John Rawls, answered from the texts and cited to the page.
The veil of ignorance is a device built into the original position to ensure that the agreement reached on principles of justice is genuinely fair. The core idea is this: when parties are choosing the basic principles that will govern their society, they must be deprived of certain information about themselves, precisely because that information would give some parties bargaining advantages over others and allow them to tailor principles to their own circumstances rather than to what is just.1
What information is excluded? The parties do not know their place in society, their class position or social status, their fortune in the distribution of natural assets and abilities, their conception of the good, the particulars of their rational plan of life, or even their distinctive psychological dispositions such as their aversion to risk.2
They do not know which generation they belong to, nor the particular economic or political situation of their society.3 The exclusion is carefully bounded: enough information is ruled out to achieve impartiality, but no more than is necessary for that purpose. The rationale behind this is straightforward. If a person knew he was wealthy, he might find it rational to propose that taxes for welfare measures be counted unjust; if he knew he was poor, he would most likely propose the contrary.4
The veil prevents precisely this kind of self-interested reasoning from contaminating the choice of principles. What remains after the veil is in place are general facts about human society, economics, and psychology — enough for rational deliberation, but nothing that would allow one party to exploit social or natural contingencies to their advantage.5
It is important to be clear about what the veil is not. It is not a metaphysical claim that persons lack attachments, ends, or identities. The parties behind the veil are representatives of free and equal moral persons, not real individuals stripped of their humanity. The device is methodological: it models the conditions under which the fairness of the original position can transfer to the principles agreed upon within it.6
The name "justice as fairness" reflects exactly this transfer — since the original position situates free and equal moral persons fairly with respect to one another, any conception of justice they adopt is likewise fair.7 One further distinction is worth drawing. There is a Humean rationale for the veil and a Kantian one, and they pull in different directions.
The Humean rationale starts with full information and excludes only what is necessary to eliminate the influence of superior bargaining position — a thin veil. The Kantian rationale, which is the one I find more compelling, starts by allowing the parties no information and adds just enough for rational agreement to be reached — a thicker veil, because the principles adopted are then connected more closely to the conception of free and equal moral persons rather than to the contingent features of any particular society's history.8
The original position: we conjecture that the fairness of the circumstances under which agreement is reached transfers to the principles of justice agreed to; since the original position situates free and equal moral persons fairly with respect to one another, any conception of justice they adopt is likewise fair.16 Kantian Constructivism in Moral Theory, p. 325
no one knows his place in society, his class position or social status; nor does he know his fortune in the distribution of natural assets and abilities, his intelligence and strength, and the like. Nor, again, does anyone know his conception of the good, the particulars of his rational plan of life, or even the special features of his psychology such as his aversion to risk or liability to optimism or pessimism.A Theory of Justice, pp. 117–118
I assume that the parties do not know the particular circumstances of their own society. That is, they do not know its economic or political situation, or the level of civilization and culture it has been able to achieve. The persons in the original position have no information as to which generation they belong.A Theory of Justice, pp. 117–118
if a man knew that he was wealthy, he might find it rational to advance the principle that various taxes for welfare measures be counted unjust; if he knew that he was poor, he would most likely propose the contrary principle.A Theory of Justice, pp. 16–17
Enough information is then ruled out to achieve impartiality in the sense of the elimination of threat advantage. The veil of ignorance is thin, because no more knowledge is excluded than is necessary to secure this result; the parties still know the general configuration of society, its political structure and economic organization, and so on.16 Kantian Constructivism in Moral Theory, pp. 351–352
the conception of moral persons as free and equal, and the distinction between rational and full autonomy, must be appropriately reflected in its description. Otherwise the original position cannot fulfill its mediating role to connect a certain conception of the person with definite first principles by means of a procedure in which the parties, as rationally autonomous agents of construction, adopt principles of justice.16 Kantian Constructivism in Moral Theory, p. 325
justice as fairness begins from the idea that the most appropriate conception of justice for the basic structure of a democratic society is one that its citizens would adopt in a situation that is fair between them and in which they are represented solely as free and equal moral persons.16 Kantian Constructivism in Moral Theory, p. 325
The Kantian rationale proceeds in the opposite direction: it starts by allowing the parties no information and then adds just enough so that they can make a rational agreement... the thicker veil of ignorance would still be preferable, since these principles are then connected more closely to the conception of free and equal moral persons.16 Kantian Constructivism in Moral Theory, pp. 351–352