The relation between the macroscopic plastic response and the corresponding grain scale plastic events for a polycrystalline aggregate was studied by using the finite element method. The numerical model used was based on the constitutive relation combining a few simple and fundamental semi-microscopic plastic mechanisms which can describe a large variety of plastic behaviors observed in lots of experiments. The numerically evaluated plastic accommodation parameter, or the principle and representative scalar function, which relates the microscopic mechanisms on the grain scale with the macroscopic behavior, was compared with those suggested by other theories accepted in polycrystalline plasticity.