| Abstract: | It is a known result that the set of distinct semiorders on n elements, up to permutation, is in bijective correspondence with the set of all Dyck paths of length 2n. I generalize this result by defining a bijection between a set of lexicographic semiorders, termed simple lexicographic semiorders, and the set of all pairs of non-crossing Dyck paths of length 2n. Simple lexicographic semiorders have been used by behavioral scientists to model intransitivity of preference (e.g., Tversky, 1969). In addition to the enumeration of this set of lexicographic semiorders, I discuss applications of this bijection to decision theory and probabilistic choice. |
