Polarization under rising inequality and economic decline

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Science Advances  11 Dec 2020:
Vol. 6, no. 50, eabd4201
DOI: 10.1126/sciadv.abd4201
  • Fig. 1 A simple model of diversity in social interactions.

    (A) From the perspective of a focal individual (black outline), a population is divided into players who are like self (blue) and unlike self (red). Each player has a strategy such that in any given interaction, they choose either a member of the in-group with probability p (blue arrow) or the out-group with probability 1 − p (red arrow). (B) If the focal player participates in an in-group interaction, then it is successful with probability qi, generating a benefit Bi > 0. Otherwise, the interaction fails with probability 1 − qi and generates no benefit. (C) Similarly, if the focal player participates in an out-group interaction, then it succeeds with probability qo, generating a benefit Bo > 0. The interaction fails with probability 1 − qo and generates no benefit. (D) We assume that the utility or fitness for an individual from engaging in multiple social interactions follows an S-shaped curve (Eq. 1), with threshold parameter θ, which describes the quality of the underlying economic environment. When the environment quality (θ, x axis) and benefits received from social interactions (y axis) are low, utility is low (black region). When θ and/or benefits from interactions are high, utility is high (yellow region). (E) Five key parameters control the overall utility or fitness of an individual.

  • Fig. 2 Polarization in a declining economy.

    Evolutionary dynamics of polarization. In the cases shown, we fix Bi = 0.5, Bo = 1, and qi = 1. Utility (Eq. 1) has threshold sharpness h = 10, and gradient α = 0.02. The number of social interactions per individual is n = 5. (A) We calculate the strategy p* that maximizes utility from Eq. 4 (see Methods). When the success of out-group interactions is independent of the strategy of the interaction partner, only one stable strategy evolves, either a highly polarized (p = 1, blue) or a highly diverse strategy (p = 0, red). (B) Individual-based simulations in which individuals copy more successful members of the population (selection strength σ = 10). The purple dotted line tracks the quality of the environment θ. The population size is fixed at N = 1000 with qo = 0.6. Shown are the mean population strategy (black line) across an ensemble of 1000 simulations and the standard deviation (SD) of the strategy distribution for the ensemble (gray region). Innovations occur at rate μ = 0.001 per copying event with size Δ = 0.01 (see section S4). (C) When the success of out-group interactions depends on the strategy of the interaction partner, two or more strategies can be bistable. Arrows indicate the direction of evolution in a large population, in a given environment θ. Blue regions indicate the basin of attraction for polarization p* = 1, while red regions indicate the basin of attraction for diversity p* = 0. We have set qo = 0.6. (D) Individual-based simulations show how polarization increases in a declining economic environment and remains even when the environment returns to being favorable. Parameters for (C) are the same as those given for (B).

  • Fig. 3 Polarization under rising inequality.

    We ran individual-based simulations in an economic environment with exogenously changing levels of inequality θg. Here, we assume sinusoidally varying inequality with a0 = 1.5, θg ∈ [0,1.1], and π = 0.1. All other parameters are those provided in Fig. 2 (C and D). (A) Under rising inequality θg (purple dashed line), polarization sharply increases (black solid line) compared to the case with no inequality (black dashed line). (B) The Gini coefficient for the population (black solid line) changes as the inequality in the underlying economic environment θg changes and as behavioral strategies evolve. Also shown for comparison are the Gini coefficients for a population using a fixed strategy of either polarization (p = 1, blue dashed line) or diversity (p = 0, red dashed line). (C) The average benefits from social interactions decline under rising inequality (solid line) and do not recover to the same levels as when inequality was absent (dashed line), even when the environment is no longer unequal.

  • Fig. 4 Affective polarization and inequality in the United States.

    We show the correlation for the pooled data across all three presidential election cycles (2008, 2012, and 2016) between state-level affective polarization estimated from (3033) and state-level Gini coefficient taken from (35). The dark gray region gives the 95% confidence interval, and the light gray region gives the 95% prediction interval for the model. The expanded region shows individual state-level values. The full dataset and additional analyses can be found in section S5.

Supplementary Materials

  • Supplementary Materials

    Polarization under rising inequality and economic decline

    Alexander J. Stewart, Nolan McCarty, Joanna J. Bryson

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    • Sections S1 to S5
    • Tables S1 to S3
    • Figs. S1 to S11

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