Apparently Russia "won" the 2014 Winter Olympics. Athletes from Russia won the most gold medals and the most overall medals [with no consideration of the number of medals per capita, medals per acre, medals per dollar of GDP assessed at purchasing power parity, medals per athlete, etc.] Numerous sites show the medal totals (e.g. here or here).
Country #Gold #Silver #Bronze Total
Russia 13 11 9 33
Norway 11 5 10 26
Canada 10 10 5 25
USA 9 7 12 28
Netherlands 8 7 9 24
Germany 8 6 5 19
The interesting thing I've noticed is that apparently the listings/rankings by International Olympics Committee use a lexicographic ordering to rank the countries: They rank by gold medals, and only if there is a tie in the number of gold medals won do they consider the number of silver medals won; and only if there is a tie in both the number of gold and silver medals won do they consider the bronze medals.
In other words, as with lexicographic preferences in economic theory, there are NO trade-offs. They do not say, "well three bronze equal two silvers" or whatever. There are no weights involved to generate a ranking. For example, with this system, you don't weight gold=1, silver=0.9, and bronze =.8 (or supply your own weights; it doesn't matter). All that matters is the lexicographic order.
Did the USA beat Canada in the medal count? Using totals (as often was emphasized on NBC), they did. And of course it is possible to come up with a weighting scheme whereby the USA topped Canada in the medal count. But with lexicographic ordering, what counts are gold medals regardless of how many silver or bronze medals were won.
Do we observe lexicographic ordering in consumer preferences? Possibly, but no example comes to mind. The case of perfect complements comes close but not quite.
Addendum: maybe the best way to weight the medals is by resale value.