  In a vintage paper concerning Parsimonious games, a subset of constant sum
homogeneous weighted majority games, Isbell introduced a twin relationship
based on transposition properties of the incidence matrices upon minimal
winning coalitions of such games. A careful investigation of such properties
allowed the discovery of some results on twin games presented in this paper. In
detail we show that a) twin games have the same minimal winning quota and b)
each Parsimonious game admits a unique balanced lottery on minimal winning
coalitions, whose probabilities are given by the individual weights of its twin
game.
