Have you ever wonder how to create cartograms in ArcGIS? In case that you do not know what a cartogram is, just have a look below:
Cartograma del Volumen de exportaciones de 2007 por países
The map represents the total USD in export per country. The three juggernauts of exports clearly stand out.
The "science" behind them is pretty well described in the wikipedia, the hardcore math is which the tool is based is in this paper: Diffusion-based method for producing density-equalizing maps.
Well, the point is that is still possible to create this fancy maps in the last versions of ArcGIS for Desktop. You just only need to dowload the Cartogram Geoprocessing Tool version 2. Although it says that works for 9.3 and is dated back in 2009, I can confirm that the tool works fine in ArcGIS for Desktop 10.3.1. In fact, the map above has been created with it.
I think that these kind of map representations offer a fancy and attractive way of showing information using maps. It can be used, not only for countries, but also for cities, counties, districts, etc... in situations where the relation between the size of a polygon and any other variable, could make sense.
More examples of cartograms can be found here. This is also the home site in witch the algorithm for this tool has been based.