Because it makes the most sense to do this. Conclusion: Smaller countries produce higher ratios of medals to population.
Population numbers taken from Google's response. Medal count as of about 11:15pm EST (11:1 am Beijing) today (Tuesday EST, Wednesday Beijing).
New Zealand: 1 medal to 514,471 people
Jamaica: 1 medal to 556,026 people
Australia: 1 medal to 583,833 people
Denmark: 1 medal to 911,353 people
Britain: 1 medal to 1,841,704 people
S. Korea: 1 medal to 2,043,532
Canada: 1 medal to 2,568,472 people
Germany: 1 medal to 2,942,893 people
Russia: 1 medal to 3,366,136 people
USA: 1 medal to 3,811,898 people*
Japan: 1 medal to 5,792,431 people
China: 1 medal to 17,392,788 people
India: 1 medal to 1,129,866,154 people
Congratulations to New Zealand, Australia and Jamaica.
Obviously, there needs to be some kind of shift for lower population values, and also one for the age range of available athletes. Some countries will have more children or more adults too old to compete in most sports. I'd love to see this done properly.
*Eight of these medals are one man's, so the US is producing fewer Olympians than this number implies. This is true for any repeat medal-winners, such as Usain Bolt of Jamaica. This is another thing to consider.