We argue that the best way to determine horizontal symmetry is from neutrino
mixing, and proceed to show that the only finite group capable of yielding the
tri-bimaximal mixing for all Yukawa couplings is S4, or any group containing
it. The method used is largely group theoretical, but it can be implemented by
dynamical schemes in which the Higgs expectation values introduced to break
S4 spontaneously are uniquely determined up to an unknown scale for each.Comment: version to appear in Phys. Rev. Letts.: one reference added and some
slight rephrasing of sentence