Duverger's Law Experiment

Multi-step simulation demonstrating Duverger's Law: FPTP tends toward two-party systems while PR maintains multi-party diversity.

run_duverger_experiment

Run a sequence of elections with strategic voting to observe convergence effects.

from electoral_sim.analysis.duverger import run_duverger_experiment

history = run_duverger_experiment(
    n_voters=2000,
    n_parties=5,
    n_steps=10,
    system="FPTP",
    seed=42,
)

Parameters: | Parameter | Type | Default | Description | |-----------|------|---------|-------------| | n_voters | int | 2000 | Number of voters | | n_parties | int | 5 | Number of initial parties | | n_steps | int | 10 | Number of sequential elections | | system | Literal["FPTP", "PR"] | "FPTP" | Electoral system to simulate | | seed | int | 42 | Random seed | | strategic_penalty | float | 50.0 | Utility penalty for voting for unviable parties | | viability_threshold | float | 0.15 | Vote share threshold for party viability | | temperature | float | 0.1 | Logit temperature (lower = sharper choices) |

Returns: List of per-step dicts, each containing: | Key | Type | Description | |-----|------|-------------| | step | int | Election number (0-indexed) | | enp | float | Effective Number of Parties | | vote_shares | list[float] | Vote share per party | | winner | int | Index of winning party |

Mechanics: The experiment uses BehaviorEngine with ProximityModel + WastedVoteModel to capture the psychological effect of Duverger's Law. After each election, vote shares become the viability signal for the next round, creating a feedback loop that amplifies strategic voting.

Example:

# Compare FPTP vs PR convergence
import polars as pl

fptp = run_duverger_experiment(n_voters=5000, system="FPTP", n_steps=15)
pr = run_duverger_experiment(n_voters=5000, system="PR", n_steps=15)

for h in fptp:
    print(f"Step {h['step']}: ENP = {h['enp']:.2f}")

# Under FPTP, ENP should converge towards ~2
# Under PR, ENP should remain close to n_parties

Research Basis

Duverger's Law mechanics rely on two effects:

Mechanical Effect: High threshold for representation in FPTP — only the largest party in each constituency wins a seat.
Psychological Effect: Strategic voting to avoid wasted votes — voters abandon unviable parties over repeated election cycles.

The experiment simulates both effects simultaneously using WastedVoteModel with a viability feedback loop.