The number of dSph and dE satellite galaxies more luminous than 0.2 × 10⁶L_⊙ is plotted versus the bulge mass of the host galaxy (MW: Zhao 1996, M 31: Kent 1989, M 33: Gebhardt et al. 2001). Only satellites within a distance of 270 kpc of the MW and M 31 are used. The solid line (slope = 4.03) is Eq. (17). The upper (slope = 5.03) and the lower (slope = 3.03) dotted lines illustrate the relative uncertainty assumed in the Monte Carlo experiment (see Sect. 4).