Statistical Mechanics of Political Polarization

Abstract

Rapidly increasing political polarization threatens democracies around the world. Scholars from several disciplines are assessing and modeling polarization antecedents, processes, and consequences. Social systems are complex and networked. Their constant shifting hinders attempts to trace causes of observed trends, predict their consequences, or mitigate them. We propose an equivalent-neighbor model of polarization dynamics. Using statistical physics techniques, we generate anticipatory scenarios and examine whether leadership and/or external events alleviate or exacerbate polarization. We consider three highly polarized USA groups: Democrats, Republicans, and Independents. We assume that in each group, each individual has a political stance s ranging between left and right. We quantify the noise in this system as a "social temperature" T. Using energy E, we describe individuals' interactions in time within their own group and with individuals of the other groups. It depends on the stance s as well as on three intra-group and six inter-group coupling parameters. We compute the probability distributions of stances at any time using the Boltzmann probability weight exp(-E/T). We generate average group-stance scenarios in time and explore whether concerted interventions or unexpected shocks can alter them. The results inform on the perils of continuing the current polarization trends, as well as on possibilities of changing course.

Keywords: agent-based modeling; agent-based models; anticipatory scenarios; opinion dynamics; political polarization; sociophysics; statistical physics approaches for social dynamics.

Figure 2

Scenario A: (a) s trajectories with competitive K12 < 0, K21 < 0, and K31 < 0, and (b) the corresponding polarization in time.

Figure 3

Competitive scenario: (a) K12 < 0, K31 < 0, and added leadership effect (magnetic field H1 > 0), and (b) the corresponding polarization in time.

Figure 4

Scenario B: (a) K12 > 0, K21 < 0, and K31 < 0, and (b) the corresponding polarization in time.

Figure 5

Phase-space limit cycle of stances in the mixed scenario.

Figure 6

Scenario C is cooperative scenario: (a) K12 > 0, K21 > 0, and K31 < 0, and (b) the corresponding polarization in time.

Figure 1

Growing Democrat–Republican division, 1994–2017 [7].

Figure 7

Robustness of model-stance (here, Democrat) trajectory to small perturbations of the parameter values in time.