, n are all bounded between −∆ and +∆ with probability at least 1/2 and since the ranking values are spaced apart by more than 2∆, the constraint ranking θ+ corresponding to the stochastic ranking vector θ + coincides with the original ranking with probability at least 1/2.
the probability mass function p D θ corresponding to this ranking vector θ according to (8) assigns more than half of the probability mass to the OT grammar corresponding to the ranking .