5.1 Little lies

Eric Deluca and Sara Nelson

All maps inherently include white lies and subtle misrepresentations: these white lies are fundamental to the very act of mapping! Think back to our discussion of projection. Recall that only a 3-dimensional object is able to preserve both shape and area, so anytime you translate a 3-dimensional object onto a 2-dimensional surface, you must choose how you are going to distort the object.

This misrepresentation is a form of lying with projection. One example that has garnered much attention is the difference between the Mercator and Gall-Peters projections. The Mercator projection was created by Flemish cartographer Gerardus Mercator in 1569 and is used in many settings, from classrooms to Google Maps and other online services. This map was primarily made for navigation and it preserves angles and shapes well. The major drawback to this projection is that it does not preserve area, so that countries near the poles appear much larger than they should relative to countries near the equator. Greenland has only 7-percent of the land area of Africa, for example, but it appears to be just as large on the map.

In contrast, the Gall-Peters projection preserves area at the cost of shape (e.g., Greenland is significantly distorted but the size of its area is correct in comparison to Africa). Dr. Arno Peters in the 1970s argued that the Mercator projection could introduce bias into the perception of the world, given that countries in the northern latitudes were perceived as much larger than those closer to the equator. As a result, Peters argued, the Mercator projection shows a northern-centric bias and alters the world’s perception of the importance of the global south. He offered an alternative, the Peters projection, that better preserved area. It turns out that this project existed long before, having actually been invented by James Gall in the 1800s, but the projection is usually termed the Gall-Peters projection to recognize Peters’ argument.

Comparing worlds maps, ones land masses are proportional while the other is not.Lying with projections. The Mercator and Gall-Peters projections are both correct in the sense of being good projections but present the world differently. [1]

5.1.2 Symbolization

Because it is impossible to show or even to acquire all of the information that could be mapped in a particular area, symbolization is a common way in which mapmakers “lie” in order to present or highlight certain information.

Compare the Google Maps road map of Boston in the figure below to its satellite image equivalent. The image and map represent the same area, but in the road map, Google uses symbolization to tell white lies—highlighting different roadways using size and hue (federal highways in thick orange, state highways in yellow, county roads in thick white, city roads in thin white), different shapes to signify different types of highways, and different label styles for different towns and neighborhoods in the area. These forms of lying with symbolization help to fulfill one of the central purposes of Google Maps: clear presentation of information. You would be hard-pressed to use the raw imagery to do useful things like drive around Boston or find locations like Cambridge. On the other hand, the image could be more useful to make guesses about urban land cover in the Boston region or how deep the water is in the harbor.

On the left, a Google Maps view of Boston, on the right, a satellite view of Boston.

Lying with symbolization. Google Maps view of Boston and satellite view of Boston are of the same area but use symbolization differently. [2]

Cartograms are another way of lying with symbolization. Cartograms are maps that distort area or distance by substituting another thematic variable. Because of the dramatic distortions that cartograms produce, you might consider them to be telling more than white lies. However, cartograms are just different ways of symbolizing the same data in order to tell a story. The big lies that we discuss in the next section are lies that are told for very specific purposes or for eliciting particular reactions. Cartograms are considered white lies here because they are just another set of symbolization choices that affect the representation of data on your map.

The figure below is an example of a map showing the number of people and the amount of wealth per country in 2015. Note how the size of any given country is not displayed in accordance with the land mass of that country, but in fact, corresponds to the number of people living there or its total wealth. This map gives you, very quickly and effectively, a read on which countries have the most people and most money.

Two world maps color coded, one shows population by country and the other shows wealth by country.
Lying with cartograms. Population total and wealth by country in 2015. Note how the size of countries on the map is not their actual area but instead proportional to the attribute being measured, population or wealth. [3]

5.1.3 Standardization

How and whether data is standardized (standardization) also has a huge impact on the story that the map tells. The maps in the figure below represent poverty data from the 2000 US census. The top map standardizes data by the percentage of the population – the number of people living in poverty relative to the total population of that census tract. The bottom map is based on raw numbers for how many people are living in poverty in the census tract. By failing to account for poverty as a percentage of the total population, the bottom map tells a much bigger lie about poverty levels in the US.

