Thus I assume that to each according to his threat advantage is not a conception of justice.

Justice as fairness provides what we want.

A scheme is unjust when the higher expectations, one or more of them, are excessive. If these expectations were decreased, the situation of the less favored would be improved.

The natural distribution is neither just nor unjust; nor is it unjust that persons are born into society at some particular position. These are simply natural facts. What is just and unjust is the way that institutions deal with these facts.

You might say that, if citizens are acting for the right reasons in a constitutional regime, then regardless of their comprehensive doctrines they want every other citizen to have justice. So you might say they're all working together to do one thing, namely to make sure every citizen has justice. Now that's not the only interest they all have, but it's the single thing they're all trying to do. In my language, they've striving toward one single end, the end of justice for all citizens.

The idea of public reason has to do with how questions should be decided, but it doesn't tell you what are the good reasons or correct decisions.

The concept of justice I take to be defined, then, by the role of its principles in assigning rights and duties and in defining the appropriate division of social advantages. A conception of justice is an interpretation of this role.