Authority distribution

Authority distribution is a solution concept in cooperative game theory formulated by Lloyd Shapley and his doctoral student Xingwei Hu in 2003 to measure the authority and power of players in well-defined hierarchical organizations. The concept provides a mathematical framework for quantifying how decision-making authority is distributed among individuals or units within hierarchical structures. Authority distribution generates the Shapley-Shubik power index as a special case and extends its application to more complex organizational settings.

The theory builds upon Shapley's earlier work on the Shapley value, which earned him the Nobel Memorial Prize in Economic Sciences in 2012. Authority distribution can be used for ranking, strategic planning, and organizational design, providing quantitative insights into optimal decision-making structures and delegation of authority.

Unlike traditional power indices, which primarily focus on voting systems, authority distribution models the nuanced relationships between superiors and subordinates in hierarchical organizations. This makes it particularly valuable for analyzing complex structures where authority flows through multiple levels.