The charm of independent voters

Abstract

Independent voters play an increasingly decisive role in contemporary elections, yet their collective behavior remains poorly understood. This paper investigates how a minority of voters with greater flexibility in their political preferences influences opinion formation in polarized electorates. Using a modified Deffuant model, we show that even simple heterogeneity in agents' openness to vote switching can generate rich and unexpected collective outcomes: "open-minded" agents may (i) prevent full convergence into established party blocs, (ii) give rise to transient centrist clusters, or (iii) align with the positions of major parties. These dynamics resemble empirical patterns observed among real-world independent voters. Our results demonstrate that small shifts in openness parameters can substantially reshape the macroscopic structure of political competition, offering a simple explanation for oscillatory electoral outcomes and the emergence of unstable centrist or cross-cutting coalitions.

Figures (7)

• Figure 1: Deffuant model with $n=1000$ agents when the parameter $\epsilon$ is $0.15$ and the parameter $\mu$ is $0.2$. On the left panel, the initial opinions of individual agents are represented by blue circles, while the right panel displays their distribution as a histogram with 10 bins. The orange crosses show the final converged state after $t=10^{5}$ iteration steps.
• Figure 2: A non-converged Deffuant model. All parameter settings are the same as in Fig. \ref{['basic_model']} expect that the simulation was stopped after $t=20000$ iteration steps.
• Figure 3: Deffuant model with $n=1000$ agents when the parameter $\epsilon$ is $0.15$ and the parameter $\mu$ is $0.2$. However, the initial opinion distribution shown by blue is non-uniform -- instead, it follows a normal distribution with $m=0.5$ mean and $\sigma=0.15$ standard deviation. The final converged states after $t=10^{5}$ iterations are shown by orange.
• Figure 4: Deffuant model with $n=1000$ agents when the parameter $\epsilon$ is $0.15$ and the parameter $\mu$ is $0.2$. However, the initial opinion distribution follows now a bimodal distribution function (a function with two Gaussian peaks) where $m_{1}=0.35$, $m_{2}=0.65$ and $\sigma=0.15$. The final converged states after $t=10^{5}$ iterations are shown by orange.
• Figure 5: Deffuant model with $n=1000$ agents where $\nu = 200$ are Open-Minded when the parameter $\epsilon$ is $0.15$ and the parameter $\mu$ is $0.2$. On the left panel, the initial -- uniform -- opinions of Normal agents are represented by blue circles while the initial -- also uniform -- opinions of Open-Minded agents are represented by red circles. Similarly, the blue and red crosses show the final converged state of the opinions of Normal and Open-Minded agents after $t=10^{5}$ iteration steps, respectively. The right panel displays the distribution of opinions as a histogram (color coding on the top-left corner of the figure).