Nonequilibrium phase transition in the coevolution of networks and opinions

Models of the convergence of opinion in social systems have been the subject of a considerable amount of recent attention in the physics literature. These models divide into two classes, those in which individuals form their beliefs based on the opinions of their neighbors in a social network of personal acquaintances, and those in which, conversely, network connections form between individuals of similar beliefs. While both of these processes can give rise to realistic levels of agreement between acquaintances, practical experience suggests that opinion formation in the real world is not a result of one process or the other, but a combination of the two. Here we present a simple model of this combination, with a single parameter controlling the balance of the two processes. We find that the model undergoes a continuous phase transition as this parameter is varied, from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion. We characterize the static and dynamical properties of this transition

Extremism propagation in social networks with hubs

One aspect of opinion change that has been of academic interest is the impact of people with extreme opinions (extremists) on opinion dynamics. An agent-based model has been used to study the role of small-world social network topologies on general opinion change in the presence of extremists. It has been found that opinion convergence to a single extreme occurs only when the average number of network connections for each individual is extremely high. Here, we extend the model to examine the effect of positively skewed degree distributions, in addition to small-world structures, on the types of opinion convergence that occur in the presence of extremists. We also examine what happens when extremist opinions are located on the well-connected nodes (hubs) created by the positively skewed distribution. We find that a positively skewed network topology encourages opinion convergence on a single extreme under a wider range of conditions than topologies whose degree distributions were not skewed. The importance of social position for social influence is highlighted by the result that, when positive extremists are placed on hubs, all population convergence is to the positive extreme even when there are twice as many negative extremists. Thus, our results have shown the importance of considering a positively skewed degree distribution, and in particular network hubs and social position, when examining extremist transmission

The Methodologies of Neuroeconomics

We critically review the methodological practices of two research programs which are jointly called ‘neuroeconomics’. We defend the first of these, termed ‘neurocellular economics’ (NE) by Ross (2008), from an attack on its relevance by Gul and Pesendorfer (2008) (GP). This attack arbitrarily singles out some but not all processing variables as unimportant to economics, is insensitive to the realities of empirical theory testing, and ignores the central importance to economics of ‘ecological rationality’ (Smith 2007). GP ironically share this last attitude with advocates of ‘behavioral economics in the scanner’ (BES), the other, and better known, branch of neuroeconomics. We consider grounds for skepticism about the accomplishments of this research program to date, based on its methodological individualism, its ad hoc econometrics, its tolerance for invalid reverse inference, and its inattention to the difficulties involved in extracting temporally lagged data if people’s anticipation of reward causes pre-emptive blood flow

Tipping Points in 1-dimensional Schelling Models with Switching Agents

Schelling’s spacial proximity model was an early agent-based model, illustrating how ethnic segregation can emerge, unwanted, from the actions of citizens acting according to individual local preferences. Here a 1-dimensional unperturbed variant is studied under switching agent dynamics, interpretable as being open in that agents may enter and exit the model. Following the authors’ work (Barmpalias et al., FOCS, 2014) and that of Brandt et al. (Proceedings of the 44th ACM Symposium on Theory of Computing (STOC 2012), 2012), rigorous asymptotic results are established. The dynamic allows either type to take over almost everywhere. Tipping points are identified between the regions of takeover and staticity. In a generalization of the models considered in [1] and [3], the model’s parameters comprise the initial proportions of the two types, along with independent values of the tolerance for each type. This model comprises a 1-dimensional spin-1 model with spin dependent external field, as well as providing an example of cascading behaviour within a network

Dynamic scaling regimes of collective decision making

We investigate a social system of agents faced with a binary choice. We assume there is a correct, or beneficial, outcome of this choice. Furthermore, we assume agents are influenced by others in making their decision, and that the agents can obtain information that may guide them towards making a correct decision. The dynamic model we propose is of nonequilibrium type, converging to a final decision. We run it on random graphs and scale-free networks. On random graphs, we find two distinct regions in terms of the "finalizing time" -- the time until all agents have finalized their decisions. On scale-free networks on the other hand, there does not seem to be any such distinct scaling regions

