What is "Fairness"?
Does "Fairness" exist in the world?
This is a very broad question and maybe primarily opinion based too. But yes, at least for some definitions it does it exist.
One possible definition of fair is envy-free. That is, you wouldn't want to switch your allocation with anyone else. If you have a last piece of cake and you have to share it with another, there is a whole class of algorithms that deliver envy-free division of the cake. The most famous member of this class of algorithms is the "divide and choose protocol" which is in active use around the world and has existed since biblical times (at least).