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The Choice Probabilities of the Latent-Scale Model Satisfy the Size-Independent Model When n Is Small.

Two probabilistic models for subset choices are compared. The first one, due to Marley (1993), was dubbed the latent-scale model by Regenwetter, Marley, and Joe (1996). The second one is Falmagne and Regenwetter's (1996) size-independent model of approval voting. We show that for up to five choice alternatives, the choice probabilities generated by the latent-scale model can be explained also by the size-independent model. The proof uses the König-Hall theorem of graph theory and the characterization of the size-independent model by the approval-voting polytope of Doignon and Regenwetter (1997). The problem remains open for the case with more than five choice alternatives. Copyright 1998 Academic Press.