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Distributive justice has been the focus of political theory with the postwar rise of the social welfare state, and Rawls' A Theory of Justice (1971) is arguably the most important work of political philosophy during that period. Parallel to this theoretical literature is a body of empirical research into distributive justice. We offer a synthesis of the theoretical and empirical approaches with an experimental study of how individuals use allocation principles in making judgments concerning income distribution under conditions of strict impartiality. Our experiment is designed in part to examine the extent to which they prioritize them consistent with Rawls' theory. We find that distributive justice judgments are complex but structured, with individuals tending to use several principles simultaneously and weighing them according to predictable factors, with sex and race being particularly important. We also find that individuals use several strategies in using competing allocation principles and that a considerable minority prioritize them consistent with a Rawlsian maximin strategy.