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Series approximations to the logarithm of the probability of a permutation of the natural numbers, 1, …, K, using an extension of the Thurstone model, are investigated. The asymptotic bias of the quadratic and cubic approximations using the normal density is shown to be small. Approximate likelihood ratio tests are considered for testing for agreement between and within groups of judges and x2 approximations seem adequate for significance levels.
A. N. Pettitt (Fri,) studied this question.