This paper reports an experiment designed to elicit social preferences over income compensation schemes, where income differences between subjects have two independent components: one due to chosen effort and the other due to random chance. These differences can be compensated through social dividends, according to principles chosen beforehand by subjects themselves from behind a stylised Rawlsian veil of ignorance, or outside the society on which the principles will be implemented. We test the attractiveness in particular of Luck Egalitarianism, compensating inequalities due to chance but not those due to choice. We find modest but not overwhelming support for these principles, suggesting that subjects’ actual preferences are more complex.