Epstein Civil Violence Model#

Summary#

This model is based on Joshua Epstein’s simulation of how civil unrest grows and is suppressed. Citizen agents wander the grid randomly, and are endowed with individual risk aversion and hardship levels; there is also a universal regime legitimacy value. There are also Cop agents, who work on behalf of the regime. Cops arrest Citizens who are actively rebelling; Citizens decide whether to rebel based on their hardship and the regime legitimacy, and their perceived probability of arrest.

The model generates mass uprising as self-reinforcing processes: if enough agents are rebelling, the probability of any individual agent being arrested is reduced, making more agents more likely to join the uprising. However, the more rebelling Citizens the Cops arrest, the less likely additional agents become to join.

How to Run#

To run the model interactively, in this directory, run the following command

    $ solara run app.py

Files#

model.py: Core model code.
agent.py: Agent classes.
app.py: Sets up the interactive visualization.
Epstein Civil Violence.ipynb: Jupyter notebook conducting some preliminary analysis of the model.

Agents#

import math
from enum import Enum

import mesa


class CitizenState(Enum):
    ACTIVE = 1
    QUIET = 2
    ARRESTED = 3


class EpsteinAgent(mesa.experimental.cell_space.CellAgent):
    def update_neighbors(self):
        """
        Look around and see who my neighbors are
        """
        self.neighborhood = self.cell.get_neighborhood(radius=self.vision)
        self.neighbors = self.neighborhood.agents
        self.empty_neighbors = [c for c in self.neighborhood if c.is_empty]

    def move(self):
        if self.model.movement and self.empty_neighbors:
            new_pos = self.random.choice(self.empty_neighbors)
            self.move_to(new_pos)


class Citizen(EpsteinAgent):
    """
    A member of the general population, may or may not be in active rebellion.
    Summary of rule: If grievance - risk > threshold, rebel.

    Attributes:
        hardship: Agent's 'perceived hardship (i.e., physical or economic
            privation).' Exogenous, drawn from U(0,1).
        regime_legitimacy: Agent's perception of regime legitimacy, equal
            across agents.  Exogenous.
        risk_aversion: Exogenous, drawn from U(0,1).
        threshold: if (grievance - (risk_aversion * arrest_probability)) >
            threshold, go/remain Active
        vision: number of cells in each direction (N, S, E and W) that agent
            can inspect
        condition: Can be "Quiescent" or "Active;" deterministic function of
            greivance, perceived risk, and
        grievance: deterministic function of hardship and regime_legitimacy;
            how aggrieved is agent at the regime?
        arrest_probability: agent's assessment of arrest probability, given
            rebellion
    """

    def __init__(
        self, model, regime_legitimacy, threshold, vision, arrest_prob_constant
    ):
        """
        Create a new Citizen.
        Args:
            model: the model to which the agent belongs
            hardship: Agent's 'perceived hardship (i.e., physical or economic
                privation).' Exogenous, drawn from U(0,1).
            regime_legitimacy: Agent's perception of regime legitimacy, equal
                across agents.  Exogenous.
            risk_aversion: Exogenous, drawn from U(0,1).
            threshold: if (grievance - (risk_aversion * arrest_probability)) >
                threshold, go/remain Active
            vision: number of cells in each direction (N, S, E and W) that
                agent can inspect. Exogenous.
            model: model instance
        """
        super().__init__(model)
        self.hardship = self.random.random()
        self.risk_aversion = self.random.random()
        self.regime_legitimacy = regime_legitimacy
        self.threshold = threshold
        self.state = CitizenState.QUIET
        self.vision = vision
        self.jail_sentence = 0
        self.grievance = self.hardship * (1 - self.regime_legitimacy)
        self.arrest_prob_constant = arrest_prob_constant
        self.arrest_probability = None

        self.neighborhood = []
        self.neighbors = []
        self.empty_neighbors = []

    def step(self):
        """
        Decide whether to activate, then move if applicable.
        """
        if self.jail_sentence:
            self.jail_sentence -= 1
            return  # no other changes or movements if agent is in jail.
        self.update_neighbors()
        self.update_estimated_arrest_probability()

