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Voter Satisfaction Efficiency (VSE)

Voting System Efficiency analysis: measures how well an electoral outcome maximizes social welfare.

VSE is defined as: 

VSE = (W_actual - W_random) / (W_optimal - W_random)

Where: - W_actual: Social welfare of the actual election winner(s) - W_optimal: Social welfare of the best possible winner(s) - W_random: Average social welfare of a random winner

Reference: Jameson Quinn, "Voting System Efficiency"

calculate_vse

Calculate Voting System Efficiency from a utility matrix and seat shares.

from electoral_sim.analysis.vse import calculate_vse

vse = calculate_vse(
    utilities=utilities,
    seat_shares=seat_shares,
    random_iterations=0,
)

Parameters: | Parameter | Type | Description | |-----------|------|-------------| | utilities | np.ndarray | (n_voters, n_parties) matrix of voter utilities | | seat_shares | np.ndarray | (n_parties,) array of seat shares (0-1) | | random_iterations | int | Unused; w_random is analytical (mean of all options) |

Returns: VSE score (typically 0.0 to 1.0). Returns 0.0 if all options have equal total utility (division by zero guard).

Algorithm: 1. W_optimal — maximum total utility across all parties (single-winner assumption) 2. W_random — mean total utility across all parties 3. W_actual — weighted average of total utility using seat shares

Example: 

import numpy as np
from electoral_sim import ElectionModel
from electoral_sim.analysis.vse import calculate_vse

model = ElectionModel(n_voters=10_000)
results = model.run_election()

# Get utility matrix and seat shares from the model
utilities = np.random.normal(50, 15, (10_000, 5))  # Example utilities
seat_shares = results["seats"] / results["seats"].sum()

vse = calculate_vse(utilities, seat_shares)
print(f"VSE: {vse:.3f}")

calculate_welfare

Calculate Social Welfare (sum of utilities) for a given outcome.

from electoral_sim.analysis.vse import calculate_welfare

welfare = calculate_welfare(utilities=np.array([0.8, 0.6, 0.3, 0.1]))

Parameters: | Parameter | Type | Description | |-----------|------|-------------| | utilities | np.ndarray | (n_voters,) utilities for the chosen outcome | | weights | np.ndarray \| None | Optional (n_voters,) voter weights |

Returns: Total welfare (weighted sum if weights provided).

Example: 

# Weighted welfare (e.g., by constituency size)
weights = np.array([1.0, 1.0, 2.0, 1.0])
welfare = calculate_welfare(utilities, weights=weights)
print(f"Weighted welfare: {welfare:.2f}")