With these natural criteria accepted, other family symmetry candidates have turned out to be at least partially discriminated. Indeed, the U ( 1 ) F family symmetry does not satisfy the criterion (i) and is in fact applicable to any number of quark-lepton families. Also, the S U ( 2 ) F family symmetry can contain, besides two light families treated as its doublets, any number of additional (singlets or new doublets of S U ( 2 ) F ) families. All global non-Abelian symmetries are excluded by the criterion (ii), while the vectorlike symmetries are excluded by the criteria (iii) and (v).