In the framework of spherical geometry for jellium and local spin density approximation, we have obtained the equilibrium r s values,r s (N, ζ), of neutral and singly ionized "generic" N -electron clusters for their various spin polarizations, ζ. Our results reveal thatr s (N, ζ) as a function of ζ behaves differently depending on whether N corresponds to a closed-shell or an openshell cluster. That is, for a closed-shell one,r s (N, ζ) is an increasing function of ζ over the whole range 0 ≤ ζ ≤ 1, and for an open-shell one, it has a decreasing part corresponding to the range 0 < ζ ≤ ζ 0 , where ζ 0 is a polarization that the cluster assumes in a configuration consistent with Hund's first rule. In the context of the stabilized spin-polarized jellium model, our calculations based on these equilibrium r s values,r s (N, ζ), show that instead of the maximum spin compensation (MSC) rule, Hund's first rule governs the minimum-energy configuration. We therefore conclude that the increasing behavior of the equilibrium r s values over the whole range of ζ is a necessary condition for obtaining the MSC rule for the minimum-energy configuration; and the only way to end up with an increasing behavior over the whole range of ζ is to break the spherical geometry of the jellium background. This is the reason why the results based on simple jellium with spheroidal or ellipsoidal geometries show up MSC rule.