The Repeated Insertion Model for Rankings: Missing Link between Two Subset Choice Models

Abstract

Several probabilistic models for subset choice have been proposed in the literature, for example, to explain approval voting data. We show that Marley et al.'s latent scale model is subsumed by Falmagne and Regenwetter's size-independent model, in the sense that every choice probability distribution generated by the former can also be explained by the latter. Our proof relies on the construction of a probabilistic ranking model which we label the “repeated insertion model.” This model is a special case of Marden's orthogonal contrast model class and, in turn, includes the classical Mallows φ-model as a special case. We explore its basic properties as well as its relationship to Fligner and Verducci's multistage ranking model.