The contributions of the relaxation of electronic polarization moments of various orders κ to the probabilities for the population transfer between the hyperfine-structure levels of an atom under the action of collisions are studied. It is shown that the contributions of higher electronic polarization moments with κ > 2 are comparable with the contributions of the orientation (κ=1) and the alignment (κ=2) or even exceed them in magnitude. This opens up the possibility of studying the collisional relaxation of higher polarization moments which are usually not observed and not involved in the emission and absorption of light under dipole transitions. The bounds for the allowable values of the rate constants for the collisional relaxation of higher polarization moments are obtained from the condition for nonnegativity of the total probabilities of population transfer between different hyperfine-structure levels under the action of collisions.