Modeling Opinion Dynamics as a Segmented Mean Field Game

Abstract

One of the most important functions of government is to pass laws and create legislation. Yet the process by which bills become laws is complicated due to a differing opinions among elected representatives in legislative bodies. In addition, associations such as political party play a significant role in determining how a representative will vote on a certain bill. Research has shown that in legislatures, people are often influenced by how a colleague voted on a certain bill with certain members wielding more in- fluence than others. This provides a motivating question to a member trying to make a law: Which representatives should be approached to influence a desired proportion of the legislative body? While the motivation is from legislatures, there are a number of other situations where this model could be applicable. Situations where individuals are asked to give an opinion on a topic that they are not well-versed in. When there is public knowledge of other people’s positions, individuals often make decisions based on how others they are familiar with voted. Things such as referendum’s and club membership can be modeled using this method. We are interested in looking at how to model this form of opinion dynam- ics. We begin with relatively simply models and slowly optimize and build upon them to create a robust framework to attempt to develop a model that allows for an accurate understanding of opinion relationships. Finally, an attempt was made to use the House of Representatives voting records to create a model. Using this model, an optimal strategy was created on which representatives should be approached for a certain type of bill.