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Opinion Dynamics

Social network-based opinion evolution system.

OpinionDynamics

Creates and manages social networks for voter opinion evolution.

from electoral_sim import OpinionDynamics

od = OpinionDynamics(
    n_agents=10_000,
    topology="barabasi_albert",
    m=3,  # edges per new node
    seed=42
)

Constructor Parameters

Parameter Type Default Description
n_agents int required Number of agents in network
topology str "barabasi_albert" Network type
m int 3 BA: edges per new node
k int 4 WS: each node connected to k neighbors
p float 0.1 WS/ER: rewiring/edge probability
seed int None Random seed

Network Topologies

Barabási-Albert (Scale-Free)

Realistic social network structure with hubs. 

od = OpinionDynamics(n_agents=1000, topology="barabasi_albert", m=3)

Watts-Strogatz (Small World)

High clustering with short path lengths. 

od = OpinionDynamics(n_agents=1000, topology="watts_strogatz", k=4, p=0.1)

Erdős-Rényi (Random)

Random graph with specified edge probability. 

od = OpinionDynamics(n_agents=1000, topology="erdos_renyi", p=0.01)

step Method

Evolve opinions by one time step.

new_opinions = od.step(
    opinions,
    model="bounded_confidence",
    epsilon=0.3,
    media_bias=0.0,
    media_strength=0.1,
    system="FPTP"
)

Parameters

Parameter Type Default Description
opinions np.ndarray required Current opinion values
model str "bounded_confidence" Opinion dynamics model
epsilon float 0.3 BC: confidence threshold
media_bias float/array 0.0 Media broadcast position
media_strength float 0.1 Media influence strength
system str "PR" Electoral system (affects susceptibility)

Opinion Models

Bounded Confidence

Agents only influence each other if opinions are within threshold ε.

opinions = od.step(opinions, model="bounded_confidence", epsilon=0.3)

Dynamics: If |opinion_i - opinion_j| < epsilon, agents move toward each other.

Noisy Voter

Random neighbor copying with mutation.

opinions = od.step(opinions, model="noisy_voter", mutation_rate=0.01)

Dynamics: With probability p, copy random neighbor's opinion. With probability mutation_rate, randomly change.

Media Effects

Scalar Media Bias

All agents receive same media signal.

opinions = od.step(
    opinions,
    media_bias=0.5,      # Right-leaning media
    media_strength=0.1   # 10% influence per step
)

Vectorized Media Bias

Agent-specific media diet (from voter media_bias column).

# Different media for each agent
media_bias_vector = np.array([-0.5] * 500 + [0.5] * 500)

opinions = od.step(
    opinions,
    media_bias=media_bias_vector,
    media_strength=0.1
)

Raducha Susceptibility

FPTP voters are more susceptible to media/waves than PR voters.

# FPTP: 1.5x media effect
opinions_fptp = od.step(opinions, system="FPTP", media_bias=0.5, media_strength=0.1)

# PR: 1.0x media effect  
opinions_pr = od.step(opinions, system="PR", media_bias=0.5, media_strength=0.1)

Integration with ElectionModel

from electoral_sim import ElectionModel, OpinionDynamics

# Create social network
od = OpinionDynamics(n_agents=10_000, topology="barabasi_albert", m=3)

# Create model with opinion dynamics
model = ElectionModel(
    n_voters=10_000,
    opinion_dynamics=od,
    seed=42
)

# Run simulation with opinion evolution
for _ in range(100):
    model.step()  # Opinions evolve

# Run election with evolved opinions
results = model.run_election()

Zealots

Fixed-opinion agents that never change.

# Mark 5% as zealots (won't change opinion)
zealot_mask = np.random.rand(1000) < 0.05
zealot_opinions = np.where(zealot_mask, 1.0, opinions)  # Fixed at 1.0

# Zealots maintain their position
new_opinions = od.step(zealot_opinions, model="bounded_confidence")
new_opinions[zealot_mask] = 1.0  # Restore zealot positions