Abstract
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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References
Mallows, C.L. Non-Null Ranling Models. I. Biometrika 44:114–130, 1957.
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© 1993 Springer-Verlag New York, Inc.
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McCullagh, P. (1993). Models on Spheres and Models for Permutations. In: Fligner, M.A., Verducci, J.S. (eds) Probability Models and Statistical Analyses for Ranking Data. Lecture Notes in Statistics, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2738-0_14
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DOI: https://doi.org/10.1007/978-1-4612-2738-0_14
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