Arrow's Impossibility Theorem outlines the flaws that effect any voting system that attempts to order a set of objects. For its entire history, American college football has been determining its champion based on a voting system. Much of the literature has dealt with why the voting system used is problematic, but there does not appear to be a large collection of work done to create a better, mathematical process. More generally, the inadequacies of ranking in football are a manifestation of the problem of ranking a set of objects. Herein, principal component analysis is used as a tool to provide a solution for the problem, in the context of American college football. To show its value, rankings based on principal component analysis are compared against the rankings used in American college football. / Thesis / Master of Science (MSc) / The problem of ranking is a ubiquitous problem, appearing everywhere from Google to ballot boxes. One of the more notable areas where this problem arises is in awarding the championship in American college football. This paper explains why this problem exists in American college football, and presents a bias-free mathematical solution that is compared against how American college football awards their championship.
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/20695 |
| Date | January 2016 |
| Creators | Earl, Jonathan |
| Contributors | McNicholas, Paul, Mathematics and Statistics |
| Source Sets | McMaster University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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