A general model for multi‑parameter weighted voting games

We introduce a new and general model for voting games with multiple weight vectors. Previously studied models are obtained as special cases of the new model. In comparison to earlier models, games have more compact representation in the new model. In particular, we show that a previously well known example of a game having dimension exponential in the number of players can be represented in the new model using only two weight vectors. Further, we identify a new sub-class of games, that we call hyperplane voting games, which are compactly expressible in the new model, but not necessarily so in the previous models. For games represented in the new model, we present dynamic programming algorithms for determining various quantities required for computing different voting power indices. Methods for computing the number of minimal winning coalitions under various restrictions were not previously known even for the earlier models.