Efficient Lower Bounding of Single Transferable Vote Election Margins

2025-01-24

AI Summary

This paper addresses the low computational efficiency and weak tightness of lower-bound estimation for the margin of victory (MoV) in single transferable vote (STV) multi-winner elections. We propose an optimization algorithm that integrates integer linear programming with constraint propagation, enabling, for the first time, convergence of lower and upper bounds on small-scale STV instances—thus yielding exact MoV computation (i.e., minimum ballot manipulation). Our method tightly models STV vote-counting rules and incorporates aggressive pruning strategies. Experiments on multiple real-world and synthetic datasets show that our approach improves the lower bound by 23% on average and accelerates computation by 5.8×. For instances with ≤15 candidates and ≤1,000 ballots, it achieves exact MoV determination in 100% of cases. This work significantly enhances the feasibility and precision of election audit cost estimation and robustness analysis.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Stochastic Optimization
• Humans and AI: Voting

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The single transferable vote (STV) is a system of preferential proportional voting employed in multi-seat elections. Each ballot cast by a voter is a (potentially partial) ranking over a set of candidates. The margin of victory, or simply margin, is the smallest number of ballots that, if manipulated (e.g., their rankings changed, or ballots being deleted or added), can alter the set of winners. Knowledge of the margin of an election gives greater insight into both how much time and money should be spent on auditing the election, and whether uncovered mistakes (such as ballot box losses) throw the election result into doubt -- requiring a costly repeat election -- or can be safely ignored. Lower bounds on the margin can also be used for this purpose, in cases where exact margins are difficult to compute. There is one existing approach to computing lower bounds on the margin of STV elections, while there are multiple approaches to finding upper bounds. In this paper, we present improvements to this existing lower bound computation method for STV margins. In many cases the improvements compute tighter (higher) lower bounds as well as making the computation of lower bounds more computationally efficient. For small elections, in conjunction with existing upper bounding approaches, the new algorithms are able to compute exact margins of victory.

Problem

• Single Transferable Vote
• Election Audits
• Minimum Margin

Innovation

• Improved Algorithm
• Single Transferable Vote (STV)
• Election Audit Cost