I just remembered that Fred told me about Peters Map a couple of weeks ago, so decided to check it out.
Basically, the standard world map - the Mercator map - accurately plots the shapes of countries, however to do this is must compromise of scale (when transferring 'data' from the surface of a shere to a rectangle there must always be a compramise).
Because it was made in the 1500s (the start of the colonial years), the positioning of Europe means that it's scale is exaggerated, and the scale of Africa and South America is shown much smaller. Worst of all is the 'Greenland Problem' - because of is northern position Greenland appears the size of China, despite the fact it is actual around a quarter of the size.
The Peters Projection Map instead compromises the shapes of the countries for an accurate scale, meaning, politically, a much 'fairer' map that represents all the countries equally.
Mercator Map
Peters Map
I also found a link to this map of the Peters Map website. Its a map of the USA, predicting the voting in different states, however, to make it communicate the information more directly they have based the map on population (which is the important part), not geography. Awesome idea - it looks good too.
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