摘要：Mallows and Plackett-Luce parametric probability distributions are the two most used and well-known in the set of complete linear orders of a finite universe. In this paper, we extend those two distributions on the set of complete preorders of the universe. For that purpose, by considering a parametric family of metrics on the set of complete pre-orders generalizing Kemeny Distance on pre-orders and Kendall metric on orders, we determine a parametric probability distribution on pre-orders generalizing Mallows Distribution. By considering pre-orders as orders on blocks of equivalent elements, we generalize the Plackett-Luce distribution on complete pre-orders.
关键词：Complete pre-orders;Generalized Mallows distribution;Generalized Plackett-Luce distribution
