We propose and axiomatically characterize a family of welfare criteria that prioritize individuals making larger sacrifices. By combining efficiency with a concern for equality of sacrifice, our criteria avoid serious shortcomings of utilitarianism. We illustrate our results within the...

Surveys and experiments suggest that people hold workers more responsible for income gains stemming from merit, such as education, than circumstances, such as parental education. This paper shows how to design income taxes that account for merits. First, we introduce social welfare functions...