A k-majority tournament is a directed graph that models a k-majority voting scenario, which is realized by 2k - 1 rankings, called linear orderings, of the vertices in the tournament. Every k-majority voting scenario can be modeled by a tournament, but not every tournament is a model for a k-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 k-majority tournaments. Thus, each tournament within these classes of tournaments is a model for a k-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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Cheney, Gina Marie"],"institution":null,"degree_name":"Master of Arts in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Aikin, Jeremy"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-06-01T07:00:00Z","date_published":"2016-06-01T07:00:00Z","updated_at":"2026-07-24T01:53:00Z","subjects":["graph theory","voting theory","k-majority tournaments","number theory","quadratic residue tournaments","Other Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/327","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Aikin, Jeremy"]},{"key":"dc:creator","label":"Author","values":["Cheney, Gina Marie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-05-18T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["graph theory","voting theory","k-majority tournaments","number theory","quadratic residue tournaments","Other Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/327"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A k-majority tournament is a directed graph that models a k-majority voting scenario, which is realized by 2k - 1 rankings, called linear orderings, of the vertices in the tournament. Every k-majority voting scenario can be modeled by a tournament, but not every tournament is a model for a k-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 k-majority tournaments. Thus, each tournament within these classes of tournaments is a model for a k-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.
"]},{"key":"dc:title","label":"Title","values":["REALIZING TOURNAMENTS AS MODELS FOR K-MAJORITY VOTING"]}]}],"canonical_facts":{"dc:contributor":["Aikin, Jeremy"],"dc:creator":["Cheney, Gina Marie"],"dc:date.available":["2016-05-18T07:00:00Z"],"dc:description.abstract":["A k-majority tournament is a directed graph that models a k-majority voting scenario, which is realized by 2k - 1 rankings, called linear orderings, of the vertices in the tournament. Every k-majority voting scenario can be modeled by a tournament, but not every tournament is a model for a k-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 k-majority tournaments. Thus, each tournament within these classes of tournaments is a model for a k-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.
"],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd/327"],"dc:subject":["graph theory","voting theory","k-majority tournaments","number theory","quadratic residue tournaments","Other Mathematics"],"dc:title":["REALIZING TOURNAMENTS AS MODELS FOR K-MAJORITY VOTING"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Arts in Mathematics"]},"updated_at":"2026-07-24T01:53:00Z"}