John Rawls, answered from the texts and cited to the page.
Reflective equilibrium is the methodological procedure by which we bring our moral principles and our considered judgments into coherence with one another — working from both ends, as I put it in A Theory of Justice, until principles and judgments coincide. The starting point is what I call considered judgments: those moral convictions we hold under favorable conditions, with care and attention, and with reasonable confidence that they are not distorted by self-interest or inattention.
Some of these are very firm — we are confident, for instance, that religious intolerance and racial discrimination are unjust, and we treat such convictions as provisional fixed points that any acceptable conception of justice must accommodate.1 But we also have much less assurance about other questions, such as the correct distribution of wealth and authority, and there we need guidance that our convictions alone cannot supply.1
The procedure works as follows. We begin by describing conditions for a hypothetical initial situation — the original position — under generally shared and preferably weak assumptions, then examine what principles those conditions yield. If the principles match our considered convictions, well and good. But discrepancies will arise, and when they do, we face a choice: revise the description of the initial situation, or revise the judgment that seemed fixed.
By going back and forth — sometimes altering the contractual conditions, sometimes withdrawing a judgment and conforming it to principle — we move toward a state in which principles and judgments mutually support one another.2 That state is reflective equilibrium: an equilibrium because principles and judgments coincide, and reflective because we know to what principles our judgments conform and the premises of their derivation.2
Now, there are several interpretations of this notion, and the distinction matters. One might present a person only with descriptions that more or less match their existing judgments, smoothing out minor irregularities. Or one might present all possible descriptions and all relevant philosophical arguments, allowing for the possibility of a radical shift in the person's moral views.3
It is clearly the second kind — wide reflective equilibrium — that moral philosophy requires. We cannot, of course, examine every possible conception; the most we can do is study the conceptions known to us through the tradition of moral philosophy and any further ones that occur to us, and compare their principles and arguments.3 The procedure is not conservative, despite how it might appear.
Considered judgments exist at every level of generality — from particular cases and institutions up through broad standards and first principles to formal conditions on moral conceptions — and none of them, on any level, is in principle immune to revision.4 Even very general first principles might, in the course of achieving equilibrium, prove so compelling that they lead us to revise all previous judgments inconsistent with them; reflective equilibrium requires only that such revisions be made with conviction and that the agent continues to affirm the principles when it comes to accepting their consequences in practice.4
When we move to the political domain specifically, the procedure draws on our public political culture — its main institutions and the historical traditions of their interpretation — as the shared fund of implicitly recognized basic ideas and principles.5 Settled convictions such as religious toleration and the rejection of slavery serve as provisional fixed points; we collect them, organize the ideas and principles implicit in them, and try to formulate a conception of political justice that coheres with our most firmly held convictions at all levels of generality.5
The goal is not to preserve what we currently believe but to render our convictions coherent and, in doing so, to justify them — or to discover that some must be abandoned.
We are confident that religious intolerance and racial discrimination are unjust... These convictions are provisional fixed points which we presume any conception of justice must fit. But we have much less assurance as to what is the correct distribution of wealth and authority.A Theory of Justice, pp. 17–18
By going back and forth, sometimes altering the conditions of the contractual circumstances, at others withdrawing our judgments and conforming them to principle, I assume that eventually we shall find a description of the initial situation that both expresses reasonable conditions and yields principles which match our considered judgments duly pruned and adjusted. This state of affairs I refer to as reflective equilibrium. It is an equilibrium because at last our principles and judgments coincide; and it is reflective since we know to what principles our judgments conform and the premises of their derivation.A Theory of Justice, pp. 17–18
In the first case we would be describing a person's sense of justice more or less as it is although allowing for the smoothing out of certain irregularities; in the second case a person's sense of justice may or may not undergo a radical shift. Clearly it is the second kind of reflective equilibrium that one is concerned with in moral philosophy... The most we can do is to study the conceptions of justice known to us through the tradition of moral philosophy and any further ones that occur to us, and then to consider these.A Theory of Justice, pp. 42–43
There are no judgments on any level of generality that are in principle immune to revision... Reflective equilibrium requires only that the agent makes these revisions with conviction and confidence, and continues to affirm these principles when it comes to accepting their consequences in practice.15 The Independence of Moral Theory, p. 304
We look, then, to our public political culture itself, including its main institutions and the historical traditions of their interpretation, as the shared fund of implicitly recognized basic ideas and principles... a political conception of justice, to be acceptable, must be in accordance with our considered convictions, at all levels of generality, on due reflection (or in what I have called 'reflective equilibrium').18 Justice as Fairness: Political not Metaphysical, p. 408