This paper studies the design of a nonlinear social security scheme in a society where individuals differ in two respects: productivity and degree of myopia. Myopic individuals may not save 'enough' for their retirement because their 'myopic self' emerges when labor supply and savings decisions are made. The social welfare function is paternalistic: the rate of time preference of the far-sighted (which corresponds to the 'true' preferences of the myopics) is used for both types. We show that the paternalistic solution does not necessarily imply forced savings for the myopics. This is because paternalistic considerations are mitigated or even outweighed by incentive effects. Our numerical results suggest that as the number of myopic individuals increases, there is less redistribution and more forced saving. Furthermore, as the number of myopic increases, the desirability of social security (measured by the difference between social welfare with and without social security) increases.