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Evolution of swing voters under strategic campaigns in presidential elections

Ziqian Liu1,2,3, Xin Wang1,2,3,4,5,6,*, Junyu Lu1,3, Longzhao Liu1,2,3,4,5, Hongwei Zheng7, and Shaoting Tang1,2,3,4,5,8,9,10,†

  • 1School of Artificial Intelligence, Beihang University, Beijing 100191, China
  • 2Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing 100191, China
  • 3Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Beihang University, Beijing 100191, China
  • 4Zhongguancun Laboratory, Beijing 100094, China
  • 5State Key Laboratory of Complex & Critical Software Environment, Beihang University, Beijing 100191, China
  • 6State Key Laboratory of General Artificial Intelligence, BIGAI, Beijing, China
  • 7Beijing Academy of Blockchain and Edge Computing, Beijing 100085, China
  • 8Hangzhou International Innovation Institute, Beihang University, Hangzhou 311115, China
  • 9Institute of Trustworthy Artificial Intelligence, Zhejiang Normal University, Hangzhou 310012, China
  • 10Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai 264003, China

  • *Contact author: wangxin_1993@buaa.edu.cn
  • †Contact author: tangshaoting@buaa.edu.cn
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Phys. Rev. Research 8, 013306 – Published 23 March, 2026

DOI: https://doi.org/10.1103/jdyh-t4rp

Abstract

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.

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Phys. Rev. Research 8, 013306– Published 23 March, 2026
  • Received 30 October 2025
  • Accepted 29 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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