Complexity measurement of macroscopic opinion dynamics to infer mechanisms within social influence networks

Social influence networks are collections of entities dealing with a shared issue on which they have individual opinions. These opinions are dynamic, changing over time due to influence from other entities. Mechanisms within the network can affect how influence leads to opinion change, such as the strength and number of social ties between agents and the decision models used by an individual to process information from its neighbors. In real-world scenarios, these mechanisms are often hidden. Much effort in social network analysis involves proposing models and attempting to replicate target output data with them. Can we instead use the evolution of opinions in a network to infer these mechanisms directly?

This work explores how opinion change in social influence networks can be used to determine characteristics of those networks. Broadly, this is accomplished by simulating social influence networks using various designs and initial conditions to generate opinion data, and then identifying relationships between response variables and changes to the simulation inputs. Key inputs include the population size, the influence model that controls how agents change their opinions, the network structure, the activation regime that controls the sequencing of opinion updates, and probability distributions for communication errors. Analyzing the opinions of individual agents can provide insights about the individuals (microscopic), but in this work, focus is on insights into the social influence network as a complete system (macroscopic), so opinion data is aggregated according to each response variable.

Response variables are designed through the lens of complexity theory. Three types of complexity measurements are applied to opinion data: regression, entropy, and a new complexity measure. In each case, relationships between design factors and response variables are diverse. The influence model and the distribution of communication errors---a factor often omitted from the literature---are consistently impactful, with their various settings producing distinct profiles in time series plots of the measurements. Activation regime is impactful to some entropy measures. Network structure has little impact on the new complexity measure, and population size has little impact in general. Overall, distinctive relationships can exist between opinions and design factors. These relationships, as well as the measures and problem-solving approaches used in this work, may be helpful to analysts working to infer the properties of real-world social influence networks from the opinion data those systems generate.