Emergence, Evolution and Manipulation of Swing Voters in Presidential Election

TL;DR

The paper addresses swing voters in polarized elections by introducing a two-dimensional opinion framework where each agent's state is $o_i(t)=(x_i(t),y_i(t))$ and an antagonism parameter $\\rho\\in[0,1]$ couples campaign pressure to interpersonal dynamics. It classifies voters into five groups and derives convex-update rules for $x_i(t+1)$ and $y_i(t+1)$, balancing initial preferences, neighbor influence, and the antagonism constraint; the framework is validated on core Twitter networks from the 2020 U.S. election. The results reveal rich regimes—fragmentation, polarization, multipolarization, and consensus—driven by open-mindedness $\\epsilon$, stubbornness $\\lambda$, and antagonism $\\rho$, including a counterintuitive voting-advantage reversal under extreme antagonism. The study demonstrates that core social-network structures can amplify or dampen these dynamics and provides a generalizable approach for analyzing opinion dynamics and potential manipulation in polarized public discourse. The framework is broadly applicable beyond elections to other polarized issues, offering insights into the balance between strategic messaging and organic interpersonal influence.

Abstract

Political polarization, fueled by public discourse and echo chambers, threatens the foundation 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 intensities 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 manipulated by the two parties, 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 validated on the core retweet networks during 2020 U.S. presidential election. Building upon multidimensional opinion model, our results highlight the possibility of manipulating 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.

Figures (10)

• Figure 1: (a) Schematic of the mesoscale multi-cognitive framework based on two-dimensional coupling opinions. Voters are divided into five categories: Party A supporters, Party A leaners, neutrals, Party B leaners, and Party B supporters according to the disparities of their opinions towards Party A and B. (b) Schematic of the multi-scale opinion dynamics which incorporates voters' initial preferences, network interactions and antagonism effect. The blue, red, and green arrows represent the interactions between opinions towards Party A, Party B, and both parties, respectively. Among them, voter 1 interacts with voter 3 and voter 4 respectively on opinions towards Party A and Party B, while voter 1 and voter 2 interact with each other on opinions towards both parties. Furthermore, the antagonism effect forces the opinions of all voters to converge in the direction of one-dimensional opposition. (c-d) An example of distributions of two-dimensional coupling opinions and voting outcomes. Polarization emerges in the group opinions of the two parties, and the voting outcomes show a trimodal distribution, with the neutral non-voting group appearing. Parameters: the example begins from an ER graph with $N=10^3$ and $\langle k \rangle=40$, $z_o=0.5$, and $z_v=0.2$. The fixed parameters are: $\epsilon=0.2$, $\lambda=0.3$, $\rho=0$.
• Figure 2: Open-mindedness and opinion evolution. (a) The open-mindedness (characterized by the interaction threshold) of voters significantly influences the distribution of two-dimensional opinions. (b) Small open-mindedness lead to opinion segmentation. (c) Under a moderate level of open-mindedness, the ideological stances of both parties emerge polarization. (d,e) The continuously enhanced open-mindedness goes through multipolarization and gradually fosters a broad consensus around neutrality. Simulation results are averaged over 100 independent runs. Parameters: simulations in (a) begin from an ER graph with $N=10^4$ and $\langle k \rangle=40$, $z_o=0.5$, $z_v=0.2$, $\rho=0$, and $\lambda=0.3$. We change (b) $\epsilon=0.1$. (c) $\epsilon=0.25$. (d) $\epsilon=0.35$. (e) $\epsilon=0.45$.
• Figure 3: The emergence of two-dimensional echo chambers under antagonism effect. Increasing the level of antagonism are sufficient to (a) promote the voting participation of swing voters and (b) reduce the diversity of opinion interactions. In (b), $I_A$, $I_B$ and $I_{AB}$ respectively denote the average number of interacting neighbors regarding $x-$opinion, $y-$opinion, and both opinions. (c)-(e) show stable voting distributions and network structures corresponding to different strength of antagonism effects, illustrating the elimination of the neutrals and the emergence of two-dimensional echo chambers. Parameters: simulations begin from an ER graph with $N=10^4$ and $\langle k \rangle=40$, $z_o=0.5$, $z_v=0.2$, $\epsilon=0.2$, and $\lambda=0.3$. We change (c) $\rho=0$. (d) $\rho=0.4$. (e) $\rho=0.8$.
• Figure 4: Nonlinear coupling between stubbornness and antagonism effect: evolution of the swing group. We show the number of neutrals at low (a, $\epsilon$=0.15), moderate (b, $\epsilon$=0.2), and high (c, $\epsilon$=0.25) open-mindedness. A relatively high value of stubbornness maintains the polarization of partisan opinions, while low stubbornness can cause complex phase transitions between polarization and consensus. (d-g)We present the distribution of two-dimensional opinions and voting outcomes under four typical cases. Simulation results are averaged over 50 independent runs. Parameters: simulations begin from an ER graph with $N=10^4$ and $\langle k \rangle=40$, $z_o=0.5$, and $z_v=0.2$. We change (d) $\epsilon=0.2, \lambda=0.3, \rho=0.1$. (e) $\epsilon=0.2, \lambda=0.3, \rho=0.5$. (f) $\epsilon=0.2, \lambda=0.1, \rho=0.2$. (g) $\epsilon=0.2, \lambda=0.1, \rho=0.7$.
• Figure 5: Manipulation on swing voters and reversal of voting advantage. We apply heterogeneous antagonism effects to voters with different party preferences and show phase diagrams (a, c, d, e) at different stubbornness levels. Under low and moderate antagonism level, the party that imposes stronger antagonism can obtain higher vote support, and this advantage weakens as the group stubbornness level increases. When both parties create extremely strong antagonism, the party with weaker antagonism strategy may obtain more votes from swing voters and surprisingly achieve a reversal of voting advantage. We verify the existence of such reversal through Figure (b). We implement a square box with a length and width of 0.4 on Figure (a), letting its center slide along the diagonal direction. The horizontal axis is the antagonism level corresponding to the center of the rectangular box, and the vertical axis is the proportion of times the party with weaker antagonism reverse the voting advantage. Figure (f) shows the evolution snapshots of voting reversal under fixed parameters. Simulation results are averaged over 50 independent runs. Parameters: simulations begin from an ER graph with $N=10^4$ and $\langle k \rangle=40$, $z_o=0.5$, $z_v=0.2$, and $\epsilon=0.2$. Other parameters: (a) $\lambda=0.2$. (c) $\lambda=0.3$. (d) $\lambda=0.4$. (e) $\lambda=0.5$. (f) $\lambda=0.2$, $\rho_A=0.6$, $\rho_B=0.9$.