We develop an ordinal method for making welfare comparisons between populations with multidimensional discrete well-being indicators observed at the micro level. The approach assumes that, for each well-being indicator, the levels can be ranked from worse to better; however, no assumptions are made about relative importance of any dimension nor about complementarity/substitutability relationships between dimensions. The method is based on the concept of multidimensional first order dominance. We introduce a rapid and reliable algorithm for empirically determining whether one population dominates another on the basis of available binary indicators by drawing upon linear programming theory. These approaches are applied to household survey data from Vietnam and Mozambique with a focus on child poverty comparisons over time and between regions.