A proportional symbol map or proportional point symbol map is a type of thematic map that uses map symbols that vary in size to represent a quantitative variable. For example, circles may be used to show the location of cities within the map, with the size of each circle sized proportionally to the population of the city. Typically, the size of each symbol is calculated so that its area is mathematically proportional to the variable, but more indirect methods (e.g., categorizing symbols as "small," "medium," and "large") are also used.
While all dimensions of geometric primitives (i.e., points, lines, and regions) on a map can be resized according to a variable, this term is generally only applied to point symbols, and different design techniques are used for other dimensionalities. A cartogram is a map that distorts region size proportionally, while a flow map represents lines, often using the width of the symbol (a form of size) to represent a quantitative variable. That said, there are gray areas between these three types of proportional map: a Dorling cartogram essentially replaces the polygons of area features with a proportional point symbol (usually a circle), while a linear cartogram is a kind of flow map that distorts the length of linear features proportional to a variable (often travel time).
History
Arthur H. Robinson credited Henry Drury Harness with the first map to clearly attempt to portray point sizes proportionally, on an 1838 map of cargo traffic in Ireland (with proportional widths) that showed city population. The technique was soon replicated and enhanced by other cartographers. The official report of the 1851 Census of Great Britain included several maps drawn by a W. Bone, showing significant towns sized proportionally to population (apparently range-graded), including one of the first useful legends. Charles Joseph Minard produced several proportional symbol maps, including the innovations of using them to represent regions rather than points, and incorporating color and statistical charts in the point symbols.
As cartography arose as an academic discipline in the early 20th Century, textbooks included detailed instructions on constructing proportional symbol maps, including calculating circle sizes. Several cartography professors began to experiment with new mapping techniques, notably the use of spheres with a proportional volume rather than area by Sten de Geer (1922) and Guy-Harold Smith (1928), and the use of transparency to resolve overlapping circles by Smith (1928) and Floyd Stilgenbauer (1932), the latter of which included a unique legend.
The rise of the map communication paradigm in academic cartography led to a number of psychophysical experiments on the effectiveness of map symbols. One of the earliest and most well-known of these studies was the PhD dissertation of James J. Flannery, who studied the ability of people to judge the relative areas of proportional circles, finding that Stevens's power law applied such that map readers underestimated circle area by a fairly predictable amount, leading to the Flannery Scaling Adjustment still in use today.
Starting in the early 1990s, almost all proportional symbol maps have been created using geographic information system (GIS) and graphics software, with increasing capability for professional design. The rise of the Internet and web mapping, especially modern tiled services with API access starting in 2005, have enabled the creation of interactive proportional symbol maps, including cloud mapping platforms such as Esri ArcGIS Online and CARTO.
Point locations
Proportional symbol maps represent a set of related geographic phenomena (e.g., cities) as point symbols. These point locations can have two different sources and meanings: A Point dataset includes a point location (i.e., a single coordinate) for each geographic feature. A variety of features may be represented this way, but common point datasets include cities, personal residences, and businesses. This does not mean that these geographic features are zero-dimensional in reality—cities are two-dimensional and buildings are three-dimensional—just that the source data consists of points that are reasonable representations of the location of the geographic features at the chosen map scale. An aggregation district dataset consists of predefined regions in which data about individuals has been aggregated to create summary statistical attributes (e.g. total population); that is, it is the same structure as is used in a choropleth map. In this case, the proportional symbol map will have a point representing the district rather than any point location therein.