Stochastic dominance (SD) is commonly used to rank income distribution and assess social policies. The literature argues that SD is a robust criterion for policy evaluation because it requires minimal knowledge of the social welfare function. We argue that, on the contrary, SD is not a robust criterion. We do this by carefully introducing microfoundations into a model by Chu and Koo (1990) who use SD to provide support to family-planning programs aiming at reducing the fertility of the poor. We show that fertility restrictions are generally detrimental for both individual and social welfare in spite of the fact that SD holds. Our findings are an application of the Lucas' Critique.