The extended rank-discounted utilitarian social welfare order introduced and axiomatized by Stéphane Zuber and Geir B. Asheim satisfies strong anonymity (J. Econ. Theory (2011), doi:10.1016/j.jet.2011.08.001). We question the appropriateness of strong anonymity in the context of a countably infinite sequence of subsequent generations. A modified criterion that is incomplete and satisfies finite anonymity is presented.