We introduce a dominance relationship in spatial voting with Euclidean preferences, by treating voter ideal points as balls of radius \(\delta\). Values \(\delta >0\) model imprecision or ambiguity as to voter preferences from the perspective of a social planner. The winning coalitions may be any consistent monotonic collection of voter subsets. We characterize the minimum value of \(\delta\) for which the \(\delta\)-core, the set of undominated points, is nonempty. In the case of simple majority voting, the core is the yolk center and \(\delta\) is the yolk radius.

中文翻译：

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不精确的理想在空间投票中占主导地位

通过将选民理想点视为半径\（\ delta \）的球，在具有欧几里德偏好的空间投票中引入优势关系。从社会计划者的角度来看，值\（\ delta> 0 \）对选民的偏好不精确或模棱两可。获胜联盟可以是选民子集的任何一致的单调集合。我们表征\（\ delta \）的最小值，其中\（\ delta \）- core（未控制点的集合）为非空。在简单多数表决的情况下，核心是蛋黄中心，\（\ delta \）是蛋黄半径。