Modeling Explosive Opinion Depolarization in Interdependent Topics

Understanding the dynamics of opinion depolarization is pivotal to reducing the political divide in our society. We propose an opinion dynamics model, which we name the social compass model, for interdependent topics represented in a polar space, where zealots holding extreme opinions are less prone to change their minds. We analytically show that the phase transition from polarization to consensus, as a function of increasing social influence, is explosive if topics are not correlated. We validate our theoretical framework through extensive numerical simulations and recover explosive depolarization also by using initial opinions from the American National Election Studies, including polarized and interdependent topics.

Figure 1

Order parameter $r(\lambda /{\lambda }_c)$, by using different initial opinion distributions from ANES data (topics described in Supplemental Material, Fig. SF 3 [43]). The theoretical threshold ${\lambda }_c$ is computed numerically from Eq. (4), by using the empirical distributions $P(\rho )$ and $P(\phi )$; see Supplemental Material SM IIB.

Figure 2

Order parameter $r(\lambda /{\lambda }_c)$ for different values of $\alpha$. The initial orientation distribution $P(\phi )$ is polarized and correlated [(a) ${\phi }_0=0$] or fully uncorrelated [(b) ${\phi }_0=\pi /4$]. Points (solid lines) represent numerical simulations (theoretical predictions). System size $N={10}^6$. For the uncorrelated case, backward continuation (blue) is plotted in empty symbols. Curves of forward continuation (red) for different $\alpha$ collapse for $\lambda \le {\lambda }_c$, while they are identical to backward continuations for $\lambda >{\lambda }_c$.

Figure 3

Inset: Order parameter $r(\lambda )$ in a forward continuation for different values of ${\phi }_0$. Points (solid lines) represent numerical simulations (theoretical predictions). Main: Threshold value ${\lambda }_c$ as a function of ${\phi }_0$. We compare it by following a forward (dashed line, ${\lambda }_c$) and backward (solid line, ${\lambda }_u$) continuations in $\lambda$ of the phase transition, obtained as the theoretical prediction given by Eq. (9) and numerical simulations, respectively. The plot is colored in red (blue) for ${\phi }_0<{\phi }_c$ (${\phi }_0>{\phi }_c$), signaling the theoretical separation between continuous and explosive transitions. System size $N={10}^3$, constant conviction $\rho =1$ ($\alpha =\infty$).

Figure 4

Main: Order parameter $r(\lambda )$ including both forward (red) and backward (blue) continuations in $\lambda$. We consider correlated (a) and uncorrelated (b) empirical opinions from ANES data as $P(\phi )$. Inset: Initial orientation distributions represented in polar coordinates at $\lambda =0$. These empirical distributions are obtained neglecting all individuals with conviction lower than the median of $P(\rho )$, approaching then the case $\alpha \to \infty$.