Semiorders induced by uniform random points

Abstract: We study semiorders induced by points drawn from a uniform random distribution. Of particular interest in this paper are the probabilities of generating specific semiorders and the equivalence classes they produce. We present a method for calculating the asymptotic probability of inducing these semiorders and describe the qualities which group these semiorders together. We also find a class of semiorders, called \emph{ladders}, whose probabilities can be calculated using the Up/Down numbers.