Models on Spheres and Models for Permutations

  • Peter McCullagh
Part of the Lecture Notes in Statistics book series (LNS, volume 80)


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


Sample Space Ordinal Number Exponential Family Ranking Model Rank Vector 
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  1. [1]
    Mallows, C.L. Non-Null Ranling Models. I. Biometrika 44:114–130, 1957.MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1993

Authors and Affiliations

  • Peter McCullagh
    • 1
  1. 1.Department of StatisticsUniversity of ChicagoUSA

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