Since when is a mathematical definition necessary for this? Finding the "exact line of separation" between a couple of individuals and a powerful megacorp sound

Since when is a mathematical definition necessary for this? Finding the "exact line of separation" between a couple of individuals and a powerful megacorp sounds like a fun mental puzzle, but it is not something that comes up in practice. What is the thought experiment in which finding the exact delineation is of importance? On the other hand, it is pretty easy to distinguish the limiting cases. This is like worrying about how large an asteroid has to be in order to be called a planet.