The non-modularity index quantifies the extent of interaction within a group of criteria in multiple criteria decision problems, or extent of interaction among players in a coalition in the context of cooperative games. This paper examines the properties of the non-modularity index in relation to dummy players and dummy partnerships. It establishes that the scaled non-modularity index is maximal at unanimity games and additive with respect to non-interacting (or dummy) coalitions and partnerships. This paper also provides an axiomatic characterisation of the non-modularity index based on linearity, dummy partnership additivity and maximality axioms.

中文翻译：

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非模指数的公理化特征

非模块化指数量化了多标准决策问题中一组标准内的交互程度，或在合作博弈的背景下联盟中参与者之间的交互程度。本文研究了与虚拟参与者和虚拟伙伴关系相关的非模块化指数的属性。它确定缩放的非模块化指数在一致博弈中是最大的，并且相对于非交互（或虚拟）联盟和伙伴关系是可加的。本文还提供了基于线性、虚拟伙伴可加性和极大值公理的非模块化指数的公理表征。