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Discovering a bucket order B from a collection of possibly noisy full rankings is a fundamental problem that relates to various applications involving rankings. Informally, a bucket order is a total order that allows "ties" between items in a bucket. A bucket order B can be viewed as a "representative" that summarizes a given set of full rankings {T1, T2, ..., Tm}, or conversely B can be an "approximation" of some "ground truth" G where the rankings {T1, T2, ..., Tm} are simply the "linear extensions" of G.
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Feng et al. (2008) studied this question.
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