Statistical graphics are most convincing when they allow for interesting comparisons. A pie- or bar-chart allows comparisons in one data dimension as does one map, it shows how one variable varies in different regions. But data analysis shouldn’t stop here. Diagrams like the animated population pyramid or the gapminder/trendalyzer allow comparisons in more than one dimension where one of the dimensions is usually time which is depicted through animation.
Comparing regional patterns is a little trickier. A standard use case could be the question if people have more children in regions where conservative votes are higher. This would statistically be done by calculating correlations. However regression analysis is not for everybody. At least it would be nice to show two related patterns side by side and give people an idea what correlated variables would look like. Below is an example of how this could be implemented:
You can check out this mapping application at
http://vis.uell.net/gsvg/electionAtlasGermany.html
it will work for at least 95% of internet users