``Counting'' power indices for games with a priori unions

The classical Owen construction of the Shapley value for games with a priori unions is adapted to extend the class of “counting” power indices — i.e., those computed by counting appropriately weighted contributions of players to winning coalitions — to simple games with a priori unions. This class contains most well-known indices, including Banzhaf, Johnston, Holler and Deegan—Packel indices. The Shapley—Shubik index for simple games with a priori unions coincides with the (restriction of) Shapley value for such games obtained by Owen’s method, but for all other indices obtained by normalization of probabilistic values our construction leads to indices different from those determined by Owen values.