In 2005, Alon, et al. proved that tournaments arising from majority voting scenarios have minimum dominating sets that are bounded by a constant that depends only on the notion of what is meant by a majority. Moreover, they proved that when a majority means that Candidate A beats Candidate B when Candidate A is ranked above Candidate B by at least two out of three voters, the tournament used to model this voting scenario has a minimum dominating set of size at most three. This result gives 2-majority tournaments some significance among all tournaments and motivates us to investigate when a given tournament can be considered a 2-majority tournament. In this thesis, we prove, among other things, that the presence of an upset path in a tournament allows us to conclude the tournament is realizable as a 2-majority tournament.
","abstract_html":"<p>In 2005, Alon, et al. proved that tournaments arising from majority voting scenarios have minimum dominating sets that are bounded by a constant that depends only on the notion of what is meant by a majority. Moreover, they proved that when a majority means that Candidate A beats Candidate B when Candidate A is ranked above Candidate B by at least two out of three voters, the tournament used to model this voting scenario has a minimum dominating set of size at most three. This result gives 2-majority tournaments some significance among all tournaments and motivates us to investigate when a given tournament can be considered a 2-majority tournament. In this thesis, we prove, among other things, that the presence of an upset path in a tournament allows us to conclude the tournament is realizable as a 2-majority tournament.</p>","abstract_has_math":false,"creators":["Alshaikh, Rana Ali"],"institution":null,"degree_name":"Master of Arts in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Jeremy Aikin"],"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":["upset paths","2-majority tournaments","UP-sets.","Discrete Mathematics and Combinatorics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/356","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jeremy Aikin"]},{"key":"dc:creator","label":"Author","values":["Alshaikh, Rana Ali"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-05-20T07:00:00Z"]},{"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":["upset paths","2-majority tournaments","UP-sets.","Discrete Mathematics and Combinatorics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/356"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In 2005, Alon, et al. proved that tournaments arising from majority voting scenarios have minimum dominating sets that are bounded by a constant that depends only on the notion of what is meant by a majority. Moreover, they proved that when a majority means that Candidate A beats Candidate B when Candidate A is ranked above Candidate B by at least two out of three voters, the tournament used to model this voting scenario has a minimum dominating set of size at most three. This result gives 2-majority tournaments some significance among all tournaments and motivates us to investigate when a given tournament can be considered a 2-majority tournament. In this thesis, we prove, among other things, that the presence of an upset path in a tournament allows us to conclude the tournament is realizable as a 2-majority tournament.
"]},{"key":"dc:title","label":"Title","values":["Upset Paths and 2-Majority Tournaments"]}]}],"canonical_facts":{"dc:contributor":["Jeremy Aikin"],"dc:creator":["Alshaikh, Rana Ali"],"dc:date.available":["2016-05-20T07:00:00Z"],"dc:description.abstract":["In 2005, Alon, et al. proved that tournaments arising from majority voting scenarios have minimum dominating sets that are bounded by a constant that depends only on the notion of what is meant by a majority. Moreover, they proved that when a majority means that Candidate A beats Candidate B when Candidate A is ranked above Candidate B by at least two out of three voters, the tournament used to model this voting scenario has a minimum dominating set of size at most three. This result gives 2-majority tournaments some significance among all tournaments and motivates us to investigate when a given tournament can be considered a 2-majority tournament. In this thesis, we prove, among other things, that the presence of an upset path in a tournament allows us to conclude the tournament is realizable as a 2-majority tournament.
"],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd/356"],"dc:subject":["upset paths","2-majority tournaments","UP-sets.","Discrete Mathematics and Combinatorics"],"dc:title":["Upset Paths and 2-Majority Tournaments"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Arts in Mathematics"]},"updated_at":"2026-07-24T01:53:00Z"}