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By Hall E. H.

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By the 6-method, the (i,j), (m,q) element of E is Eij mq = n---+oo lim n Cov(Pij,Pmq)/[D'(D- 1 (Pij»D'(D- 1 (Pmq»]. J 16 D. E. Critchlow and M. A. Lm), where d = D' is the density corresponding to D. d. f. F. Lj) if i, j, and m are distinct. d. dJ. F. Acknowledgements: The authors thank the referees for helpful comments that improved the presentation. The work of both authors was supported by a grant from the National Science Foundation. 8 REFERENCES [1] R. A. Bradley. Science, statistics and paired comparisons.

Srivastava. An ideal-point probabilistic choice model for heterogeneous preferences. Marketing Science, 5:199-218, 1986. [15] N. Kousgaard. Analysis of a sound field experiment by a model for paired comparisons with explanatory variables. Scandinavian Journal of Statistics, 11:51-57, 1984. [16] R. D. Luce. Individual Choice Behavior. Wiley, New York, 1959. 18 D. E. Critchlow and M. A. Fligner [17] C. L. Mallows. Non-null ranking models. I. Biometrika, 44:114-130, 1957. [18] P. McCullagh. Models on spheres and models for permutations, 1990.

Alternatively, w(2) Aw A 21. = = = 22 H. A. David and D. M. 1. 3712 Note that not only have all ties been broken at this stage but G5 has moved ahead of G3 although W5 < W3. Neither of these events (breaking of all ties, reversal of some rankings) need happen and one may wish to continue the reallocation process to obtain w(3) = A 3 1, etc. This is a slight simplification (Moon [13]) of the Kendall-Wei procedure (Kendall [12]) in which B = A + ~ I rather than A is powered, where I is the identity matrix.

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