        net_risk = self.risk_aversion * self.arrest_probability
        if (self.grievance - net_risk) > self.threshold:
            self.state = CitizenState.ACTIVE
        else:
            self.state = CitizenState.QUIET

        self.move()

    def update_estimated_arrest_probability(self):
        """
        Based on the ratio of cops to actives in my neighborhood, estimate the
        p(Arrest | I go active).
        """
        cops_in_vision = 0
        actives_in_vision = 1  # citizen counts herself
        for neighbor in self.neighbors:
            if isinstance(neighbor, Cop):
                cops_in_vision += 1
            elif neighbor.state == CitizenState.ACTIVE:
                actives_in_vision += 1

        # there is a body of literature on this equation
        # the round is not in the pnas paper but without it, its impossible to replicate
        # the dynamics shown there.
        self.arrest_probability = 1 - math.exp(
            -1 * self.arrest_prob_constant * round(cops_in_vision / actives_in_vision)
        )


class Cop(EpsteinAgent):
    """
    A cop for life.  No defection.
    Summary of rule: Inspect local vision and arrest a random active agent.

    Attributes:
        unique_id: unique int
        x, y: Grid coordinates
        vision: number of cells in each direction (N, S, E and W) that cop is
            able to inspect
    """

    def __init__(self, model, vision, max_jail_term):
        """
        Create a new Cop.
        Args:
            x, y: Grid coordinates
            vision: number of cells in each direction (N, S, E and W) that
                agent can inspect. Exogenous.
            model: model instance
        """
        super().__init__(model)
        self.vision = vision
        self.max_jail_term = max_jail_term

    def step(self):
        """
        Inspect local vision and arrest a random active agent. Move if
        applicable.
        """
        self.update_neighbors()
        active_neighbors = []
        for agent in self.neighbors:
            if isinstance(agent, Citizen) and agent.state == CitizenState.ACTIVE:
                active_neighbors.append(agent)
        if active_neighbors:
            arrestee = self.random.choice(active_neighbors)
            arrestee.jail_sentence = self.random.randint(0, self.max_jail_term)
            arrestee.state = CitizenState.ARRESTED

        self.move()

Model#

import mesa
from mesa.examples.advanced.epstein_civil_violence.agents import (
    Citizen,
    CitizenState,
    Cop,
)


class EpsteinCivilViolence(mesa.Model):
    """
    Model 1 from "Modeling civil violence: An agent-based computational
    approach," by Joshua Epstein.
    http://www.pnas.org/content/99/suppl_3/7243.full

    Args:
        height: grid height
        width: grid width
        citizen_density: approximate % of cells occupied by citizens.
        cop_density: approximate % of cells occupied by cops.
        citizen_vision: number of cells in each direction (N, S, E and W) that
            citizen can inspect
        cop_vision: number of cells in each direction (N, S, E and W) that cop
            can inspect
        legitimacy:  (L) citizens' perception of regime legitimacy, equal
            across all citizens
        max_jail_term: (J_max)
        active_threshold: if (grievance - (risk_aversion * arrest_probability))
            > threshold, citizen rebels
        arrest_prob_constant: set to ensure agents make plausible arrest
            probability estimates
        movement: binary, whether agents try to move at step end
        max_iters: model may not have a natural stopping point, so we set a
            max.
    """

    def __init__(
        self,
        width=40,
        height=40,
        citizen_density=0.7,
        cop_density=0.074,
        citizen_vision=7,
        cop_vision=7,
        legitimacy=0.8,
        max_jail_term=1000,
        active_threshold=0.1,
        arrest_prob_constant=2.3,
        movement=True,
        max_iters=1000,
        seed=None,
    ):
        super().__init__(seed=seed)
        self.movement = movement
        self.max_iters = max_iters

        self.grid = mesa.experimental.cell_space.OrthogonalVonNeumannGrid(
            (width, height), capacity=1, torus=True, random=self.random
        )

