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.

There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry.

A just system must generate its own support.

We must choose for others as we have reason to believe they would choose for themselves if they were at the age of reason and deciding rationally.

Peace surely is a good reason, yes. But there are other reasons too.

Justice is the first virtue of social institutions.

The fairest rules are those to which everyone would agree if they did not know how much power they would have.