Date of Award

Spring 5-11-2026

Document Type

Undergraduate Honors Thesis

Degree Name

Bachelor of Arts in Mathematics

Department

Mathematics

Advisor

Dr. Cameron Parker

Abstract

This thesis develops a computational framework for measuring the vulnerability of voting rules to coordinated strategic manipulation. While classical results show that most voting systems are theoretically manipulable, less is known about the magnitude of coordination required to alter outcomes or how that magnitude varies across institutional designs. I define the minimal manipulating coalition size k* as the smallest number of voters whose strategic ballot changes can overturn a sincere election outcome under a given rule. To enable cross-election comparison, I introduce the normalized manipulation threshold θ = k*/n . Using algorithmic search procedures and Monte Carlo simulation, I estimate θ for plurality, Borda count, instant runoff voting, and sequential pairwise voting. The results provide a systematic quantitative comparison of structural robustness, offering a practical framework for comparing the susceptibility of voting systems to manipulation.

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