Axiomatizations of a positional power score and measure for hierarchies

Power is a core concept in the analysis and design of organizations. One of the problems with the extant literature on positional power in hierarchies is that it is mainly restricted to the analysis of power in terms of the bare positions of the actors. While such an analysis informs us about the authority structure within an organization, it ignores the decision-making mechanisms completely. The few studies which take into account the decision-making mechanisms make all use of adaptations of well-established approaches for the analysis of power in non-hierarchical organizations such as the Banzhaf measure; and thus they are all based on the structure of a simple game, i.e. they are `membership-based'. In van den Brink and Steffen (2008) it is demonstrated that such an approach is in general inappropriate for characterizing power in hierarchies as it cannot be extended to a class of decision-making mechanisms which allow certain actors to terminate a decision before all other members have been involved. As this kind of sequential decision-making mechanism turns out to be particularly relevant for hierarchies, we suggested an action-based approach - represented by an extensive game form - which can take the features of such mechanisms into account. Based on this approach we introduced a power score and power measure that can be applied to ascribe positional power to actors in sequential decision making mechanisms. In this paper we provide axiomatizations of this power score and power measure for one of the most studied decision models, namely that of binary voting.