Sub-semiorder: a model of multidimensional choice with preference intransitivity

The paper develops a model of choice called a sub-semiorder which is a generalization of Luce's semiorder to multidimensional choice. The same reason (imperfect discrimination) that gives rise to the intransitivity of indifference in a semiorder gives rise to the intransitivity of preference in a sub-semiorder. This provides a rational explanation of intransitivity of preference without resorting to the lexicographic semiorder of Tversky. It is shown that the "apparent underlying preference" of a sub-semiorder is transitive but unfortunately it is not complete. However, with a mild condition, there exists a maximal element.