A hole is the lack of an electron.
Thus, if we consider for example a N doped semiconductor. The so-called "majority charge carriers" are the electrons. But whenever there is a mobile electron that moves from a site to another site, the former site will have a hole, thus I don't see why there would not be exactly the same number of holes as the number of electrons.
Thus, I don't catch why the electrons would be really "majoritary", for example in a N semiconductor.