Ben Orlin in Math with Bad Drawings:
A few days into these Olympics, my friend Ryan lobbed me an alley-oop question via email:
Which brings to the next point, what is the ideal medal count ranking to your estimation? I figure this is something you probably have the correct answer to.
Alas, I told him, I don’t. There are three basic options, all of them bad.
First, the standard solution is to rank by gold medals. But like many standard things, this is deeply problematic. Did Ireland really outperform Brazil, even though the latter won 7 more silvers and 7 more bronzes?
Second is an alternative practiced sometimes in the U.S. and never anywhere else: to rank by total number of medals, treating gold, silver, and bronze as equals. But this is no better. Which would you prefer: Great Britain’s 7 extra bronzes, or France’s 2 extra golds + 4 extra silvers?
The third solution is to strike a balance between these deficient extremes; that is, to weight the medals. A gold is worth X silvers, and a silver is worth Y bronzes. But this has its own problem: what weights do you use? Is a gold worth 2 silvers, or 10? Is a silver worth 1.5 bronzes, or 15? Who knows! It’s inescapably arbitrary.
More here.
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