A commonly used model, adopted widely in machine learning is the Mallows φ-model (Mallows, 1957). It is parameterized by a modal or reference ranking σ and a dispersion parameter φ ∈ (0, 1]; and for any rank- ing r we define: P (r; σ, φ) = 1 Z φ d(r,σ ) , where d is the Kendall tau distance and Z = r φ d(r ,σ ) = 1 ·(1 + φ) · (1 +φ + φ 2 ) ···(1 +···+φ m−1 ) is a normalization constant. 6 When φ = 1 we obtain the uniform distribution over rankings (i.e., impar- tial culture), and as φ → 0 we approach the distribution that concentrates all mass on σ .
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