Final answer:
Political corruption most influenced the end of Roman democracy, as politicians attempted to gain support by providing free food and entertainment instead of reliable governance.
Step-by-step explanation:
According to the provided excerpt, the factor that most influenced the end of Roman democracy was political corruption. The growth of the proletariat led to a disruption of the Roman political system, resulting in the collapse of the traditional patron-client system. In response to the changing dynamic, politicians began to rely on offering free food, entertainment, and promises of public works projects to gain the support of the urban masses. This fostered an environment of widespread dissatisfaction with the government of the republic, indicating that political corruption played a significant role in the decline of Roman democracy.