the distribution on partitions should be invariant to a relabeling of the data points. The notion of an exchangeable random partition has been formalized by Kingman, Aldous, and others [@kingman:1978:representation; @aldous:1985:exchangeability], and has led to the definition of an *exchangeable partition probability function* (EPPF) [@pitman:1995:exchangeable]. The EPPF is a mathematical function of the cardinalities of the groups in a partition. Exchangeability of the random partition is captured by the requirement that the EPPF be a symmetric function of these cardinalities. Furthermore, the exchangeability of a partition can be related to the exchangeability of a sequence of random variables representing the assignments of data points to clusters, for which a de Finetti mixing measure necessarily exists. This de Finetti measure is known as the *Kingman paintbox* [@kingman:1978:representation]. The relationships among this circle of ideas are well understood: it is known that there is an equivalence among the class of exchangeable random partitions, the class of random partitions that possess an EPPF, and the class of random partitions generated by a Kingman paintbox; see @pitman:2006:combinatorial for an overview of these relations. A specific example of these relationships is given by the Chinese restaurant process and the Dirichlet process, but several other examples 