Different ways to represent weighted majority games

It is well known that every simple game is the intersection of weighted majority games. the aim of this paper is to gather together various ways of expressing weighted majority games and, for each game of this type, to give the simplest way to define it. Normalized representations, the parameters of a simple game and the characteristic invariants of a complete game merit special attention. Research partially supported by projects PR9509 of the Polytechnic University of Catalonia and PB96-0493 of DGES