors (represented by yellow ellipses). For instance, the groups represented by the ellipses iv contain all neighbors of individuals with number 4 (including the focal individual). The motifs presented in (a) and (b) differ in the overlap of the groups where the blue nodes take part, and consequently, the influence that those neighbors exert and are subject to. In (a), none of the 1st neighbors of the focal individual are 1st neighbors of each other; thus, the focal individual only meets each of her/his neighbors in two groups. In (b), all 1st neighbors of the focal individual are directly connected, which means that individuals 2, 3 and 4 take part in all the groups where the focal individual also takes part. Thus, they influence each-other more in (b) than in (a). The structural power (SP, defined in Methods and based on the prevalence of one individual in the interaction groups of another), provides a quantitative measure of the influence capacity of any node onto another (see Methods where we show that the influence extends to second neighbors). When applied to the entire network, the SP is thus higher in (b) than in (a).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5391959&req=5

pone.0175687.g001: Examples of group formation.We represent all the groups where a focal individual, positioned in the blue node, participates. In both (a) and (b), the focal individual has a connectivity of 3 (blue links) thereby playing in 4 different groups: one centered on herself (represented by a grey circle) and the 3 others centered on her (numbered) neighbors (represented by yellow ellipses). For instance, the groups represented by the ellipses iv contain all neighbors of individuals with number 4 (including the focal individual). The motifs presented in (a) and (b) differ in the overlap of the groups where the blue nodes take part, and consequently, the influence that those neighbors exert and are subject to. In (a), none of the 1st neighbors of the focal individual are 1st neighbors of each other; thus, the focal individual only meets each of her/his neighbors in two groups. In (b), all 1st neighbors of the focal individual are directly connected, which means that individuals 2, 3 and 4 take part in all the groups where the focal individual also takes part. Thus, they influence each-other more in (b) than in (a). The structural power (SP, defined in Methods and based on the prevalence of one individual in the interaction groups of another), provides a quantitative measure of the influence capacity of any node onto another (see Methods where we show that the influence extends to second neighbors). When applied to the entire network, the SP is thus higher in (b) than in (a).
Mentions: As detailed in Methods, we start from a population of size Z, much larger than the group size N, and equip individuals with values of p and q drawn from a discretized uniform probability distribution in the interval [0,1] containing 101 values (discretized to the closer multiple of 0.01). As already mentioned, to model the interplay between different interaction group assortments, we assume that individuals in the population are arranged in a graph (or network). In line with previous studies [25–27], each neighborhood defines a group, whereas the fitness Fi of an individual i of degree k is determined by the payoffs resulting from the game instances occurring in k+1 groups: one centered on her neighborhood plus k others centered on each of her k neighbors. In other words, each node with degree k defines a group with size N = k+1, including that node (focal) and the neighbors. Fig 1 provides pictorial representations of this group formation process. In homogeneous populations, every individual participates in the same number of groups (and MUG instances), all with the same size. Often, however, individuals face different numbers of collective dilemmas (depending, e.g., on their social position) that may also have different sizes. Such a dimension of social diversity is introduced here (Fig 4) by considering heterogeneous networks [30].

View Article: PubMed Central - PubMed

ABSTRACT

Mug: From work contracts and group buying platforms to political coalitions and international climate and economical summits, often individuals assemble in groups that must collectively reach decisions that may favor each part unequally. Here we quantify to which extent our network ties promote the evolution of collective fairness in group interactions, modeled by means of Multiplayer Ultimatum Games (). We show that a single topological feature of social networks—which we call structural power—has a profound impact on the tendency of individuals to take decisions that favor each part equally. Increased fair outcomes are attained whenever structural power is high, such that the networks that tie individuals allow them to meet the same partners in different groups, thus providing the opportunity to strongly influence each other. On the other hand, the absence of such close peer-influence relationships dismisses any positive effect created by the network. Interestingly, we show that increasing the structural power of a network leads to the appearance of well-defined modules—as found in human social networks that often exhibit community structure—providing an interaction environment that maximizes collective fairness.

No MeSH data available.