David Miller has objected to the cosmopolitan argument that it is arbitrary and hence unfair to treat individuals differently on account of things for which they are not responsible. Such a view seems to require, implausibly, that individuals be treated identically even where (unchosen) needs differ. The objection is, however, inapplicable where the focus of cosmopolitan concern is arbitrary disadvantage rather than arbitrary treatment. This 'unfair disadvantage argument' supports a form of global luck egalitarianism. Miller also objects that cosmopolitanism is unable to accommodate special obligations generated by national membership. Cosmopolitanism can, however, accommodate many special obligations to compatriots. Those which it cannot accommodate are only morally compelling if we assume what the objection claims to prove - that cosmopolitanism is mistaken. Cosmopolitanism construed as global luck egalitarianism is therefore able to withstand both of Miller's objections, and has significant independent appeal on account of the unfair disadvantage argument.