Proportional symbol map

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 are also used.
While all dimensions of geometric primitives 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 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, while a linear cartogram is a kind of flow map that distorts the length of linear features proportional to a variable.

History

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 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, 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 and Guy-Harold Smith, and the use of transparency to resolve overlapping circles by Smith and Floyd Stilgenbauer, 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 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 and .

Point locations

Proportional symbol maps represent a set of related geographic phenomena as point symbols. These point locations can have two different sources and meanings:

A Point dataset includes a point location 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 ; 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.
Variables

The second part of the proportional symbol map is the choice of variable to represent by symbol size. The best variables to use in this technique are ones in which size will be interpreted intuitively by most map readers. In Semiology of Graphics, Jacques Bertin argued that of all of his visual variables, size was most intimately tied to a single interpretation. That is, a larger symbol looks like more of something and thus more important, and it is very difficult to interpret it any other way. A second tendency is for users to interpret relative sizes: a symbol that is twice as large will be interpreted as representing twice the quantity. The absence of a circle would be interpreted as the complete absence of the phenomenon, and negative values cannot be shown.
Based on these principles, only ratio variables are appropriate to represent with size, specifically those in which negative values are not possible. Within this set, the most intuitive are those that measure the total amount/count/volume of something, such as total population, volume or weight of agricultural production, or shipping tonnage. These are all spatially extensive variables, which happen to be the most problematic choices for choropleth maps, making these two thematic mapping techniques complimentary.
Some ratio variables can be appropriate for both choropleth and proportional symbol maps, especially those that are spatially intensive but still represent an amount or count in some way. A common type of variable that meets these criteria is an allotment, calculating how one amount is theoretically distributed among individuals, such as GDP per capita or the crude birth rate. Other non-negative spatially intensive ratio variables can technically be mapped as proportional symbols, such as proportions, but can lead to misinterpretations because they do not represent amounts. Ordinal qualitative variables can also be appropriate, if the goal is a simple representation of "small," "medium," and "large."
Variables that are inappropriate for proportional symbols include those that may include negative values and qualitative categories. Another consideration in selecting a variable is the degree of variance in the statistical distribution. If there is a high degree of variation, the largest symbols will be overcrowded and entirely overlapping while the smallest symbols will be nearly invisible. If there is a low degree of variation, most of the symbols will look nearly the same size and the map will be relatively uninformative.

Symbol design

The primary goal in selecting a point symbol to use in a proportional symbol map is that users should be able to accurately judge sizes, both in comparison to the legend to estimate data values, and in comparison to each other to judge relative patterns. Secondary goals include aesthetic appeal and an intuitive shape that is easy to interpret.
The point symbols that represent each data value can be of any shape. In most proportional symbol maps, the shape does not vary, so it does not represent any information on its own. Differences in shape can be used to represent a nominal variable can make judging relative sizes more difficult. Pictorial or pictographic symbols, which use an iconic shape that evokes the represented phenomenon can give the map an intuitive look, but their complexity can increase the overall feel of clutter, and it can be more difficult to judge their size than simple geometric shapes like circles or squares, especially if they are in a congested area where individual symbols overlap. This difference is lessened if the shape is compact.
Among geometric symbols, circles have been the predominant shape since this type of thematic map was invented. Several advantages of circles over other geometric shapes have been cited, such as:

The simple shape does not attract attention itself, instead diverting attention to judging individual sizes and recognizing broad distribution patterns among circles.
When circles overlap, they are easy to distinguish.
Their compact form minimizes the overall amount of underlying map space they obscure.
They are relatively easy to scale and draw.
They are easy to combine with other visual variables to represent additional attributes, such as colors and pie charts.

However, disadvantages of circles have also been raised, especially that circles are aesthetically uninteresting, and that psychophysical studies have suggested that people are worse at judging the relative areas of circles than other shapes, especially squares. The best way to increase the reader's ability to correctly estimate the size of a circle is through effective legend design, including providing examples of different sized circles which will be shown in the map.
Three dimensional symbols, such as spheres or cubes, are sometimes used. They can add an aesthetic appeal, but they were originally designed for their function, to allow large symbols to be smaller because the value would be proportional to volume rather than area. However, it appears that most map readers will interpret a three dimensional symbol by projected area, not by volume, so they are only useful as decorative two dimensional symbols.

Isotype maps

A very different approach to proportional symbols is the isotype symbol, named after an approach to information graphics developed by the Austrian Otto Neurath in the 1930s. This uses a composite point symbol composed of a multitude of small point symbols to represent the value of the variable. The technique is most effective when the variable represents a relatively small number of distinct individuals, rather than a mass amount. Eduard Imhof argued against this technique for point locations, on the grounds that it tends to be much larger and more complex than a simple point symbol, covering more of the underlying geography; however, he found them effective on region locations, especially if the count consists of different types of individuals.