民主选举中失败的公理

An Analysis of Random Elections with Large Numbers of Voters

In an election in which each voter ranks all of the candidates, we consider the head-to-head results between each pair of candidates and form a labeled directed graph, called the margin graph, which contains the margin of victory of each candidate over each of the other candidates. A central issue in developing voting methods is that there can be cycles in this graph, where candidate $\mathsf{A}$ defeats candidate $\mathsf{B}$, $\mathsf{B}$ defeats $\mathsf{C}$, and $\mathsf{C}$ defeats $\mathsf{A}$. In this paper we apply the central limit theorem, graph homology, and linear algebra to analyz…

Selecting Matchings via Multiwinner Voting: How Structure Defeats a Large Candidate Space

Given a set of agents with approval preferences over each other, we study the task of finding $k$ matchings fairly representing everyone's preferences. We model the problem as an approval-based multiwinner election where the set of candidates consists of all possible matchings and agents' preferences over each other are lifted to preferences over matchings. Due to the exponential number of candidates in such elections, standard algorithms for classical sequential voting rules (such as those proposed by Thiele and Phragmén) are rendered inefficient. We show that the computational tractability o…

提出或投票：一种民主程序

Propose or Vote: A Canonical Democratic Procedure

本文提出了一种无需中央机制设计的民主程序PoV，通过提案制定与投票结合的方式实现Condorcet赢家，并解决了偶数成员数量下的唯一性问题。

分裂循环的公理化刻画

An Axiomatic Characterization of Split Cycle

本文通过引入相干击败和击败中的正参与性两个新公理，证明分裂循环是唯一满足Holliday和Pacuit公理体系的多数循环解决规则，并将其刻画扩展到社会选择对应及允许平局的选票剖面。