关于德博尔达投票规则的资格
On eligibility by the de Borda voting rules
摘要：
本文利用文献[H. Moulin（1988），合作决策公理]是不充分的，我们得到了一个版本的准则。令$r(a_i)$为候选$a_i$的得分向量，$R$为所有向量$r(a_i)$的集合，并且令$R'$为凸包$\conv R$的帕累托边界。然后存在评分$s$，使得当且仅当$r(a)\in R'$时，候选$a$关于de Borda投票规则$β_s$获胜。
英文摘要：
We show that a necessary condition for eligibility of a candidate by the set of de Borda's voting rules in [H. Moulin (1988), Axioms of cooperative decision making] is not sufficient and we obtain a version of the criterion. Let $r(a_i)$ be the score vector of a candidate $a_i$, $R$ be the set of all vectors $r(a_i)$, and let $R'$ be the Pareto boundary of the convex hull $\conv R$. Then there is a scoring $s$ such that a candidate $a$ wins with respect to the de Borda voting rule $β_s$ if and only if $r(a)\in R'$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
