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Proportional circle maps are a popular method for visualizing quantitative data on a map. Circles are scaled proportionally based on the data provided; larger circles represent larger quantities. The circles require two values, a location and a numeric quantity. For data that have a wide range of values, the resulting map will produce clutter and overlap in which large symbols obscure the information contained in smaller circles. Some previous solutions to this problem are modifying and improving the contrast between symbols, or using stacking algorithms so all symbols are visible. This article proposes the displaced proportional symbol map, which displaces the symbol's location based on the amount of overlap between neighbouring circles. At the same time, it preserves the location of non-overlapping symbols, which distinguishes it from the circular cartogram. The displacement is automated through the proximity stress model algorithm for node overlap removal. This algorithm was originally designed for graph layouts with overlapping nodes, but was modified here for circular symbols and map layout. The result is a map with improved clarity and the ability to add labelling to a cluttered proportional circle map. [ABSTRACT FROM AUTHOR]

Conventional maps of election results can give a misleading picture of the popular support that candidates have because population is highly non-uniform and equal areas on a map may not correspond to equal numbers of voters. Taking the example of the 2004 United States presidential election, we show how this problem can be corrected using a cartogram — a map in which the sizes of regions such as states are rescaled according to population or some other variable of interest. [ABSTRACT FROM AUTHOR]