Strategic Partitioning and Manipulability in Two-Round Elections

2026-03-16

AI Summary

This study investigates how to maximize the winning probability of a target candidate in two-round elections through strategic initial grouping of candidates. Building upon spatial voting models and cyclic preference structures, the authors derive an asymptotic expression for the target candidate’s victory probability using probabilistic analysis, asymptotic theory, and Monte Carlo simulations. Both theoretical and simulation results demonstrate that, as the number of candidates grows large, the optimal width of the primary cluster converges to one-fifth of the total candidate pool. Furthermore, with an increasing electorate size, the global winning probability of the target candidate rapidly approaches unity. Confidence intervals from simulations corroborate the accuracy of the theoretical predictions.

Technology Category

Game Theory and Economic Paradigms: Social Choice / VotingSearch and Optimization: Combinatorial OptimizationHumans and AI: Voting

Application Category

User Modeling, Personalization and Recommendation: Practical large-scale studies of user experienceSecurity and Privacy: Large-scale security measurementsEconomics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

We consider a two-round election model involving $m$ voters and $n$ candidates. Each voter is endowed with a strict preference list ranking the candidates. In the first round, the candidates are partitioned into two subsets, $A$ and $B$, and voters select their preferred candidate from each. Provided there are no ties, the two respective winners advance to a second round, where voters choose between them according to their initial preference lists. We analyze this scenario using a probabilistic framework based on a spatial voting model with cyclically constructed preference lists and uniformly distributed ideal points. Our objective is to determine the optimal initial partition of $A$ and $B$ that maximizes a target candidate's probability of winning. We analytically evaluate this success probability and derive its asymptotic behavior as the number of candidates $n \to \infty$. A key finding is that the asymptotically optimal relative width of the main discrete cluster converges precisely to one-fifth of the total number of candidates. Finally, we provide computational results and confidence intervals derived from simulation algorithms that validate the analytical framework. Specifically, we demonstrate that the probability of the universal victory event rapidly approaches $1$ as the electorate size increases.

Problem

• two-round elections
• strategic partitioning
• manipulability
• voting model
• candidate partitioning

Innovation

• strategic partitioning
• two-round elections
• spatial voting model
• asymptotic analysis
• manipulability