In programming, should collision detection take place in each object class or within a game controlling class?

Is it better to program collision detection into each object or to program it into a class that accesses all objects?In programming, should collision detection take place in each object class or within a game controlling class?
I would do it for classes. it shouldn't take as long, because you do it once per class, not per object. but I use GM, not C++, so i'm not sure..........