It has probably not escaped your attention that the Olympic Games are happening in London. A lot of people, myself included, study the medal table to compare countries. The table, as shown in British media is a curious phenomenon in the way it is constructed. It ranks countries by the number of gold medals won. For two countries with the same number of golds, it ranks them by the number of silvers and if they have the same number of silvers, by the number of bronzes (henceforth G for Gold, S for Silver & B for bronze.). It is what economists would call lexicographic preferences. See here for example.
What is odd about this, to my mind, is that there is no substitutability between different class of medals: one gold trumps any number of silver or bronze. For example, currently Germany has 5G, 10S & 7B medals but is judged to be behind Kazakhstan with 6G and 1B. That seems a bit hard on the Germans. There are other anomalies, Russia has a huge number of S and B medals but relatively few G so it is “only” 6th in the table. An American friend tells me that in the US, the table is based on total medals with the class of medal deciding tie-breaks.
It seems to me that a sensible way of doing things would be to weight the medals somehow. I think most people accept that there is something special about gold such that the margin over silver should be greater than that of silver over bronze. So a weighting of 4: 2: 1 for G:S:B makes sense. Needless to say I am not the first to have this idea and here is a spreadsheet by someone which calculates the medal table as it currently stands using that weighting (& sensibly normalizing on G=1). Russia and Germany do much better by this criterion whereas Kazakhstan moves down quite a lot.
It would be interesting to see an econometric analysis of this data once the Olympics are over and we have nothing else to do with our spare time.
POST-SCRIPT: Another obvious adjustment to the medal table is for population size. This site here has a table with gold medals per million and also the weighted average (using the same 4,2,1 weighting) per million. Well done Grenada! The US and China of course plummet in these tables.
(h/t Kim Bielenberg)
Totally agree about having some sort of weighted medal count. Maybe we should go a step further and give each individual medal a weight relative to the others based on the number of athletes competing for it (the more people you beat out to win it the more it should count, right?).