We discuss conditions under which binary and ternary choice probabilities are induced by various kinds of binary relations, such as: weak, partial, semi, and interval orders. These order conditions take the form of a family of convex polytopes when represented in the appropriate vector space. We illustrate these conditions with applications to empirical choice data. We also present results pertaining to the identification of these order polytopes, i.e., the enumeration of their facet-defining inequalities. |