TRC

In a regular map, land area is used as the mapping variable. A cartogram is a type of map in which some other variable (such as country population) has been used in place of land area. This can reveal insights that are otherwise hidden.

Danny Dorling is a Professor of Geography at the University of Sheffield and Mark Newman is a Professor of Physics at the University of Michigan. They and others have a project called Worldmapper where hundreds of world map cartograms have been created.   

Here is a video from sciencefriday.com  of how the US map from the 2008 election changes based on voting trends.

Here is an article from The Atlantic with examples of interesting maps.