On subgame consistency of the Shapley-Shubik power index

We present a new axiomatization of the Shapley-Shubik power index based on three axioms. The central axiom—occasional subgame-consistency on average (OSCoA)—requires the power of a player to coincide with the average of his power in one-player-out subgames, for just one game v on any given support (which must be essential for the game). The choice of v may be player-dependent but v must have no veto players. The other two axioms are the standard Transfer and Dummy. We also formulate some stronger variants of OSCoA that do not explicitly require the support of v as above to be essential.