Enriching the Felsenthal index with a priori unions for decision-making processes

Within the domain of game theory, power indexes are defined as functions that quantify the influence of individual participants in collective decision-making processes. Felsenthal [D. Felsenthal. A Well-Behaved Index of a Priori P-Power for Simple N-Person Games. Homo Oeconomicus, 33, 2016] proposed a power index with a focus on least size winning coalitions, i.e., those coalitions capable of determining the final outcome and with the smallest number of players among all winning coalitions. However, the Felsenthal index overlooks pre-existing affinities between the players, a common and impactful factor in real-world political and economic contexts. This paper introduces the Felsenthal Owen power index, a novel index based on Felsenthal's approach that integrates player affinities using Owen's a priori unions framework. The new 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 policymakers a more sophisticated tool for measuring influence in complex decision-making scenarios.