Justice

Justice is the virtue of judging people by the same standard one applies to anything else in reality, and of treating them accordingly. Objectivism describes it as the application of rationality to the evaluation of other men: identifying their character and actions accurately, then granting or withholding value on that basis.

“Justice is the recognition of the fact that you cannot fake the character of men as you cannot fake the character of nature.”
~ Ayn Rand, Atlas Shrugged

Judgment is the whole of the virtue

Justice has two parts and the second follows from the first. The part usually overlooked is the cognitive one: forming an accurate estimate of a person before any question of reward or penalty arises.

It is an identification, not a verdict handed down. What a person has actually done, over time, in circumstances one knows about, is a matter of fact. See Objectivity.
It requires context. A conclusion about a man's character drawn from one action, without knowing what he knew or what alternatives he had, is not justice but carelessness.
Errors of knowledge are not breaches of morality. Objectivism distinguishes sharply between a man who is mistaken and a man who is evading. Only the second is a moral matter.

The second part is acting on the estimate: paying for value received, praising what deserves praise, and refusing sanction, trust or association to those who have earned the opposite. Rand's emphasis fell heavily on the positive side, which she thought was the neglected one. Withholding deserved admiration is as much an injustice as extending undeserved trust.

Moral judgment and its cost

"Judge, and be prepared to be judged" was Rand's formulation, in deliberate opposition to the injunction not to judge at all. Her argument is that suspending moral judgment does not produce neutrality:

Refusing to distinguish the good from the evil does not leave both untouched. It removes from the good the recognition his actions earned, while granting the evil the appearance of respectability.
The person who abstains has not avoided a judgment. He has made one — that the difference does not matter enough to act on.
Objectivism calls the resulting posture the sanction of the victim when the person paying the cost is the one whose approval is being extracted.

This does not license snap condemnation. Rand's own standard was that a moral judgment must be based on evidence sufficient to support it, and that pronouncing on people whose situation one has not troubled to understand is itself an injustice.

In the political sphere

Applied to social organisation, justice is the principle that a person is entitled to what he has earned and to nothing he has not. This is the root of the Trader Principle, and through it of rights and of the case for capitalism: a system in which values change hands only by voluntary trade is one in which the connection between what a person produces and what he receives is preserved.

Objectivism rejects the notion of "social justice" understood as distribution according to need, on the grounds that it severs exactly that connection. See Altruism and Collectivism.

Common misunderstandings

That it means treating everyone equally. It means applying one standard to everyone, which produces different treatment for people who have done different things. Equality before the law is that principle applied to government; equal esteem regardless of conduct is its opposite.
That it is about punishment. Retribution is one application. Most of the virtue is exercised in ordinary dealings — hiring, trusting, paying, admiring — where nobody is being punished at all.
That mercy is a higher virtue. Objectivism holds that undeserved forgiveness transfers the cost of a wrong from the person who committed it to someone who did not.
That judging others is arrogant. The alternative is not humility but abdication: dealing with people while refusing to form any estimate of them.

Discussion

References

Rand, Ayn. "The Objectivist Ethics", The Virtue of Selfishness. New American Library, 1964.
Rand, Ayn. "How Does One Lead a Rational Life in an Irrational Society?", The Virtue of Selfishness.
Rand, Ayn. Atlas Shrugged — Galt's speech, on justice and on the sanction of the victim.
Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapter 8.

External links

Justice at the Ayn Rand Lexicon