In this dissertation, I discuss two distributive principles in moral philosophy:Derek Parfit's Prioritarianism and Egalitarianism. I attempt to defenda version of Egalitarianism, which I call Weighted Egalitarianism. AlthoughParfit claims that Egalitarianism is subject to what he calls the LevellingDown Objection, I show (a) that my proposed Weighted Egalitarianism isnot subject to the Objection, and (b) that it gives priority to the worseoff people. The real difference between the two principles lies in how theweight of each person's well-being is determined. Prioritarianism assumesthat there is a moral scale of the goodness of well-being, independently ofdistributions of people's well-being. I raise two objections to this claim:firstly, it is hard to believe that the choice of the level of well-being affectsour distributive judgement; secondly, it is hard to believe that there is sucha moral scale independently of distributions of people's well-being. On theother hand, Weighted Egalitarianism claims that the weight is given by therank order position of the person in the ranking by well-being level. Thismeans that, in Weighted Egalitarianism, the goodness of a distribution isan increasing, linear function of people's well-being. Weighted Egalitarianismis not affected by the choice of the level of people's well-being. Nordoes it require require the moral scale of the goodness of well-being independentlyof distributions of people's well-being. Leximin, which might bea version of Prioritarianism, avoids my objections. But it is hard to supportLeximin, because it rules out the trade off between the better off and theworse off. I conclude that Weighted Egalitarianism is more acceptable thanPrioritarianism.