Different political views, even if they're all liberal, in the sense of supporting liberal constitutional democracy, undoubtedly have some notion of the common good in the form of the means provided to assure that people can make use of their liberties, and the like.

Justice as fairness provides what we want.

There are various ways you might define the common good, but that would be one way you could do it.

An intuitionist conception of justice is, one might say, but half a conception.

Ideally a just constitution would be a just procedure arranged to insure a just outcome.

Justice is the first virtue of social institutions, as truth is of systems of thought. A theory however elegant and economical must be rejected or revised if it is untrue; likewise laws and institutions no matter how efficient and well-arranged must be reformed or abolished if they are unjust.

The fault of the utilitarian doctrine is that it mistakes impersonality for impartiality.