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Mapping Rates

A recurring question that we are asked is: can you make a map of rates? There are several reasons why people are interested in mapping rates, which are detailed below. We are grateful to viewers of Worldmapper for provoking this discussion. The reasons why on this project we have decided not to map rates are below.

Comment 1. The statistics that you show are not using the most useful units. I would prefer them to be per person or per land area. Raw counts are hugely skewed by the territory or population size. For example, on the rainfall map you cannot find the wettest place, as total rainfall is shown. So large dry territories can be larger than small wet territories. Similarly, a population density map would be useful.

Response 1. The maps are best understood as pie charts where the segment of the pie is reshaped to look like a territory.  For example the area of a territory on a population map is adjusted according to the proportion of the world total of a variable that is found there.  Just as a pie chart would.  As such, we can only map counts or totals.  We cannot map rates because they are not additive, that is to say that they do not add up to a meaningful total.  To return to the pie chart analogy, you would not draw a pie chart of population density but one of total population.

Of course rates cartograms would show a very different pattern. One way around this is to read map in conjunction with the land area or population map. Another way is to consult the rates data, found in the excel sheets available on the website.

Comment 2. You could conceptualise these maps as being equivalent to a simple bar chart (rather than pie chart). Instead of rectangular bars positioned along a straight line axis where bar height represents the value, we have variable size blobs distributed across a plane. Thus the area of the blob can represent a rate, if there is no presumption that adjacent blobs can be summed to give the equivalent value for the combined territories. If the map shows a rate then I don't think viewers would expect to be able to "add up" in their minds the areas of adjacent countries to get an overall figure. If the values are normalised so that the sizes are not all too big or all too small this should allow meaningful analysis. On the rainfall map, wetter territories would be larger, and drier territories smaller,

Response 2. This is true, and it would be possible to do (although people do tend to sum, albeit subconsciously). There are two reasons not to. Firstly, mapping rates would privilege territory boundaries as a grid through which to understand these variables far more than mapping totals does. This is because whilst a map of totals shows the distribution of a variable in a continuous manner; if two territories merged to become one, the shape of the map would not change greatly. However, on a rates map if two territories merged the total area allocated to those two territories is likely to reduce. As such the area allocated is heavily dependent upon boundaries which are often relatively recent constructions.

The second concern is that showing two very different methods of mapping could confuse people. Whether we are showing rates or totals greatly affects the shape of a map and how it should be read. One of the aims of this project is to make world data widely accessible to a range of people, in a legible form. Mapping rates could detract from this.

Comment 3. It would be fairer to show the carbon emissions on a per person basis because every citizen of the world should have an equal right to the same sized carbon footprint. Mapping rates would allow us to compare people.

Response 3. Fairness is an important consideration when developing a world social atlas. This project hopes to represent people more fairly that many earlier maps have done, by showing many aspects of people’s lives. Whilst maps of rates are informative of territory averages, we argue that it is often fairer to show totals than rates. Working with the example of the population cartogram: should the 200 hectare territory of Monaco with 34 thousand people living there be larger on a population map than China with 1.3 billion people living in 933 million hectares? Monaco would be 126 times larger than China on a population density map, despite the Monaco population being just 0.003% of China’s. Thus the map could become heavily distorted by places where a very small proportion of the world’s population lives. To return to fairness, it is more fair to give each person an equal area on this map. A population-scaled map could be coloured by population density – but that is another project!

The second point with regards to fair representations was introduced in Comment 2, where it is noted that rates maps over-emphasize territory boundaries.

Comment 4. Here are suggestions of some other map types:

1. Territory area as proportional to the variable multiplied by the original territory land area. Anomalies could be recognized by distortions from the "normal" look, which would be much easier to read.

2. Area is proportional to the variable multiplied by the land area of the territory, divided by the population living there. If the population density map still looked like a “normal” map, this would mean that everywhere population density is the same.

Response 4. We have experimented with maps of the kind you describe. For some of the data sets they work well, while for others they don't. These rely strongly on the viewer being familiar with the true sizes of the countries, so that they can tell whether the country is bigger than normal (higher than average income) or smaller (lower than average).

Overall, we think it's worth looking at a variety of visualizations to find ones that best communicate the content of a particular data set, and we continue to experiment with different types of maps. For the moment, however, we have only the simple area cartograms on the web site. Perhaps we will put up some of the others at some point.

Further, one element of the Worldmapper project is to challenge the primacy of land area maps. Thus to make maps that refer back to a form that we question when this can also add confusion is of questionable advantage.

Many thanks for Richard Blundell, Santanu Pal and Andreas Schilling for their questions and comments. These have formed the basis for this section.



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