Journal article: Opinion leaders are actors who have some power over their followers as they are able to influence their followers' choice of action in certain instances. In van den Brink et al. (2011) we proposed a two-action model for societies with opinion leaders. We introduced a power and a satisfaction score and studied some common properties. In this paper we strengthen two of these properties and present two further properties, which allows us to axiomatize both scores for the case that followers require unanimous action inclinations of their opinion leaders to follow them independently from their own action inclinations.