Modeling the Ballot: Agent-Based Insights into Representation, Coalitions, and Welfare

We present an agent-based simulation of democratic decision-making in which autonomous learning agents interact under alternative electoral institutions and social structures. The model integrates six voting mechanisms (Plurality, Approval, Borda, IRV, STV, PR with D'Hondt and Sainte-Laguë divisors), a multi-round coalition protocol with binding/non-binding contracts and side-payments, turnout and ballot-error realism, and networked interaction on Erdös–Rényi, Barabási–Albert, and Watts–Strogatz graphs with homophily. Agents use reinforcement learning algorithms (PPO, A2C, A3C) with a social-welfare objective based on the inequality-averse Atkinson function, augmented by fairness regularizers (representation loss, participation fairness, envy-freeness proxy) and explicit participation costs. We report diagnostics-rich evaluations covering representation and proportionality (e.g., Gallagher, Loosemore–Hanby), fragmentation (effective number of parties), strategic behavior, coalition stability, and welfare/inequality. Classic regularities emerge—e.g., two-bloc competition under Plurality (Duverger-consistent), greater proportionality and fragmentation under PR, and differential seat allocation under D'Hondt vs Sainte-Laguë—providing face validity. The framework delivers a reproducible virtual laboratory for mechanism comparison, institutional design, and welfare–fairness trade-off analysis at population scale.