On the combinatorial structure of the approval-voting polytope

Falmagne and Regenwetter (1996) proposed a probabilistic choice model of approval voting called the size-independent model. This model was investigated geometrically by Doipon and Regenwetter (1997), who introduced the approval-voting polytope associated with the choice model. In an effort to get closer to a full linear description of the polytope, we provide all edges, two-dimensional faces, and a large group of combinatorial automorphisms. Despite the new insights gathered from these results, the main challenge of listing all facets remains an open problem. (C) 2002 Elsevier Scicnce (USA).