Cycling of simple rules in the spatial model
Cycling of simple rules in the spatial model
复制标题
空间模型中简单规则的循环
DOI：
10.1007/s003550050167
复制
发表时间：
1999
影响因子：
0.9
通讯作者：
J. Banks
中科院分区：
文献类型：
--
作者：
D. Austen;J. Banks
McKelvey [4]证明，对于应用于多维备选方案集的强简单偏好聚集规则，典型情况是核心非空或顶循环集包括所有可用的备选方案。但是，规则必须是强有力的这一要求，除其他外，排除了所有的绝对多数规则。在本文中，我们表明，麦凯维定理进一步意味着，任何简单的规则的典型情况是，要么核心是非空的或弱顶循环集（相当于，规则的传递闭包的核心）包括所有可用的替代品。而且，这两种说法往往都成立。
McKelvey [4] proved that for strong simple preference aggregation rules applied to multidimensional sets of alternatives, the typical situation is that either the core is nonempty or the top-cycle set includes all available alternatives. But the requirement that the rule be strong excludes,inter alia, all supermajority rules. In this note, we show that McKelvey's theorem further implies that the typical situation for any simple rule is that either the core is nonempty or the weak top-cycle set (equivalently, the core of the transitive closure of the rule) includes all available alternatives. Moreover, it is often the case that both of these statements obtain.