In this study, we explore a method of ranking nomination rules as a collective decision-making procedure. Nomination rules determine which alternatives are eligible for collective decision-making by aggregating the opinions of nominators, which are expressed positively or negatively. It is possible to compare nomination rules based on their “nominating power” distributions because they can be seen as multiple simple games. Our nomination rules ranking has a two-step aggregation representation. In the first step, the distribution of nominating power with regard to each issue is aggregated into an indicator based on the sign inversion of the inequality measure of voting power in simple games, as proposed by Laruelle and Valenciano (2004). Subsequently, in the second step, the aggregator sums the indicator on each issue. We add a separability axiom to the set of Laruelle and Valenciano's axioms to characterize our nomination rules ranking that has the two-step aggregation representation.

中文翻译：

---

根据提名权力分配排名提名规则

在本研究中，我们探索了一种将提名规则排序为集体决策程序的方法。提名规则通过汇总提名人的正面或负面意见来确定哪些备选方案有资格进行集体决策。可以根据“提名权”分布来比较提名规则，因为它们可以被视为多个简单的游戏。我们的提名规则排名有两步聚合表示。第一步，根据 Laruelle 和 Valenciano (2004) 提出的简单博弈中投票权不平等度量的符号反转，将每个问题的提名权分布聚合成一个指标。随后，在第二步中，聚合器对每个问题的指标求和。