Appears in collection : 11e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay

Summarising a distribution over rankings by a single Kemeny median fails whenever the distribution is multimodal or heterogeneous. Drawing on the histogram analogy, we introduce Consensus Ranking Distributions (CRD): sparse mixtures of local Kemeny medians indexed by a partition of the space of rankings, interpolating between a single consensus ranking and the raw empirical distribution. We propose the COAST algorithm, a top-down decision tree that learns the partition from data using pairwise comparison splits, and establish a PAC-style generalisation bound. Experiments on synthetic mixtures and real preference data illustrate the method's ability to recover modes and produce interpretable summaries.