What makes a distribution of wealth and income just?
Nozick vs. Rawls on distributive justice
What Robert Nozick argues
A distribution is just if it came about by just steps from a just starting point. Whatever people acquire fairly and transfer voluntarily is theirs, whatever overall pattern results. Justice is historical: you cannot read it off the final shape of who has what. Taxing earnings to fund redistribution treats people as partly owned by others, so the only legitimate state is a minimal one that protects rights, enforces contracts and rectifies past injustice.
What John Rawls argues
The principles of justice are the ones free and equal people would choose behind a veil of ignorance, not knowing their class, talents or place in society. They would secure equal basic liberties first, then fair equality of opportunity, and accept social and economic inequalities only when they work to the greatest benefit of the least advantaged: the difference principle. Natural talent and social starting point are morally arbitrary, so the basic institutions of society must be arranged so that the fortunes they produce benefit everyone.
Where they part ways
Whether justice judges the pattern of outcomes or the history of how holdings came about. Rawls asks what the basic structure of society should secure for its least advantaged members. Nozick answers that any pattern, however attractive, can only be maintained by continually interfering with free exchanges between people, and so violates their rights.
The strongest objection from each side
Robert Nozick
The Wilt Chamberlain argument. Start from any distribution Rawls approves of, let a million fans each freely pay twenty-five cents to watch a great basketball player, and the pattern is broken without anyone being wronged. Keeping it would mean forbidding capitalist acts between consenting adults or taxing them away. Nozick adds that treating natural talents as a common asset fails to take seriously the separateness of persons.
John Rawls
A series of individually fair transactions can still add up to unjust background conditions, so fairness has to be secured at the level of institutions, not exchange by exchange. Rawls makes this reply in "The Basic Structure as Subject" (1977). Critics add that Nozick never fully states his principle of just acquisition, and that actual holdings descend from conquest and expropriation, so his own principle of rectification would demand sweeping redistribution.
What changed afterward
Anarchy, State, and Utopia (1974) made libertarianism a serious position in academic political philosophy, and the exchange set the terms for what followed: G. A. Cohen's critique of self-ownership, the luck egalitarianism that grew out of Dworkin's work, and left-libertarians who accept self-ownership but hold natural resources in common. Rawls turned in Political Liberalism (1993) to how a society divided by reasonable disagreement can still share principles of justice. Nozick himself later wrote, in The Examined Life (1989), that the libertarian position he had once propounded now seemed to him seriously inadequate.