The problem is that there isn't one universal definition of fair. Conservatives, liberals, libertarians, socialists, they generally all (with individual exceptions of course) want a society that is fair, but with different, mutually incompatible definitions of fair.
Conservatives tend to preach that in a fair society, everyone gets what they deserve. Harder working, more talented? Then you deserve more. Socialists tend to preach that in a fair society, everyone gets what they need.
The group who need the most doesn't overlap with the group who is most talented and able to work hard, so conservatives and socialists will never agree on what is fair, or even that the other group believes in fairness.