Rawls thinks he is able to prove that procedural justice requires that we cannot choose utilitarian principles of justice. When we consider what rules are just for society without considering how we could personally benefit from those rules, what rules would we pick?
Rawls does think we will accept the following principles of justice: a Principle of Equal Liberty, a Principle of Fair Equality of Opportunity and the Difference Principle. The principle of equal liberty says that basic liberties are to be as expansive as possible so long as it does not interfere with others' liberty. The principle of fair equality of opportunity says that positions high up in society (president, rock stars, etc) must be available to all groups (gender, race, age) and that everyone who has similar talent, ability and ambition has the same opportunity for success regardless of what class they are born into. The difference principle says that the distribution of wealth and goods should be equal unless the inequal distribution benefits the people who are worst off in the society. For example, we may give the president more power or more wealth, but this is only because this position is necessary to keep society going, so it benefits the people who are worse off. Another example is that we give police officers more power but this is because we expect that because they have power, they can protect the weakest members of society.
Rawls gives two arguments for the Difference Principle. First is his formal argument. This is the argument that when we are in the original position, it is only a matter of rational choice that we will choose the difference principle. According to the maximin rule, which says that we should make the worst position in society as good as possible, it is only rational to choose the difference principle. Second is is informal argument. Because where in society we are born is arbitrary from a moral point of view, we should not give our rewards and benefits based on lucky facts about when and where we are born.