Electoral Systems Simulator: An Open Framework for Comparing Electoral Mechanisms Across Voter Distribution Scenarios

2026-03-06

AI Summary

This study addresses the lack of a unified, scalable framework for systematically comparing electoral mechanisms under diverse voter preference distributions. The authors propose an open-source Python simulation framework that embeds voters and candidates in a two-dimensional ideological space, generates sincere ballots based on Euclidean distances, and evaluates outcomes primarily by their proximity to the geometric median of the voter distribution. Innovatively, they introduce a theoretical upper-bound benchmark derived from a Boltzmann softmax kernel. The framework enables fair, reproducible comparisons across major voting systems—including plurality, instant-runoff, approval, score, Condorcet, and proportional representation—across empirical scenarios ranging from consensus to polarization. Through 200 Monte Carlo simulations, the study quantifies each mechanism’s accuracy and stability, with all code publicly released to enhance scalability and transparency in electoral system research.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Humans and AI: Voting
• Machine Learning: Learning Preferences or Rankings

Application Category

• Economics, Online Markets and Human Computation: Economics and fairness of platforms and recommendation systems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Here we present \texttt{electoral\_sim}, an open-source Python framework for simulating and comparing electoral systems across diverse voter preference distributions. The framework represents voters and candidates as points in a two-dimensional ideological space, derives sincere ballot profiles from Euclidean preference distances, and evaluates several standard electoral mechanisms -- including plurality, ranked-choice, approval, score, Condorcet, and two proportional representation systems -- against a common primary metric: the Euclidean distance between the electoral outcome and the geometric median of the voter distribution. We evaluate these systems across many empirically-grounded scenarios ranging from unimodal consensus electorates to sharply polarised bimodal configurations, reporting both single-run and Monte Carlo stability results across 200 trials per scenario. As a case study in framework extensibility, we implement and evaluate a novel hypothetical mechanism that is not currently implemented in any jurisdiction -- in which each voter's influence is distributed across candidates via a Boltzmann softmax kernel. This system is included as a theoretical benchmark characterising an approximate upper bound on centroid-seeking performance, rather than as a policy proposal. All code is released publicly at https://github.com/mukhes3/electoral_sim.

Problem

• electoral systems
• voter distribution
• election simulation
• preference aggregation
• comparative evaluation

Innovation

• electoral simulation
• ideological space
• geometric median
• Boltzmann softmax
• Monte Carlo stability