This paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and exponential codimension with respect to the number of players.
Kurz, S., Molinero, X., Olsen, M., Serna, M. Dimension and codimension of simple games. "Electronic notes in discrete mathematics", 1 Novembre 2016, vol. 55, p. 147-150.