### Abstract

A majority digraph is a finite simple digraph G = (V,→) such that there exist finite sets A_{v} for the vertices v ∈ V with the following property: u → v if and only if “more than half of the A_{u} are A_{v}”. That is, u → v if and only if (formula presented). We characterize the majority digraphs as the digraphs with the property that every directed cycle has a reversal. If we change to any real number α ∈ (0, 1), we obtain the same class of digraphs. We apply the characterization result to obtain a result on the logic of assertions “most X are Y ” and the standard connectives of propositional logic.

Original language | English |
---|---|

Pages (from-to) | 3701-3715 |

Number of pages | 15 |

Journal | Proceedings of the American Mathematical Society |

Volume | 144 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2016 |

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### Cite this

*Proceedings of the American Mathematical Society*,

*144*(9), 3701-3715. https://doi.org/10.1090/proc/13038

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*Proceedings of the American Mathematical Society*, vol. 144, no. 9, pp. 3701-3715. https://doi.org/10.1090/proc/13038

**Majority digraphs.** / Lai, Tri; Endrullis, Jörg; Moss, Lawrence S.

Research output: Contribution to Journal › Article › Academic › peer-review

TY - JOUR

T1 - Majority digraphs

AU - Lai, Tri

AU - Endrullis, Jörg

AU - Moss, Lawrence S.

PY - 2016

Y1 - 2016

N2 - A majority digraph is a finite simple digraph G = (V,→) such that there exist finite sets Av for the vertices v ∈ V with the following property: u → v if and only if “more than half of the Au are Av”. That is, u → v if and only if (formula presented). We characterize the majority digraphs as the digraphs with the property that every directed cycle has a reversal. If we change to any real number α ∈ (0, 1), we obtain the same class of digraphs. We apply the characterization result to obtain a result on the logic of assertions “most X are Y ” and the standard connectives of propositional logic.

AB - A majority digraph is a finite simple digraph G = (V,→) such that there exist finite sets Av for the vertices v ∈ V with the following property: u → v if and only if “more than half of the Au are Av”. That is, u → v if and only if (formula presented). We characterize the majority digraphs as the digraphs with the property that every directed cycle has a reversal. If we change to any real number α ∈ (0, 1), we obtain the same class of digraphs. We apply the characterization result to obtain a result on the logic of assertions “most X are Y ” and the standard connectives of propositional logic.

UR - http://www.scopus.com/inward/record.url?scp=84975166280&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975166280&partnerID=8YFLogxK

U2 - 10.1090/proc/13038

DO - 10.1090/proc/13038

M3 - Article

VL - 144

SP - 3701

EP - 3715

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -