Solidarity, synchronization and collective action

For people to act collectively in actual situations—in contrast to public goods experiments—goal ambiguity, diversity of interests, and uncertain costs and benefits stand in their way. Under such conditions, people seem to have few reasons to cooperate, yet the Arab revolutions, as conspicuous examples, show that collective action can take place despite the odds. I use the Kuramoto model to analyze how people in a cohesive network topology can synchronize their salient traits (emotions, interests or other), and show that synchronization happens in a phase transition, when group solidarity passes a critical threshold. This model can yield more precise predictions of outbursts of collective action under adverse conditions, and casts a new light on different measures of social cohesion. A remarkable feature of humans is that they can act collectively, even though individuals are tempted to defect and reap the benefits of others’ efforts [19]. This achievement is even more remarkable if one realizes that in contrast to public goods experiments of collective action, where the collective good—money—is clearly defined at the outset, public goods in actual situations, from revolutions to reorganizations, are often ambiguous. Yet more challenging, participants differ in their interests in, and shares of, those public goods. Under conditions of ambiguity, uncertainty and diversity, most people seem to have few reasons to cooperate. Nevertheless we can witness that in numerous cases, people somehow manage to get to action in the face of all odds. ∗Department of Sociology and Anthropology, University of Amsterdam, Oudezijds Achterburgwal 185, 1012 DK Amsterdam, the Netherlands.  j.p.bruggeman@uva.nl. 1 ar X iv :1 31 2. 68 09 v3 [ ph ys ic s. so cph ] 2 8 Ja n 20 14 In this note I ask the question if under adverse conditions, when neither cost-benefit ratios nor reputations can win people over to contribute to collective goods, dilemma’s of cooperation can be solved through “interaction rituals” wherein individuals’ traits (emotions, interests or other) are synchronized. To this end I use Yoshiki Kuramoto’s model of synchronization , to be discussed first. Because synchronization is highly sensitive to network topology, I compare two concepts of social cohesion, k -core and k -connectivity, for their synchronization potential. Results are somewhat ambiguous and require laboratory experiments on human subjects. Solidarity and synchronization According to one of the founders of sociology, Emile Durkheim, groups of people are bond together by social cohesion . With modern network theory in mind, one could say that cohesion consists in part of social ties that people have with others, and for another part of solidarity that people have with their group as a whole. Importantly, people are not identical, and i ∈ {1, 2, . . . , N} group members each have their own character ωi, shaped prior to current interactions on a given network. Their solidarity λ can be enhanced through intensified interaction, such as collective singing or noise making (see documentaries on protests such as Tahrir square), religious practices , initiation boot camps in organizations [13], military training or other interaction rituals with a shared focus [6]. In some of these interaction rituals, people perform synchronized body movements , as to induce their emotional synchronization. Future research should detail out the relation between interaction rituals and solidarity; here I assume a monotonic relationship, exogenous to the model. Although for the model (Eq.1) it makes no difference whether an interaction ritual increases solidarity, the strength of network ties, or both, I assume for simplicity that only solidarity varies; all ties between individuals are symmetric, Wij = Wji = 1 (and absent ties Wij = 0), such that connected i and j mutually influence each other; and, the network does not change over the period of observation. For the moment I also assume that everybody has the same solidarity value (coupling strength), which will be loosened to individualized λi in the next section. An individual’s current trait—emotion, A generalization of the Kuramoto model  allows for the network and its synchronization to co-evolve, such that the ties and their strengths Wij(t) change according to homophily and homeostasis. For homophily, see the main text below; homeostasis means individuals’ limited capacity to maintain ties, such that stronger ties with some people imply weaker or no ties with others, empirically found by [16] and others.