A Fractional Optimal Control Model of Electoral Behavior in A Multi-Party Democracy

Abstract

Political participation is a cornerstone that enables citizens to shape their nation's political system in every democratic environment. Registering on electoral lists, joining a political party of choice, and voting during the election collectively contribute to the selection of representatives for political positions. In this work, we propose a fractional optimal control strategy for an awareness program aimed at increasing the number of registered voters participating in elections. To accurately capture desirable properties such as non-locality and non-singularity in the kernel, we employ the Atangana-Baleanu derivative. Additionally, the existence and uniqueness of the model's solutions are established. The political party reproduction number is also achieved. The stability of the model is demonstrated through the Hyers-Ulam stability criteria. The model is validated using empirical data from the 2020 Ghana presidential elections. We considered three controls: firstly, the awareness campaign effort- this control represents the resources dedicated to motivate registered voters to join the political party P1 and cast their votes during an election; secondly, the persuasion effort- this control measures the effort required to persuade registered voters to change their allegiance to party P2 and vote during an election; and thirdly, the electoral campaign effort- this control focuses on convincing non-participating registered voters to support a political party by joining and voting during an election. Our findings suggest that implementing all three control measures is essential for increasing voter participation in elections. This multifaceted approach will not only increase the participation rate but will also have a significant political impact. Again, this will help reduce the number of registered voters who do not cast their ballots, making the elections more representative and inclusive. By focusing on these three control areas, we can address the underlying issues that lead to low voter turnout.