Beyond the Felsenthal Index: a New Power Measure Incorporating a Priori Unions

Abstract

[Abstract]: Within the domain of game theory, power indices are defined as functions that quantify the influence of individual participants in collective decision-making processes. Felsenthal proposed a power index with a focus on winning coalitions of least size, i.e., those coalitions that are capable of determining the final outcome and with the smallest number of players among all winning coalitions. However, the Felsenthal index overlooks preexisting affinities among the players, a common and impactful factor in real-world political and economic contexts. This paper introduces a new index based on Felsenthal’s approach, which integrates player affinities through an a priori union framework. The proposed index is rigorously characterised by two distinct sets of axiomatic properties. We demonstrate its practical utility by applying it to the International Monetary Fund’s voting system, revealing how strategic alliances significantly reshape power distributions. The index thus offers policy-makers a more sophisticated tool for measuring influence in complex decision-making scenarios.