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Size-constrained clustering (SCC) refers to the dual problem of usingobservations to determine latent cluster structure while at the same timeassigning observations to the unknown clusters subject to an analyst definedconstraint on cluster sizes. While several approaches have been proposed, SCCremains a difficult problem due to the combinatorial dependency betweenobservations introduced by the size-constraints. Here we reformulate SCC as adecision problem and introduce a novel loss function to capture various typesof size constraints. As opposed to prior work, our approach is uniquely suitedto situations in which size constraints reflect and external limitation ordesire rather than an internal feature of the data generation process. Todemonstrate our approach, we develop a Bayesian mixture model for clusteringrespondents using both simulated and real categorical survey data. Ourmotivation for the development of this decision theoretic approach to SCC wasto determine optimal team assignments for a Harry Potter themed scavenger huntbased on categorical survey data from participants.

The Bayesian Sorting Hat: A Decision-Theoretic Approach to Size-Constrained Clustering