Mobility measures which induce order in the semiring of transition bistochastic matrices

Paper shows different aspects of mobility measures with special attention to mobility as movement. Examples of mobility measures which induce order in the semiring of transition matrices are given and Shorrocks axioms are consistent on that domain. There are no mobility measure in the semiring of all transition bistochastic matrices which satisfies all requared conditions and induces order. It has been shown that on the reduced domain of transition bistochastic matrices three measures induce order.