Introducing non-Markovian and empirical effects into social interaction models

Abstract

Stochastic models of opinion spread are a popular method for simulating and predicting the social behaviors of large populations. Though classical models in this field have proven to be accurate towards their intended purpose, often they fall short when applied to more specific scenarios. Many of the assumptions made in these base models have proven to be quite different from the natural behavioral patterns of real people, making further updates and extensions of the original models imperative to understand these shortcomings. This work presents two such model extensions, building off of the basic examples of the naming game and voter models to create more in depth systems and describe complex phenomenon.

Finally, in addition to the new model extensions, a brief overview of relevant empirical investigations is provided to inform on future work in this area. First, data mining techniques are employed to find frequent response patterns in a large survey data set on opinion formation with regards to media consumption. These results serve to identify both groups of individuals that behave similarly and the general trends that shape their responses. Then, a large scale cell phone data set is analyzed for its capability to provide an empirical social network. Two separate network building schemes are compared and used to provide effective networks that may serve as the setting for future simulations.

The first of the two models presents a system in which opinions maintain a set inertia value that dictates the degree to which a node holding that opinion will resist switching opinions. The second replaces the speaker selection mechanic to allow for non-exponential waiting time distributions that vary the activity patterns of the nodes. In both of these scenarios it is shown that the symmetry of the system is broken, creating well defined tipping points where the advantaged opinion is able to build a consensus quickly and consistently. Further, despite both extensions breaking the Markov property maintained in the more basic models, analytic approximations that accurately describe the behavior of the systems are provided.