I seem to recall that Vampire The Masquerade functioned sort of like that, but they only had one roll. It seems slightly illogical that the most aware character would act after less aware characters. Maybe simply roll initiative and have the players declare their actions in the reverse order of initiative, then resolve in the usual order. Personnally, having played Vampire The Masquerade, I found the system rather tedious and that it slowed down the battles.