Aaron Bramson

Statistical physics of balance theory

Triadic relationships are accepted to play a key role in the dynamics of social and political networks. Building on insights gleaned from balance theory in social network studies and from Boltzmann-Gibbs statistical physics, we propose a model to quantitatively capture the dynamics of the four types of triadic relationships in a network. Central to our model are the triads’ incidence rates and the idea that those can be modeled by assigning a specific triadic energy to each type of triadic relation. We emphasize the role of the degeneracy of the different triads and how it impacts the degree of frustration in the political network. In order to account for a persistent form of disorder in the formation of the triadic relationships, we introduce the systemic variable temperature. In order to learn about the dynamics and motives, we propose a generic Hamiltonian with three terms to model the triadic energies. One term is connected with a three-body interaction that captures balance theory. The other terms take into account the impact of heterogeneity and of negative edges in the triads. The validity of our model is tested on four datasets including the time series of triadic relationships for the standings between two classes of alliances in a massively multiplayer online game (MMOG). We also analyze real-world data for the relationships between the “agents” involved in the Syrian civil war, and in the relations between countries during the Cold War era. We find emerging properties in the triadic relationships in a political network, for example reflecting itself in a persistent hierarchy between the four triadic energies, and in the consistency of the extracted parameters from comparing the model Hamiltonian to the data.

Benchmarking Measures of Network Influence

Identifying key agents for the transmission of diseases (ideas, technology, etc.) across social networks has predominantly relied on measures of centrality on a static base network or a temporally flattened graph of agent interactions. Various measures have been proposed as the best trackers of influence, such as degree centrality, betweenness, and k-shell, depending on the structure of the connectivity. We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infection given the removal of each agent at each time: its temporal knockout (TKO) score. We argue that this TKO score is an effective benchmark measure for evaluating the accuracy of other, often more practical, measures of influence. We find that none of the network measures applied to the induced flat graphs are accurate predictors of network propagation influence on the systems studied; however, temporal networks and the TKO measure provide the requisite targets for the search for effective predictive measures.

An agent-based model of indirect minority influence on social change and diversity

Abstract The present paper describes an agent-based model of indirect minority influence. It examines whether indirect minority influence can lead to social change as a function of cognitive rebalancing, a process whereby related attitudes are affected when one attitude is changed. An attitude updating algorithm was modelled with minimal assumptions drawing on social psychology theories of indirect minority influence. Results revealed that facing direct majority influence, indirect minority influence along with cognitive rebalancing is a recipe for social change. Furthermore, indirect minority influence promotes and maintains attitudinal diversity in local ingroups and throughout the society. We discuss the findings in terms of social influence theories and suggest promising avenues for model extensions for theory building in minority influence and social change.

Diversity, Ability, and Expertise in Epistemic Communities

The Hong and Page ‘diversity trumps ability’ result has been used to argue for the more general claim that a diverse set of agents is epistemically superior to a comparable group of experts. Here we extend Hong and Page’s model to landscapes of different degrees of randomness and demonstrate the sensitivity of the ‘diversity trumps ability’ result. This analysis offers a more nuanced picture of how diversity, ability, and expertise may relate. Although models of this sort can indeed be suggestive for diversity policies, we advise against interpreting such results overly broadly.

Measuring Propagation with Temporal Webs

We present a form of temporal network called a “temporal web” that connects nodes across time into a single temporally extended acyclic directed graph as a way to capture contingent behaviors. This representation is especially useful for uncovering and measuring social influence. We first present the general temporal web technique and then use it to analyze three empirical datasets: political relationships in the game EVE Online, interbank loans of the Russian banking system, and Twitter posts regarding the H1N1 vaccine. For each dataset we provide a detailed breakdown of the contingent behaviors using an approach we call temporal influence abduction. We then construct a temporal web for each one and describe the patterns of propagation found. Based on these patterns of propagation we infer more general properties of influence and the impact of certain types of behaviors in each system.