The aim of this work is to give a characterization of the Shapley–Shubik and the Banzhaf power indices for (3,2)-simple games. We generalize to the set of (3,2)-simple games the classical axioms for power indices on simple games: transfer, anonymity, null player property and efficiency. However, these four axioms are not enough to uniquely characterize the Shapley–Shubik index for (3,2)-simple games. Thus, we introduce a new axiom to prove the uniqueness of the extension of the Shapley–Shubik power index in this context. Moreover, we provide an analogous characterization for the Banzhaf index for (3,2)-simple games, generalizing the four axioms for simple games and adding another property.

Electronic version of an article published as International Game Theory Review, Vol. 21, Issue 1, 1940001, 2019, p. 1-24. DOI: 10.1142/S0219198919400012] © World Scientific Publishing Company https://www.worldscientific.com/doi/10.1142/S0219198919400012