Generally, when people categorize economic and political philosophies, they do so according to a left-right spectrum. Writers group all of the philosophical arguments that tend towards right-wing conclusions together, and then do the same for philosophies that tend towards left-wing conclusions. Although helpful for some purposes, those actually interested in the philosophical moves in economic and political theory should split the philosophies, not into the categories of left and right, but into the categories of procedural and distributive. As the names suggest procedural justice refers to the use of just processes, and distributive justice refers to the achievement of just distributions of things like resources, capabilities, benefits, burdens, and welfare.
Procedural justice approaches to economic and political philosophy ground the justness of a particular system in the processes the system follows. On this view, any system that follows just processes is just, no matter what else obtains about it. In the contemporary era, there are two philosophical approaches that primarily concern themselves with issues of procedural justice: right-libertarianism and left-libertarianism (sometimes called anarchism).
On the right-libertarian line, just processes are those which are “non-aggressive” and therefore voluntary and non-coercive. Right-libertarians like Murray Rothbard and Robert Nozick argue that a free market, laissez-faire, capitalist system (perhaps one without a government at all) is the only one that follows just processes. They regard taxation as a form of aggression that is wrong in itself, no matter what its impact on overall social welfare might be. A very strict procedural right-libertarian would think that it is more just to permit hundreds of millions of people to starve to death than to feed them by levying a tax. The starvation of hundreds of millions does not relate to justice in this worldview because only just processes matter for justice.
The same holds true for regulation. Although they will not do so often, committed procedural right-libertarians may very well concede that regulations of various sorts on business actually improve social welfare. They may also concede that anti-discrimination regulations may actually reduce the amount of discrimination. Nonetheless, because process matters and not social welfare or racial equality, they will still object to regulations of this sort. As with taxes, governments ultimately back up these regulations with the threat of state violence, something right-libertarians view as inherently unjust no matter what other good results from it.
Left-libertarians (or anarchists) are similarly obsessed with procedural components of justice. Anarchists think that just economic and political processes are those which involve non-hierarchical, consensus-based decision-making. Although anarchists generally have egalitarian ideas as well, the primary emphasis of the view — at least among actual self-identified anarchists — is on process. A just system is one that follows the procedural requirements of non-hierarchy and consensus, regardless of what results from it.
Anarchists oppose state governments and capitalism because neither follow their rules for just process. State governments as they exist are inherently hierarchical. One person or a set of persons makes decisions over everyone else. Government representatives impose their decisions without the full consensus of the population. The representatives may have received a majority or a plurality of the votes cast in their elections, but such a voting system does not meet the rigors of consensus-based decision-making and imposes a hierarchy. Capitalism, according to anarchists, also fails to follow just processes. In the workplace, the bosses and the owners are above the low-level workers. They make the decisions and the workers must follow them. Thus, such a system violates procedural justice because it is hierarchical and not based on complete consensus.
These are just two short examples of ideologies in which procedural justice is central. But once you get the idea of procedural justice, you can probably spot at least some procedural-focused arguments in almost any political theory or modern-day movement. For example, peer mentors as the University of Massachusetts who were fired recently have launched a campaign in which they object, not to the substance of the policy decision to eliminate peer mentors, but to the unjust process that decision followed: it did not include student input.