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Majority Dynamics With Almost Balanced Initial Settings: The Power of Few Phenomenon
Majority Dynamics With Almost Balanced Initial Settings: The Power of Few Phenomenon
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103035
- ISBN
- 9798286442133
- DDC
- 510
- 저자명
- Tran, Linh.
- 서명/저자
- Majority Dynamics With Almost Balanced Initial Settings: The Power of Few Phenomenon
- 발행사항
- [Sl] : Yale University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 100 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: Vu, Van Ha.
- 학위논문주기
- Thesis (Ph.D.)--Yale University, 2025.
- 초록/해제
- 요약A community of n people participate in a parliamentary election with two major parties. Every person initially supports one side, and with each day, changes their opinion to match the majority among their friends. This process, commonly known as Majority Dynamics in literature, and similar processes, have been studied in many different contexts, including Statistical Physics, Computer Science, Economics and Ecology, as discussed in the influential survey by Mossel and Tamuz (2014).Tran and Vu (2019) considered the process on a Erdos-Renyi G(n, p) random graph and discovered the "Power of Few" phenomenon: Starting from a balanced initial state, one side can bribe a surprisingly small amount of voters to win every single vote a few days later. Since then, there has been a search for the minimum number of defectors needed for unanimous victory, for the widest possible range of the density p. This thesis aims to introduce the most recent results in this problem, proven by the author and collaborators, and how they correspond to progresses in another setting, where everyone chooses their initial opinions randomly and independently.Our first of two main theorem extends the Power of Few phenomenon for the widest possible range of densities: everything down to the connectivity threshold. Our second theorem is a substantially stronger version of the first, for half of the possible densities. This result also leads to a new best-known bound on the density required for unanimity in the settings with random initial opinions. We also briefly demonstrate two additional results: (1) the robustness of "Power of Few" in a more realistic setting where voters do not reliably change sides, and (2) the "Power of Few" effect in the sub-connectivity regime.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 일반주제명
- Applied mathematics
- 키워드
- Election
- 키워드
- Graph theory
- 키워드
- Percolation
- 키워드
- Random graphs
- 기타저자
- Yale University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798286442133
■035 ▼a(MiAaPQ)AAI31846177
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aTran, Linh.
■24510▼aMajority Dynamics With Almost Balanced Initial Settings: The Power of Few Phenomenon
■260 ▼a[Sl]▼bYale University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a100 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: Vu, Van Ha.
■5021 ▼aThesis (Ph.D.)--Yale University, 2025.
■520 ▼aA community of n people participate in a parliamentary election with two major parties. Every person initially supports one side, and with each day, changes their opinion to match the majority among their friends. This process, commonly known as Majority Dynamics in literature, and similar processes, have been studied in many different contexts, including Statistical Physics, Computer Science, Economics and Ecology, as discussed in the influential survey by Mossel and Tamuz (2014).Tran and Vu (2019) considered the process on a Erdos-Renyi G(n, p) random graph and discovered the "Power of Few" phenomenon: Starting from a balanced initial state, one side can bribe a surprisingly small amount of voters to win every single vote a few days later. Since then, there has been a search for the minimum number of defectors needed for unanimous victory, for the widest possible range of the density p. This thesis aims to introduce the most recent results in this problem, proven by the author and collaborators, and how they correspond to progresses in another setting, where everyone chooses their initial opinions randomly and independently.Our first of two main theorem extends the Power of Few phenomenon for the widest possible range of densities: everything down to the connectivity threshold. Our second theorem is a substantially stronger version of the first, for half of the possible densities. This result also leads to a new best-known bound on the density required for unanimity in the settings with random initial opinions. We also briefly demonstrate two additional results: (1) the robustness of "Power of Few" in a more realistic setting where voters do not reliably change sides, and (2) the "Power of Few" effect in the sub-connectivity regime.
■590 ▼aSchool code: 0265.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■650 4▼aApplied mathematics
■653 ▼aElection
■653 ▼aGraph theory
■653 ▼aMajority dynamics
■653 ▼aPercolation
■653 ▼aRandom graphs
■690 ▼a0405
■690 ▼a0642
■690 ▼a0364
■71020▼aYale University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0265
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356785▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
