Olympics time, and once again we see every news site in the country splash up the medals table. Invariably with USA or China at the top. The intention is clear that the top of the table are better at Olympics in some way. Sites might even refer to the top of the table as the Olympics winners.
This is unfortunate for two reasons. Firstly, there is no the medals table. Most of the world sort by golds, then by silvers then by bronze. Parts of the US sort by total medal count (for obvious reasons). The New York Times has suggested a weighting were one gold is worth two silvers, which is worth two bronzes.
The reason there is no one ranking is that the Olympics does not recognise any ranking table, not does it recognise a winning country. It only recognises medals to individuals. The ranking tables are not any official part of The Olympics, they are something pushed by the media, who presumably are more interested in political rivalries.
Anyway, the bigger reason this is unfortunate, is that total medals is an exceedingly unfair way to rank performance of a country. Tuvalu would need 30 thousand times the rate of medals to get the glory of matching the US on the medals table. Even larger countries like Iceland would need 900 times the rate of medal winning. The figures are even more skewed when compared to China. So why doesn't the media do the obvious thing and report medals per capita in the ranking tables?
We can get a clue by looking at the last five winners of the medals per capita (I'm using the NYT weighting here but it doesn't make much difference):
Dominica, San Marino, Grenada, Grenada, Jamaica
These are all very low population countries, and the winner varies a lot each Olympics. The problem is two-fold. Firstly, low-population countries will have far higher variance in their medal count than large ones, so the 'lucky outliers' will be small countries, and big ones like China would stand no chance of winning even if they have about the same quality of athletes, due to the lower variation.
Secondly, while this may seem unfair, the fact is that having the larger countries at the top of the table pleases more people, and so as a method is supported by more people. I'm sure that San Marino people would love to see the medals per capita plastered over the media, but their opinion is drowned out by a bigger market of people from the US and China who enjoy seeing their own country near the top.
So we are being pulled in two directions. Logic and fairness pulls us towards publishing the medals per capita, but popular interest and lucky outliers pulls us towards showing the total medal count.
This is a multi-objective problem, which can be resolved using the concept of Pareto fronts. The nice thing about this is that it admits multiple first-place 'winners' and multiple second places etc. None of these several winners can claim to be better than any other, so the slightly oppressive nature of placing every country in the world into a pecking order is relieved.
Anyway, here is how it works. In my case I will use the NYT medal weighting as the 'medals' count. The Pareto winning countries are those on the Pereto front of the two objectives: medals and medals-per-capta. They are the countries that: have more medals or more medals-per-capita than every other country.
So for any two Pareto winners, either can claim superiority to the other on one objective only, so it is a tie.
In order to get Pareto second place, we just remove the Pareto winners and apply the same search again. Likewise for third and fourth place, etc.
For 2024's Olympics we have:
- Pareto first place: Dominica, Saint Lucia, New Zealand, Netherlands, Australia, France, United States
- second place: Grenada, Bahrain, Georgia, Hungary, Great Britain, China
- third place: Slovenia, Jamaica, Croatia, Norway, Sweden, South Korea, Italy, Japan
They are in population order. The table now is satisfying for people from large and small countries.
We can see that the usual hegemony of US/China is replaced by a hegemony of New Zealand, Australia, Great Britain, and United States. Also with winning by Grenada, the Bahamas, Netherlands and Russia.
It is actually rather sad to see that there is still Anglosphere privilege throughout the Olympics, and it isn't as egalitarian as the Olympic Committee (and the world) would like it to be. But at least now this hegemony is visible, it is not just USA battling it out with China.
Media companies would do well to present the Olympics this way. It shows what is really going on, and gives honour to some of the smaller countries with incredible rates of medals.
Update: This is a different attempt to solve the same problem with total medals and medlas-per-capita by trying to find a happy medium between the two extremes. I don't think it is the best answer for a few reasons- 1. it rates all medals the same regardless of colour, 2. it uses a model that is at the same time too complicated for audiences to adopt and too simple to represent what's going on. For instance it assumes all actions are independent. 3. it continues to squeeze all countries onto one strict ordering, rather than treating the medal rates of tiny and huge countries as effectively incomparible.