Phonon-defect scattering in doped silicon by molecular dynamics simulation

Molecular dynamics simulations are used to study the scattering of phonon wave packets of well-defined frequency and polarization from individual point defects and from a field of point defects in Si. The relative amounts of energy in the transmitted and reflected phonon fields are calculated and the parameters that influence the phonon scattering process are determined. The results show that the fractions of transmitted and reflected energies strongly depend on the frequency of the incident phonons and on the mass and concentration of the defects. These results are compared with the classic formula for the scattering strength for point defects derived by Klemens, which we find to be valid when each phonon-defect scattering event is independent. The Klemens formula fails when coupled multiple scattering dominates. The phonon density of states is used to characterize the effects of point defects on mode mixing

Analysis of a threshold model of social contagion on degree-correlated networks

We analytically determine when a range of abstract social contagion models permit global spreading from a single seed on degree-correlated random networks. We deduce the expected size of the largest vulnerable component, a network's tinderbox-like critical mass, as well as the probability that infecting a randomly chosen individual seed will trigger global spreading. In the appropriate limits, our results naturally reduce to standard ones for models of disease spreading and to the condition for the existence of a giant component. Recent advances in the distributed, infinite seed case allow us to further determine the final size of global spreading events, when they occur. To provide support for our results, we derive exact expressions for key spreading quantities for a simple yet rich family of random networks with bimodal degree distributions.Comment: 7 Pages, 1 figure, submitted to Phys. Rev.

Rise of the centrist: from binary to continuous opinion dynamics

We propose a model that extends the binary ``united we stand, divided we fall'' opinion dynamics of Sznajd-Weron to handle continuous and multi-state discrete opinions. Disagreement dynamics are often ignored in continuous extensions of the binary rules, so we make the most symmetric continuum extension of the binary model that can treat the consequences of agreement (debate) and disagreement (confrontation) within a population of agents. We use the continuum extension as an opportunity to develop rules for persistence of opinion (memory). Rules governing the propagation of centrist views are also examined. Monte Carlo simulations are carried out. We find that both memory effects and the type of centrist significantly modify the variance of average opinions in the large timescale limits of the models. Finally, we describe the limit of applicability for Sznajd-Weron's model of binary opinions as the continuum limit is approached. By comparing Monte Carlo results and long time-step limits, we find that the opinion dynamics of binary models are significantly different to those where agents are permitted more than 3 opinions

“An ethnographic seduction”: how qualitative research and Agent-based models can benefit each other

We provide a general analytical framework for empirically informed agent-based simulations. This methodology provides present-day agent-based models with a sound and proper insight as to the behavior of social agents — an insight that statistical data often fall short of providing at least at a micro level and for hidden and sensitive populations. In the other direction, simulations can provide qualitative researchers in sociology, anthropology and other fields with valuable tools for: (a) testing the consistency and pushing the boundaries, of specific theoretical frameworks; (b) replicating and generalizing results; (c) providing a platform for cross-disciplinary validation of results

Byzantine Gathering in Networks

This paper investigates an open problem introduced in [14]. Two or more mobile agents start from different nodes of a network and have to accomplish the task of gathering which consists in getting all together at the same node at the same time. An adversary chooses the initial nodes of the agents and assigns a different positive integer (called label) to each of them. Initially, each agent knows its label but does not know the labels of the other agents or their positions relative to its own. Agents move in synchronous rounds and can communicate with each other only when located at the same node. Up to f of the agents are Byzantine. A Byzantine agent can choose an arbitrary port when it moves, can convey arbitrary information to other agents and can change its label in every round, in particular by forging the label of another agent or by creating a completely new one. What is the minimum number M of good agents that guarantees deterministic gathering of all of them, with termination? We provide exact answers to this open problem by considering the case when the agents initially know the size of the network and the case when they do not. In the former case, we prove M=f+1 while in the latter, we prove M=f+2. More precisely, for networks of known size, we design a deterministic algorithm gathering all good agents in any network provided that the number of good agents is at least f+1. For networks of unknown size, we also design a deterministic algorithm ensuring the gathering of all good agents in any network but provided that the number of good agents is at least f+2. Both of our algorithms are optimal in terms of required number of good agents, as each of them perfectly matches the respective lower bound on M shown in [14], which is of f+1 when the size of the network is known and of f+2 when it is unknown