Evolution of swing voters under strategic campaigns in presidential elections

Political polarization, fueled by public discourse and echo chambers, has profound implications for the functioning of democratic elections. However, traditional one-dimensional opinion models—assuming “support for one party equals opposition to another”—fail to capture the nuanced dynamics of swing voters (including neutrals, left leaners, and right leaners), who are critical for the final election outcomes. This study introduces a two-dimensional opinion model that classifies voters into five groups, enabling precise characterization of the swing group's interactive behaviors. Importantly, we introduce antagonism effect to describe the intensity with which the two camps incite opposition and exert voting pressure in the run-up to the election, typically via Us-versus-Them framing. By integrating the open-mindedness of voters, the stubbornness of opinion interactions, and the antagonism effect arising from strategic campaigns, we systematically explore the intricate interplay between top-down political campaigns and bottom-up interpersonal opinion dynamics, unveiling their nonlinear coupling impacts on the emergence and evolution of swing voters. Counterintuitively, we find that extreme antagonism effects might backfire in presidential election: When both parties adopt intense antagonistic strategies, the party that polarizes more strongly risks alienating swing voters, thereby enabling its ostensibly weaker opponent to prevail. These insights are also illustrated on the core retweet networks during the 2020 U.S. presidential election. Building upon multidimensional opinion model, our results highlight the possibility of mobilizing swing voters and shaping electoral outcomes through antagonistic strategies of political parties. Our work also provides a nuanced and generalizable framework for analyzing opinion dynamics in other polarized public discourse.