What did Singapore do to so totally own the health list?
Top 3:
Singapore 0.979
Iceland 0.926
Japan 0.907
And if their health care is so awesome, why don't other countries just copy it?
It's probably too socialist for some countries... 
Since Singapore's healthcare is more based on private funding than the American system and their government spends about 90% less than the US (relative to GDP) on healthcare, that is obviously the entire answer.
It's not for nothing that Singapore is usually hailed as an international beacon of socialism.
I'd like to learn more about it, actually. Medisave, yes? Funded by CPF accounts?
But most of these lists are next to nonsense.
