Medals

 

The Best

You're simply the best
Better than all the rest
Better than anyone
Anyone I've ever met

In the upcoming Olympics, which country is the best?

In the upcoming summer Olympics in Paris, during the opening ceremony there will be a parade of Nations of every athlete who participates in the Olympics.  During the closing ceremonies, the athlete participants are supposed to mingle without regard for country.  Between the Opening Ceremonies and the Closing ceremonies will be the events of the Olympics where medals will be awarded.  The closing ceremonies indicate that everyone gets a participation ribbon, but how should you count the medals by Nation during the events to determine which country is the best?

In each event, there are Gold, Silver, and Bronze medals awarded.  To be the Gold medalist in an event is to say that during that event you were the best.  But that does not mean that you are always the best, because that event can be viewed as a random event.  The gold medal indicates dominance on that day in that event, but it does not indicate certainty.  How can you indicate both?

In some countries only the number of Gold medals are considered.  I.e. each Gold medal is worth one point.  The country with the most points is considered the best.  But since the finish is random, that only indicates dominance, not certainty.  In some countries, each medal is awarded a point. Then the question becomes why stop at 3 medals for each event.  Why not award everyone who participates a medal.  Sounds like the political debate of woke vs. non-woke!

It is typical  in the United States, for each Bronze medal to be awarded one point, each Silver medal to be awarded 2 points, and each Gold medal to be awarded 3 points.  The points are totaled and the country with the most points is considered to be not only dominant but certain.

This is a Nash Equilibrium between the User Optimum of considering only Gold medals and the System Optimal of considering all medals as equal.  Is it perfect?  It does not consider Users who shop for a country which allows them the best chance to compete, nor does it consider a country which offers citizenship and/or rewards to athletes who have the best chance of winning.  But it considers the difference among medals, and awards no points to athletes who merely wish to compete with no expectation of winning, such as the Jamaican bobsled team. So arguably the US system is the best at determining the best country with dominance AND certainty.