In China it's done on the height of the child! Many trains have a measure in the coaches.
Its BOTH age and height. These rules are uniform for any train anywhere in China. I do not know the exact ages (as I guess its for half fare), but its like: Untill (xy) years AND as long as the child is also no longer as 1m(xx). Is in fact pretty common in many Asian countries. Penalizes the westener kids, who tend to be taller. Height measures can often also be noted at ticketing windows.
For children about any country in Europe has:free untill (mostly) 4, and half (or approximate half, here in NL its 60% train or 66% bus) untill xx years. This xx can vary enormously and likely affects more people. Ranges from 8 till 18 (Sweden). 10 or 12 is most common. In fact for a child of 11 on INTernational ticketing, it may have to pay 50% in country 1 and 100% in country 2 and 75% in country 3. or mixed.
Small children untill 4 must be kept on lap of parent if there is lack of space. Also an age-old rule that most people tend to be unaware of.