The commentary is still running on Greg Mankiw’s joke of a paper “Defending the One Percent.” Due to Mankiw’s nominal endorsement of a Just Deserts economic justice philosophy, a number of the posts have engaged Mankiw on the philosophical level (most recently Noah Smith). I wrote two myself. (I, II).
Seeing as the bulk of this discussion is being driven by economists who have little knowledge of the vast philosophy at the core of the dispute, I figured it might be good to give an introduction to the philosophical ideas at the core of this kind of discussion. The question presented in this debate is: what kind of economic distribution is just?
Process
One way to answer this question is to say: just distributions are those that result from just processes. On this view, economic justice is not patterning our distribution according to some principle (whether that be desert or utility or fairness or whatever). Rather, economic justice is simply the following of just processes, whatever distribution they happen to generate. On the right-wing, libertarians like Robert Nozick, Murray Rothbard, and Hans-Hermann Hoppe subscribe to this kind of theory. On the left-wing, consensus anarchists can probably be grouped under this heading. The various camps under this heading have different views about what processes are just processes, but what they have in common is that they locate justice almost exclusively in the processes the economy follows, not the distribution it generates.
Desert
Desert theory is a non-procedural theory of economic justice. It essentially requires that our economic distribution be patterned so that each individual is distributed a share of the economy that matches their individual contribution. This is what Mankiw claims to be. In particular, Mankiw claims each individual should be distributed the share of the economy that matches their marginal product. As I wrote elsewhere, Mankiw has no clue what this would mean in reality. But nonetheless, that’s his view.
Utility
Utilitarianism is a non-procedural theory of economic justice. It requires that we organize our economic distribution so as to maximize overall utility (e.g. happiness, welfare, and so on). There are right-wing adherents to utilitarianism, e.g. Milton Friedman. And there have been left-wing adherents to utilitarianism, e.g. John Stuart Mill. The differences between them are primarily empirical. That is, they debate what in fact maximizes overall utility in society. Most economists seem to, at least implicitly, buy into utilitarianism. It is also what most wonky analysis appeals to (usually under the pretenses of being non-ideological, which it is not).
Egalitarianism
Egalitarianism is a non-procedural theory of economic justice. There are various strands of it, but they are all similar in the sense that they favor substantially equal economic distributions. John Rawls is sort of the father of modern-day egalitarianism. On his view, we should distribute everything equally except to the extent that distributing things unequally benefits everyone, especially those that wind up with less. Or to put it more simply: Rawls believes that the economic distribution should be organized so that the worst off are as well off as they can possibly be. Other famous egalitarians in this camp include Brian Barry, Amartya Sen, and G.A. Cohen. I also count myself under this heading.
One particular strand of this camp is luck egalitarianism, which appears to be what Noah Smith subscribes to (at least the view he puts forward to critique Mankiw). Under this view, the distribution should be arranged to match the responsible choices people make. That is, our distribution should reflect something like desert, but with all of the luck that goes into desert (genetics, family background, and so on) completely stripped out.
Conclusion
These are not the only frameworks, but they cover a substantial number of them. It should also be mentioned that they occasionally overlap. In particular, people often have procedural and non-procedural views about what economic justice requires. Many socialists, for instance, are egalitarians in the non-procedural sense, but also think a just economy is one that follows certain kinds of processes, e.g. democratic control of resources. Nonetheless, the above or some combination of the above accounts for the overwhelming majority of what people tend to appeal to (whether they know it or not) when talking about distributive justice.