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Mathematical Olympic silliness At some point last week, while the Olympics were on TV, there was a five-minute segment mentioning that although China was at the top of the medals table by the IOC's official ranking, the USA's internal news services all put it at the top of the table – because the IOC likes to count gold medals and use the others to break ties, whereas the USA prefers to count total medals first and break ties by means of how many of them are which colour. (It was claimed that the USA has always counted this way, and that it was pure happenstance that on this occasion it happened to be a method of counting which put it at the top.) So, just out of interest, I've prepared an alternative view of the final medals table for the 2008 Olympics, which simply does not take sides in debates of this sort: it shows which countries must be considered to have got a better medal haul than which other countries by any sensible ranking policy, and doesn't try to make arbitrary judgments between the rest. http://tartarus.org/simon/2008-olympics-hasse/ I'm slightly surprised at how that turned out; I'd have guessed there'd be at least a few more unambiguous pinch points. As it is, the only countries in the entire table which can be sure of their position in the ranking are Russia, Great Britain, and the group at the bottom with one bronze medal each. |