REALIZING TOURNAMENTS AS MODELS FOR K-MAJORITY VOTING

<p>A <em>k</em>-majority tournament is a directed graph that models a <em>k</em>-majority voting scenario, which is realized by 2<em>k</em> - 1 rankings, called linear orderings, of the vertices in the tournament. Every <em>k</em>-majority voting scenario can be modeled by a tournament, but not every tournament is a model for a <em>k</em>-majority voting scenario. In this thesis we show that all acyclic tournaments can be realized as 2-majority tournaments. Further, we develop methods to realize certain quadratic residue tournaments as <em>k</em>-majority tournaments. Thus, each tournament within these classes of tournaments is a model for a <em>k</em>-majority voting scenario. We also explore important structures specifically pertaining to 2- and 3-majority tournaments and introduce the idea of pseudo-3-majority tournaments and inherited 2-majority tournaments.</p>

Name thesis:degree_name

Master of Arts in Mathematics

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2016

Author dc:creator

• Cheney, Gina Marie

Contributors dc:contributor

• Aikin, Jeremy

• graph theory
• voting theory
• k-majority tournaments
• number theory
• quadratic residue tournaments
• Other Mathematics

Repository record dc:identifier

https://scholarworks.lib.csusb.edu/etd/327

OAI identifier oai:identifier

oai:scholarworks.lib.csusb.edu:etd-1384