I'm surprised GBR did so well, given the variety of the Olympics, and our comparative tinyness.

I think your method of explaining the ranking is best, but for the record, I wasn't sure if it fit my intuition better to say any scoring system must assign x, y and z points for each gold, silver and bronze medal respectively, and have:

0<x 0<=y<=x 0<=z<=y Which I think is completely equivalent, but made it immediately obvious that you really, really must do it that way.

No, wait, cancel that. That's an obvious way of doing it, but yours is more general, because it would (I think) cover any formula, whereas mine covers only linear ones.

Also, mine covers non-Archimedean orders. The IOC's ranking system, for instance, is a lexicographic order in which one gold beats any number of silvers; that can't be expressed at all as an additive scheme with a positive real score for each of gold, silver and bronze, because for any additive scheme there must be some number of silvers large enough to beat one gold.

Good point. I think I assumed x,y and z would be rational numbers (equivalent to integers), and ignored tie-breaking as some extra step that might or might not involve counting red-haired witch-doctors in each team :)

(Although, I could retrospectively pretend that I intended the domain to include infinite ordinals.)

And yes, everyone's a bit surprised GBR did so well. That's why all the news has been saying "wow, we've had a great Olympics"!

Oh, right. I haven't been watching any Olympic news whatsoever. (Which I haven't put a lot of effort into avoiding, but I guess I must concede must have been difficult :)) I assumed that was normal and was surprised we usually did that well, rather than surprised we did that well this time :)

I know where some of the Olympics have been, but I slightly embarrassedly admit I don't think I know any of the results, ever.