What is fair medal counting?

So how to count an overall result based on winning the medals? I have an idea! Why not to give 197 for the gold, 108 for the silver and 64 for the bronze(copper)? What are these numbers - you will probably ask. You can see it in the picture above. It is the atomic weight for Olympic metals based on periodic table. Isn't that fair enough?
The official Olympic medal table places the teams based on the number of gold medals won. If the number of gold medals is equal, silver medals will be counted etc. I don't think it is fair enough. There are teams that get many silver or bronze medals but placed quite low in table.