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On Generalized Tournament Matrices. , 12:384-399, 1970. [15] S. Nishisato. Analysis of Categorical Data: Dual Scaling and its Applications. University of Toronto Press. Toronto, 1980. [16] M. J. Prentice. On the Problem of m Incomplete Rankings. Biometrika, 66:167-170, 1979. [17] T. A. Prigarina, P. Y. Chebotariov and D. S. Schmerling. R. Unpublished manuscript. 1991. [18] C. Ramanujacharyulu. Analysis of Preferential Experiments. Psychometrika, 29:257-261, 1964. [19] E. Seneta. Non-Negative Matrices.

10] H. Gulliksen. A Least Squares Solution for Paired Comparisons with Incomplete Data. Psychometrika, 21:125-134, 1956. [11] H. F. Kaiser and R. C. Serlin. Contributions to the Method of Paired Comparisons. Applied Psychological Measurement, 2:421430, 1978. 36 H. A. David and D. M. Andrews [12] M. G. Kendall. Further Contributions to the Theory of Paired Comparisons. Biometrics, 11:43-62, 1955. [13] J. W. Moon. Topics on Tournaments. Holt, Rinehart and Winston, New York. 1968 [14] J. W. Moon and N.

V, with v'v 1, and happens to give the same ranking as w(2). = = Interesting related methods have been put forward by Daniels [6) and Moon and Pullman [14). However, it is dubious whether the resulting ranking as well as those corresponding to w(2) and v are really an improvement over the simple row-sum score w. The common feature of the more elaborate methods is to give more credit to a player for defeating a high scoring than a low scoring opponent, but this means, of course, that a loss to the latter is punished less than a loss to the former.

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