Who's going to win? Modelling elections with an adapted Hegselmann-Krause model and data assimilation.

Modelling the opinions of voters in a population has been studied for a long time. The Hegselmann-Krause model treats voters as having a continuous opinion and updates voter opinions assuming a local mean-field effect. The Hegselmann-Krause model only considers the opinions of voters - we extend it here by introducing the notion of political parties which influence and are influenced by voters in an opinion space. Further, we adapt the model to the Australian electoral system so that it is subject to a preferential voting system. We discuss the mean-field limit by determining the associated Fokker-Planck equation representing this model. We discuss how forecast models such as the Hegselmann-Krause model can, in principle, be used to estimate the outcome of an election result when combined with incoming observational data. The problem of finding an optimal estimate given an uncertain model and noisy observations is dealt within the framework of data assimilation and Kalman filters. We implement an ensemble Kalman filter and show its efficacy in determining the primary votes and two party preferred.