A General Model for Multi-Parameter Weighted Voting Games

This article introduces a general model for voting games with multiple weight vectors. Each weight vector characterises a parameter representing a distinct aspect of the voting mechanism. Our main innovation is to model the winning condition by an arbitrary dichotomous function which determines whether a coalition is winning based on the weights that the coalition has for the different parameters. Previously studied multi-parameter games are obtained as particular cases of the general model. We identify a new and interesting 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 the general model of voting games that we introduce, we describe dynamic programming algorithms for determining various quantities required for computing different voting power indices. Specialising to the known classes of multi-parameter games, our algorithms provide unified and simpler alternatives to previously proposed algorithms.