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 2 n . 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 2 n . 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.
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