Local monotonicity of power: Axiom or just a property?

This paper discusses whether Local Monotonicity (LM) should be regarded as a property of the power distribution of a specific voting game under consideration, indicated by a power measure, or as a characteristic of power per se. The latter would require reasonable power measures to satisfy a corresponding LM axiom. The former suggests that measures which do not allow for a violation of LM fail to account for dimensions of power which can cause nonmonotonicity in voting weight. Only if a measure is able to indicate nonmonotonicity, it can help design voting games for which power turns out to be monotonic. The argument is discussed in the light of recent extensions of traditional power indices.