Dynamical Properties of Interaction Data

Network dynamics are typically presented as a time series of network properties captured at each period. The current approach examines the dynamical properties of transmission via novel measures on an integrated, temporally extended network representation of interaction data across time. Because it encodes time and interactions as network connections, static network measures can be applied to this "temporal web" to reveal features of the dynamics themselves. Here we provide the technical details and apply it to agent-based implementations of the well-known SEIR and SEIS epidemiological models.Comment: 29 pages, 15 figure

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 the exhaustive approach of the TKO score makes it an effective benchmark measure for evaluating the accuracy of other, often more practical, measures of influence. We find that none of the common 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 hunt for effective predictive measures

Evolution of Prosocial Behavior through Preferential Detachment and Its Implications for Morality.

The current project introduces a general theory and supporting models that offer a plausible explanation and viable mechanism for generating and perpetuating prosocial behavior. The proposed mechanism is preferential detachment and the theory proposed is that agents utilizing preferential detachment will sort themselves into social arrangements such that the agents who contribute a benefit to the members of their group also do better for themselves in the long run. Agents can do this with minimal information about their environment, the other agents, the future, and with minimal cognitive/computational ability. The conclusion is that self-organizing into groups that maintain prosocial behaviors may be simpler and more robust than previously thought. The primary contribution of this research is that a single, simple mechanism operating in different contexts generates the conceptually distinct prosocial behaviors achieved by other models, and in a manner that is more amenable to evolutionary explanations. It also bears importantly on explanations of the evolution of our moral experiences and their connection with prosociality.Ph.D.Political Science and PhilosophyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91448/1/bramson_1.pd

Measuring Dynamical Uncertainty With Revealed Dynamics Markov Models

Concepts and measures of time series uncertainty and complexity have been applied across domains for behavior classification, risk assessments, and event detection/prediction. This paper contributes three new measures based on an encoding of the series' phase space into a descriptive Markov model. Here we describe constructing this kind of “Revealed Dynamics Markov Model” (RDMM) and using it to calculate the three uncertainty measures: entropy, uniformity, and effective edge density. We compare our approach to existing methods such as approximate entropy (ApEn) and permutation entropy using simulated and empirical time series with known uncertainty features. While previous measures capture local noise or the regularity of short patterns, our measures track holistic features of time series dynamics that also satisfy criteria as being approximate measures of information generation (Kolmogorov entropy). As such, we show that they can distinguish dynamical patterns inaccessible to previous measures and more accurately reflect their relative complexity. We also discuss the benefits and limitations of the Markov model encoding as well as requirements on the sample size

The impact of functional and social value on the price of goods

According to hedonic pricing theory (HPT) market forces operate on individual characteristics of a good, and the price of a product is the aggregate of the price across those characteristics. The relationship between price and characteristics remains poorly understood because characteristic qualities are hard to quantify, people have varying levels of information about characteristics, and people have heterogeneous preferences over characteristics. By analyzing data from a large, market-driven virtual world we are able to test HPT, while largely avoiding these pitfalls. We find that a linear model with functional characteristics predicts the prices poorly, but a log-linear model performs quite well. Adding social characteristics to this log-linear model improves the predictions substantially. This work strongly supports HPT and demonstrates a "rational" calculus including social value

Social Stability and Extended Social Balance - Quantifying the Role of Inactive Links in Social Networks

Structural balance in social network theory starts from signed networks with active relationships (friendly or hostile) to establish a hierarchy between four different types of triadic relationships. The lack of an active link also provides information about the network. To exploit the information that remains uncovered by structural balance, we introduce the inactive relationship that accounts for both neutral and nonexistent ties between two agents. This addition results in ten types of triads, with the advantage that the network analysis can be done with complete networks. To each type of triadic relationship, we assign an energy that is a measure for its average occupation probability. Finite temperatures account for a persistent form of disorder in the formation of the triadic relationships. We propose a Hamiltonian with three interaction terms and a chemical potential (capturing the cost of edge activation) as an underlying model for the triadic energy levels. Our model is suitable for empirical analysis of political networks and allows to uncover generative mechanisms. It is tested on an extended data set for the standings between two classes of alliances in a massively multi-player on-line game (MMOG) and on real-world data for the relationships between countries during the Cold War era. We find emergent properties in the triadic relationships between the nodes in a political network. For example, we observe a persistent hierarchy between the ten triadic energy levels across time and networks. In addition, the analysis reveals consistency in the extracted model parameters and a universal data collapse of a derived combination of global properties of the networks. We illustrate that the model has predictive power for the transition probabilities between the different triadic states.Comment: 21 pages, 10 figure

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

Diversity and Democracy: Agent-Based Modeling in Political Philosophy

Agent-based models have played a prominent role in recent debates about the merits of democracy. In particular, the formal model of Lu Hong and Scott Page and the associated “diversity trumps ability” result has typically been seen to support the epistemic virtues of democracy over epistocracy (i.e., governance by experts). In this paper we first identify the modeling choices embodied in the original formal model and then critique the application of the Hong-Page results to philosophical debates on the relative merits of democracy. In particular we argue that the “best-performing agents” in Hong-Page model should not be interpreted as experts. We next explore a closely related model in which best-performing agents are more plausibly seen as experts and show that the diversity trumps ability result fails to hold. However, with changes in other parameters (such as the deliberation dynamic) the diversity trumps ability result is restored. The sensitivity of this result to parameter choices illustrates the complexity of the link between formal modeling and more general philosophical claims; we use this debate as a platform for a more general discussion of when and how agent-based models can contribute to philosophical discussions