Abstract

While the study of election theory is not a new field in and of itself, recent research has applied various concepts in computer science to the study of social choice theory, which includes election theory. From a security perspective, it is pertinent to investigate how stable election systems are in the face of noise, disruption, and manipulation. Recently, work related to computational election systems has also been of interest to artificial intelligence researchers, where it is incorporated into the decision-making processes of distributed systems. The quantitative analysis of a voting rule's resistance to noise is the robustness, the probability of how likely the outcome of the election is to change given a certain amount of noise. Prior research has studied the robustness of voting rules under very small amounts of noise, e.g. swapping the ranking of two adjacent candidates in one vote. Our research expands upon this previous work by considering a more disruptive form of noise: an arbitrary reordering of an entire vote. Given k noise disruptions, we determine how likely the election is to remain unchanged (the k-robustness) by relating the k-robustness to the 1-robustness. We can thereby provide upper and/or lower bounds on the robustness of voting rules; specifically, we examine five well-established rules: scoring rules (a general class of rules, containing Borda, plurality, and veto, among others), Copeland, Maximin (also known as Minimax or Simpson-Kramer), Bucklin, and plurality with runoff.

Publication Date

5-30-2008

Document Type

Thesis

Student Type

Graduate

Advisor

Christopher M. Homan

Advisor/Committee Member

Piotr Faliszewski

Advisor/Committee Member

Charles Border

Campus

RIT – Main Campus

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