Over the years, egalitarian philosophers have made some challenging claims about the nature of egalitarianism. They have argued that egalitarian reasoning should make us reject the Pareto principle; that the Rawlsian leximin principle is not an egalitarian idea; that the Pigou–Dalton principle needs modification; that the intersection approach faces deep problems; that the numbers should not count within an egalitarian framework, and that egalitarianism should make us reject the property of transitivity in normative reasoning. In this paper, taking the recent philosophical debate on equality versus priority as the starting point, I review these claims from the point of view of an economist.