Mathematical Models for Ranking from Paired Comparisons
نویسندگان
چکیده
منابع مشابه
An Extension of Zermelo’s Model for Ranking by Paired Comparisons
In 1929, Zermelo proposed a probabilistic model for ranking by paired comparisons and showed that this model produces a unique ranking of the objects under consideration when the outcome matrix is irreducible. When the matrix is reducible, the model may yield only a partial ordering of the objects. In this paper, we analyze a natural extension of Zermelo’s model resulting from a singular pertur...
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We investigate by means of a simulation study whether standard structural equation modeling techniques are suitable for estimating an unrestricted Thurstonian model to: (a) multiple judgment paired comparisons data, and (b) ranking data. We point out that Thurstone's (1927) original model is not a proper model for multiple judgment paired comparisons data as it assigns zero probability to all i...
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The paper reveals that the Weighted Logarithmic Least Squares Method used for deriving evaluations of alternatives from incomplete pairwise comparison matrices (iWLLSM) coincides with the recursive Buchholz ranking method applied in generalized tournaments, despite their different approach and calculation. We study it with respect to a set of new properties and present the strength of the metho...
متن کاملInterval Scales From Paired Comparisons
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متن کاملEfficient Ranking from Pairwise Comparisons
The ranking of n objects based on pairwise comparisons is a core machine learning problem, arising in recommender systems, ad placement, player ranking, biological applications and others. In many practical situations the true pairwise comparisons cannot be actively measured, but a subset of all n(n−1)/2 comparisons is passively and noisily observed. Optimization algorithms (e.g., the SVM) coul...
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ژورنال
عنوان ژورنال: Journal of the American Statistical Association
سال: 1960
ISSN: 0162-1459
DOI: 10.2307/2281911