Neutrino oscillations and the exact parity model

We re-examine neutrino oscillations in exact parity models. Previously it was shown in a specific model that large neutrino mixing angles result. We show here that this is a general result of neutrino mixing in exact parity models provided that the neutrino mass matrix is real. In this case, the effects of neutrino mixing in exact parity models is such that the probability of a given weak eigenstate remaining in that eigenstate averages to {\it less} than a half when averaged over many oscillations. This result is interesting in view of the accumulating evidence for a significant deficit in the number of solar neutrinos. It may also be of relevance to the atmospheric neutrino anomaly.