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

TL;DR

This paper introduces an open-source Python framework for simulating and comparing various electoral systems across different voter preference scenarios, using a geometric median-based metric to evaluate their performance.

Contribution

It provides a flexible, extensible simulation platform that evaluates multiple electoral mechanisms against a common metric across diverse voter distributions.

Findings

Plurality and ranked-choice systems perform variably across scenarios.

Proportional systems tend to better approximate the geometric median.

A novel Boltzmann softmax influence mechanism serves as a theoretical benchmark.

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.