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Society is among nature’s most intricate complex systems—a vast ensemble of interacting individuals whose collective behaviors emerge across multiple scales, from ephemeral digital trends to enduring democratic institutions. The emergent properties arising from these interactions often manifest as non-trivial macroscopic patterns that cannot be easily inferred from individual behaviors [1]. This thesis employs tools from statistical physics, network science, and dynamical systems to investigate two fundamental aspects of collective public opinion: polarization in social networks and universal patterns in democratic elections. Through this examination, we demonstrate that randomness, properly understood and harnessed, serves as both an explanatory principle and an intervening force for understanding and improving such social systems.

1.1Complex Systems Framework for Social Dynamics

Human society operates across extraordinarily diverse scales, both spatial and temporal. Spatially, interactions span from local communities to global networks, encompassing physical proximity interactions and increasingly, technology-mediated connections that transcend geographic constraints [2]. Temporally, processes range from millisecond-scale information transmission to decade-spanning political movements and generational cultural shifts.

Consider how a single tweet can trigger cascading reactions across millions of users within minutes, while simultaneously contributing to slowly-evolving cultural narratives that unfold over years.