Empirical social triad statistics can be explained with dyadic homophylic interactions

Abstract

The remarkable robustness of many social systems has been associated with a peculiar triangular structure in the underlying social networks. Triples of people that have three positive relations (e.g., friendship) between each other are strongly overrepresented. Triples with two negative relations (e.g., enmity) and one positive relation are also overrepresented, and triples with one or three negative relations are drastically suppressed. For almost a century, the mechanism behind these very specific (“balanced”) triad statistics remained elusive. Here, we propose a simple realistic adaptive network model, where agents tend to minimize social tension that arises from dyadic interactions. Both opinions of agents and their signed links (positive or negative relations) are updated in the dynamics. The key aspect of the model resides in the fact that agents only need information about their local neighbors in the network and do not require (often unrealistic) higher-order network information for their relation and opinion updates. We demonstrate the quality of the model on detailed temporal relation data of a society of thousands of players of a massive multiplayer online game where we can observe triangle formation directly. It not only successfully predicts the distribution of triangle types but also explains empirical group size distributions, which are essential for social cohesion. We discuss the details of the phase diagrams behind the model and their parameter dependence, and we comment on to what extent the results might apply universally in societies.

Networks of Beliefs: An Integrative Theory of Individual- and Social-Level Belief Dynamics

“…They enable us to model how belief dynamics emerges at the level of internal networks (from interactions between personal and social beliefs within individuals) and at the level of external networks (from interactions between individuals). Second, we can build on already existing statistical physics models at the internal level (Dalege et al, 2018;Schweighofer, et al, 2019;van der Maas et al, 2020) and at the external level (Castellano et al, 2009;Pham et al, 2022;Redner, 2019). We use the structure of a broad statistical physics framework to specify our particular theory of belief dynamics based on the premises described above.…”

“…Given this feature list, this means that many prominent belief dynamic models will be left out in this comparison. These include models that only represent one belief or vectors of noninteractive beliefs (features 1 and 2), such as French's (1956) formal model of social power, Harary's (1959) generalization of French's model, and DeGroot's (1974) consensus formation model and others that followed in this and other traditions such as the bounded confidence models (Deffuant et al, 2000;Hegselmann & Krause, 2002;Weisbuch et al, 2002), vector models based on attraction or assimilation and rejection or repulsion mechanisms (Flache & Macy, 2011;Huet & Deffuant, 2010;Jager & Amblard, 2005), social influence network theory (e.g., Friedkin & Johnsen 1990;, computational implementations of social impact theory (Nowak et al, 1990), models of the dissemination of culture (Axelrod, 1997), vector models that combine demographic and belief representations (Flache & Mäs, 2008), and several models inspired by statistical physics (e.g., Galesic & Stein, 2019;Pham et al 2022; for reviews of models inspired by statistical physics see Castellano et al, 2009 and for a general overview of social influence models see Flache et al, 2017).…”

“…For a full understanding of belief dynamics, a comprehensive theory of belief dynamics should include mechanisms that go beyond the goal of dissonance or energy reduction, although several mechanisms of belief change can be incorporated in a framework that is assumed to minimize energy. For example, another form of consistency criterion that has been applied to several belief dynamic models is triangle balance (e.g., Pham et al, 2022;Rodriguez et al, 2016;. That is, a triangle of nodes is balanced if it includes zero or two negative links, otherwise it is unbalanced.…”

“…That is, a triangle of nodes is balanced if it includes zero or two negative links, otherwise it is unbalanced. This form of consistency mechanism could be incorporated as a separate term in the energy function (see e.g., Pham et al, 2022). Going beyond dissonance, balance, and minimization of energy, other mechanisms have been proposed…”

New Forms of Collaboration Between the Social and Natural Sciences Could Become Necessary for Understanding Rapid Collective Transitions in Social Systems

“…The possibilities for triggering systemic failure in the context of supply chains was recently quantified on the basis of detailed national firm-to-firm supply-chain data (Diem et al, 2022), explicitly accounting for large levels of heterogeneity in socioeconomic systems. Network-based computational models address classic topics of sociology, such as homophily, triadic closure (Davidsen et al, 2002;Klimek & Thurner, 2013), and social balance (Górski et al, 2020;Korbel et al, 2023;Pham et al, 2020Pham et al, , 2021Pham et al, , 2022.…”