This thesis is concerned with the evolution of opinions among voters during election processes. We employ dynamical systems and methodologies developed in physics and mathematics to model such election processes. We investigate the opinion formation process among an ensemble of interacting individuals modeled by a dynamical system. The problem we form on is the following: There have been numerous recent instances of social networks being actively utilized to influence elections by disseminating rumors and misleading information. The possibility of manipulating elections using external influence directly raises the question of the intrinsic robustness of existing electoral systems. Identifying the social characteristics of a voter population that make it resilient to opinion manipulation is particularly interesting. Determining which among the existing democratic electoral systems is more resilient to external influences is equally important.

We address these questions using a well-designed opinion dynamics model. Building on earlier works in computational social sciences, we adapt a mathematical model of opinion dynamics, where agents represent voters interacting with one another. The model includes (i) a natural opinion that represents the opinion of each voter in the absence of interaction with other voters, (ii) a confidence bound that determines whether a voter interacts with others, (iii) an external influence field trying to change the voters’ opinion, and (iv) a differential equation governing the time evolution of the opinion of voters.

There are many models of opinion dynamics, however only a few have been validated with real data. The validation of the models is challenging due to the need for more real data that can be transformed into a metric that can quantitatively or even qualitatively validate these models. One of the main results is the validation of our model. We validate the model we constructed using historical data of the US House of Representative elections from 2012 to 2020. The model captures qualitatively, if not quantitatively, the US House of Representatives election’s volatility, which we consider a solid validation of our approach.

We evaluate the robustness of different electoral systems to external influences. An external influence is introduced in the system as an influence field to change the election outcome. We then quantify the total effort the influence field has to exert to change the electoral outcome as a function of agent polarization, confidence bound, different electoral systems, and the number of political parties. We present a detailed study on the robustness of bipartite electoral systems (i.e., with two major parties) and extend it to multipartite (i.e., with multiple major parties) electoral systems.

All our results and conclusions are independent of the number of existing political parties. Our results emphasize the need to encourage public debates and discussions during political campaigns to strengthen democratic processes. However, different electoral processes behave remarkably differently under the influence of external manipulation, and proportional representation makes for a more robust electoral process. This thesis can be extended to include all other different electoral systems, including two-round system, block-voting and so forth.