Arrow's Impossibility Theorem and American Idol
Event Type
Research Presentation
Academic Department
Mathematics and Statistics
Location
Dana Science Building, 2nd floor
Start Date
24-4-2026 1:00 PM
End Date
24-4-2026 2:30 PM
Description
This paper explores both the mathematical foundations and real-world applications of voting theory by examining the proof of Arrow's Impossibility Theorem and its relevance to modern systems such as American Idol. The first part of this study provides a detailed explanation of Arrow's Theorem, including the formal definitions of key fairness criteria: Non-dictatorship, Pareto efficiency, Independence of Irrelevant Alternatives (IIA), and unrestricted domain. Building on this, I then apply these concepts to the voting structure used in American Idol, which primarily follows a plurality voting system. By analyzing how audience voting determines winners, the study investigates whether the system satisfies Arrow's fairness criteria and identifies the ways in which it falls short, particularly through violations of independence of irrelevant alternatives.
Arrow's Impossibility Theorem and American Idol
Dana Science Building, 2nd floor
This paper explores both the mathematical foundations and real-world applications of voting theory by examining the proof of Arrow's Impossibility Theorem and its relevance to modern systems such as American Idol. The first part of this study provides a detailed explanation of Arrow's Theorem, including the formal definitions of key fairness criteria: Non-dictatorship, Pareto efficiency, Independence of Irrelevant Alternatives (IIA), and unrestricted domain. Building on this, I then apply these concepts to the voting structure used in American Idol, which primarily follows a plurality voting system. By analyzing how audience voting determines winners, the study investigates whether the system satisfies Arrow's fairness criteria and identifies the ways in which it falls short, particularly through violations of independence of irrelevant alternatives.
Comments
Under the direction of Dr. Molly Weselcouch.