This paper proposes a ‘left-side monotone likelihood ratio’ (L-MLR) order which is a more restrictive concept than the ‘monotone probability ratio’ (MPR) order and generalizes the comparative static result for the MPR change to the non-linear case in the standard one-argument decision model. The L-MLR defines an order on random distribution that lies between ‘monotone likelihood ratio’ (MLR) and MPR. Transitivity, however, does not hold for L-MLR and we show that an important relationship exists between the orders, L-MLR and MPR. This paper also shows that an MPR change can always be decomposed into a sequence of L-MLR shifts.