Considering Opinion Dynamics and Community Structure in Complex Networks: A view towards modelling elections and gerrymandering

Electoral districting and gerrymandering are problems as old at the United States itself. In this project, by employing opinion dynamics on some social networks and using their community structure, we seek to model elections in a two party political system like the USA and simulate the phenomenon that gerrymanders attempt to use to their advantage electorates within different districts or spheres of influence tend to vote for different parties. We show that this effect can be modelled successfully on a network by the voter model if community structure is strong, or by slightly altering the dynamics of the voter model to include a feedback mechanism.