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The consensus ranking problem has received much attention in the statistical literature. Given m rankings of n objects the objective is to determine a consensus ranking. The input rankings may contain ties, be incomplete, and may be weighted. Two solution concepts are discussed, the first maximizing the average weighted rank correlation of the solution ranking with the input rankings and the second minimizing the average weighted Kemeny–Snell distance. A new rank correlation coefficient called τx is presented which is shown to be the unique rank correlation coefficient which is equivalent to the Kemeny‐Snell distance metric. The new rank correlation coefficient is closely related to Kendall's tau but differs from it in the way ties are handled. It will be demonstrated that Kendall's τb is flawed as a measure of agreement between weak orderings and should no longer be used as a rank correlation coefficient. The use of τx in the consensus ranking problem provides a more mathematically tractable solution than the Kemeny–Snell distance metric because all the ranking information can be summarized in a single matrix. The methods described in this paper allow analysts to accommodate the fully general consensus ranking problem with weights, ties, and partial inputs. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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Dr. Philip Bobko 《Psychometrika》1977,42(2):311-314
A measure of multiple rank correlation,T
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2, is proposed for the situation with no tied observations in the variables. The measure is a weighted average of two squared Kendall taus. It is shown thatT
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2 is equivalent to a statistic previously proposed by Moran and thus a new interpretation is given to Moran's statistic.The author wishes to thank Nancy Anderson, Willard Larkin, and Kent Norman for their helpful comments. 相似文献
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Vernat, J.‐P. & Gordon, M.S. (2011). Indirect interception actions by blind and sighted perceivers: The role of modality and tau. Scandinavian Journal of Psychology 52, 83–92. Acoustic and visual interceptive actions were tested in this research by comparing the performance of blind, blind‐folded, and sighted individuals. An indirect interception method was employed in which the participant had to roll an intercepting ball towards a moving target on a perpendicular track. The interception task used conditions that varied the speed, rolling distance, and target size/intensity. While performance was highly consistent and accurate for visual participants in this research, the blind and blind‐folded participants demonstrated much more performance variability in response to changes in speed and distance. Manipulation of target size and intensity did not affect judgments, however performance tended to be more accurate at shorter distances and with faster target speeds. Results from this research are discussed in terms of their implications for tau in acoustic interception, and the use of spatial and temporal cues for guiding interceptive actions. 相似文献
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