Models on Spheres and Models for Permutations
It is shown that the space of permutations is naturally ordered in a circular or spherical manner. By exploiting the geometry of the sample space it is shown that Mallows’s ϕ-model with the Spearman metric is essentially equivalent to the Mallows-Bradley-Terry ranking model, which is essentially equivalent to the von Mises-Fisher model on the sphere. Extensions to bi-polar models are discussed briefly. References
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