        model_reporters = {
            "active": CitizenState.ACTIVE.name,
            "quiet": CitizenState.QUIET.name,
            "arrested": CitizenState.ARRESTED.name,
        }
        agent_reporters = {
            "jail_sentence": lambda a: getattr(a, "jail_sentence", None),
            "arrest_probability": lambda a: getattr(a, "arrest_probability", None),
        }
        self.datacollector = mesa.DataCollector(
            model_reporters=model_reporters, agent_reporters=agent_reporters
        )
        if cop_density + citizen_density > 1:
            raise ValueError("Cop density + citizen density must be less than 1")

        for cell in self.grid.all_cells:
            klass = self.random.choices(
                [Citizen, Cop, None],
                cum_weights=[citizen_density, citizen_density + cop_density, 1],
            )[0]

            if klass == Cop:
                cop = Cop(self, vision=cop_vision, max_jail_term=max_jail_term)
                cop.move_to(cell)
            elif klass == Citizen:
                citizen = Citizen(
                    self,
                    regime_legitimacy=legitimacy,
                    threshold=active_threshold,
                    vision=citizen_vision,
                    arrest_prob_constant=arrest_prob_constant,
                )
                citizen.move_to(cell)

        self.running = True
        self._update_counts()
        self.datacollector.collect(self)

    def step(self):
        """
        Advance the model by one step and collect data.
        """
        self.agents.shuffle_do("step")
        self._update_counts()
        self.datacollector.collect(self)

        if self.steps > self.max_iters:
            self.running = False

    def _update_counts(self):
        """Helper function for counting nr. of citizens in given state."""
        counts = self.agents_by_type[Citizen].groupby("state").count()

        for state in CitizenState:
            setattr(self, state.name, counts.get(state, 0))

App#

from mesa.examples.advanced.epstein_civil_violence.agents import (
    Citizen,
    CitizenState,
    Cop,
)
from mesa.examples.advanced.epstein_civil_violence.model import EpsteinCivilViolence
from mesa.visualization import (
    Slider,
    SolaraViz,
    make_plot_component,
    make_space_component,
)

COP_COLOR = "#000000"

agent_colors = {
    CitizenState.ACTIVE: "#FE6100",
    CitizenState.QUIET: "#648FFF",
    CitizenState.ARRESTED: "#808080",
}


def citizen_cop_portrayal(agent):
    if agent is None:
        return

    portrayal = {
        "size": 50,
    }

    if isinstance(agent, Citizen):
        portrayal["color"] = agent_colors[agent.state]
    elif isinstance(agent, Cop):
        portrayal["color"] = COP_COLOR

    return portrayal


def post_process(ax):
    ax.set_aspect("equal")
    ax.set_xticks([])
    ax.set_yticks([])
    ax.get_figure().set_size_inches(10, 10)


model_params = {
    "seed": {
        "type": "InputText",
        "value": 42,
        "label": "Random Seed",
    },
    "height": 40,
    "width": 40,
    "citizen_density": Slider("Initial Agent Density", 0.7, 0.0, 0.9, 0.1),
    "cop_density": Slider("Initial Cop Density", 0.04, 0.0, 0.1, 0.01),
    "citizen_vision": Slider("Citizen Vision", 7, 1, 10, 1),
    "cop_vision": Slider("Cop Vision", 7, 1, 10, 1),
    "legitimacy": Slider("Government Legitimacy", 0.82, 0.0, 1, 0.01),
    "max_jail_term": Slider("Max Jail Term", 30, 0, 50, 1),
}

space_component = make_space_component(
    citizen_cop_portrayal, post_process=post_process, draw_grid=False
)

chart_component = make_plot_component(
    {state.name.lower(): agent_colors[state] for state in CitizenState}
)

epstein_model = EpsteinCivilViolence()

page = SolaraViz(
    epstein_model,
    components=[space_component, chart_component],
    model_params=model_params,
    name="Epstein Civil Violence",
)
page  # noqa