Properly Weighting Olympic Medal Counts
The weighting
scheme is simple: the weightings for gold, silver and bronze are
6, 3 and 2 respectively (before normalization). The weighting is based Zipf's
Law, which states that the importance of a thing is inversely
proportional to its rank. In this case, we have rankings 1, 2 and
3, and so we weight by the inverse of those ranks: 1/1, 1/2 and 1/3. Normalizing these
values, we have 3*6/11, 3*3/11 and 3*2/11, so that the total weighted
value of all medals equals the actual number of medals.
We can
also think of this metric as the "exclusiveness of the club."
Namely, the bronze medal winner is in the club of 3 people as good
has he or she is. The silver medal winner is in the club of 2
people as good as he or she is. The gold medal winner is the sole
member of his or her club. And so the gold medal club is 2 times as
exclusive as the silver medal club, and 3 times as exclusive as
the bronze medal club. And so we weight accordingly.