A General Form of Opinion Dynamics for Modeling Diverse Political Networks

Abstract

Understanding the emergent properties of large networks comprised of individuals is one of the foundational goals of the political and social sciences. Mathematical modeling of complex adaptive systems can yield valuable insights into behavior such as political partisanship, polarization, and cooperation, but does so at the cost of model generality. This paper proposes a model of individual-level opinion dynamics on large networks which minimizes the number of assumptions made about the individuals comprising the network, while shifting valuable assumptions to the structure of the network itself.

This paper demonstrates that the proposed model can not only recreate emergent system behaviors seen in the existing literature, but can provide novel insights into these behaviors. Particularly, we will look at trends in political polarization, and show the effects of affective partisanship and echo-chambers on various network structures. We then challenge our understanding of issue-space dimensionality in the context of James Madison's notion of ``factions," and show that contrary to existing literature, it is not always optimal for individuals to only care about a small fraction of issues in the available issue-space. We also examine the various effects that a third, independent class of individuals can have on a largely bipartisan network, and describe the conditions under which these independents can play a critical role in determining network behavior.

We end with an example practical application of the model to an outside agent who wishes to optimize their ``impact" on the opinions of the individuals on the network over time. Overall, we conclude that this general model of opinion dynamics is capable of producing very interesting network behavior on par with the existing literature, and show that its potential for practical applications is far-reaching.