A Geometric Model of Opinion Polarization

Abstract

We introduce a simple geometric model of opinion polarization. It is a model of political persuasion as well as marketing and advertising, utilizing social values. It focuses on the interplay between different topics and persuasion efforts. We demonstrate that societal opinion polarization often arises as an unintended by-product of influencers attempting to promote a product or idea. We discuss a number of mechanisms for the emergence of polarization involving one or more influencers, sending messages strategically, heuristically, or randomly. We also examine some computational aspects of choosing the most effective means of influencing agents and the effects of those strategic considerations on polarization. Funding: J. Hązła was partially supported by the National Science Foundation [Grant DMS-1737944] and later, the Alexander von Humboldt Foundation [African Institute for Mathematical Sciences Rwanda research chair funding] as well as the German Academic Exchange Service (DAAD) [grant in cooperation with Goethe University in Frankfurt]. Y. Jin was partially supported by the Department of Defense [Grant ARO MURI W911NF1910217]. E. Mossel was partially supported by the Simons Investigator in Mathematics [Award 622132], the National Science Foundation [Awards DMS-1737944 and CCF-1918421] and the Department of Defense [Grant ARO MURI W911NF1910217] and Vannevar Bush [Faculty Fellowship ONR-N00014-20-1-2826]. G. Ramnarayan was partially supported by the National Science Foundation [Grant DMS-1737944] and the Department of Defense [Grant ARO MURI W911NF1910217].