A New Correlation Coefficient for Aggregating Non-strict and Incomplete Rankings
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We introduce a correlation coefficient that is specifically designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., null) preferences. The new measure, which can be regarded as a generalization of the seminal Kendall tau correlation coefficient, is proven to be equivalent to a recently developed axiomatic ranking distance. In an effort to further unify and enhance the two robust ranking methodologies, this work proves the equivalence an additional axiomatic-distance and correlation-coefficient pairing in the space of non-strict incomplete rankings. In particular, the bridging of these complementary theories reinforces the singular suitability of the featured correlation coefficient to solve the general consensus ranking problem. The latter premise is further bolstered by an accompanying set of experiments on random instances, which are generated via a herein developed sampling technique connected with the classic Mallows distribution of ranking data. To carry out the featured experiments we devise a specialized branch and bound algorithm that provides the full set of alternative optimal solutions efficiently. Applying the algorithm on the generated random instances reveals that the featured correlation coefficient yields consistently fewer alternative optimal solutions as data becomes noisier.
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