Two maps of the United States showing poverty percentages, one more accurate than the other.

Lying with standardization. Poverty as a percentage versus poverty as a raw number. These maps represent poverty data from the 2000 US Census but differ in their standardization. [4]

5.1.4 Classification

Classification matters. Choices you make about how to classify your data can have a big impact on the story that your map tells. The maps here show how you can lie with classification. The three maps in the figure below each use the same data, the same number of classes, the same color scheme, and the same standardization, yet each tells a very different story about poverty in the US, depending upon the classification scheme. The first map classifies the data using equal interval, the second using natural breaks, and the third using a quantile scheme.

Three different maps of the United States, presenting the same data but each paints a different picture.
Lying with classification. Poverty via equal interval, natural breaks, and quantile classifications. The three maps use the
same data, the same number of classes, the same color scheme, and standardization, yet each tells a very different story about poverty in the US. [5]

The figure below shows three maps of 2000 census poverty data. Each uses a quantile classification scheme. The only difference is the number of classes. See how the number of classes impacts your perception of poverty levels in the US. Although there are some areas that demonstrate patterns of poverty across the three maps, as you increase the number of classes, you get a more nuanced picture of how poverty is distributed across the country.

Three maps of the United States, each one is more dense than the last as the classes (data range) increases.
Lying with classes. Poverty via quantile classifications with a differing number of classes. The three maps use the same data and color scheme yet tell a different story about poverty in the US. [6]

5.1.5 Aggregation, Classification, and the Ecological fallacy

Recall that data are often aggregated. They are often collected at one scale, such as the household or neighborhood, and then reported at much broader scales, such as the census tract or county. This is termed aggregating the data. While aggregation can be very helpful in terms of preserving privacy or presenting a broader and synoptic view, it can also lead to the ecological fallacy, or the assumption that a characteristic or value calculated for a group in aggregate can be applied to an individual member of that group. In other words, aggregated data makes it hard to assume or guess at the characteristics of any given individual found in that aggregated area.

Imagine you are comparing the income of two blocks, each being composed of five households. Block A has an average household income of $48,000 while Block B has an average household income of $40,000, per the figure below. In which area are you more likely to find a household with a higher income? If you chose Block A—the area with the higher average income total—then you were tricked by the ecological fallacy. In fact, there is no way to know from aggregated data alone what the situation is like for an individual within a group. The figure shows one of many possible scenarios under which four out of five households in Block B have higher incomes than households in Block A.

Shows the average income of blocks a $48,000 and b $40,000.
Ecological fallacy. Consider this scenario in which Block A has a higher aggregated average income but mostly lower individual values than Block B. [7]

Watch out for the ecological fallacy whenever you are interpreting maps, or you might come to false conclusions about the people who live in a neighborhood or other areas!

The danger of the ecological fallacy for the map reader is closely tied to the subtle ways that mapmakers can lie with aggregation, often in combination with classification. The figure below illustrates voting returns for the 2012 US presidential election. The map on the left represents counties by their majority vote in the election. Red signifies counties where a majority of residents voted for the Republican candidate, Mitt Romney; blue signifies counties with a majority vote for the Democratic candidate Barack Obama. The map on the right attempts to reveal a little more nuance in voting patterns, by using a red-purple—blue scale to indicate percentages of votes, while the one on the left is simpler and more prone to the ecological fallacy. These maps are both entirely correct. They differ in how they classify their underlying data into either two categories or by not classifying the data and instead of using hue and value to represent fine differences among counties.

Two maps of the United States, the one of the left is less accurate while the one on the right gives a true image of the 2012 elections results.
Lying with aggregation and classification. Lying, or rather telling different truths, about the United States presidential election in 2012. The map on the left shows counties by their majority vote in the election, where red means counties where a majority of residents voted for the Republican candidate and blue signifies counties voting Democrat. [8]

From your knowledge of the ecological fallacy, you know that even at the level of the county, this map does not accurately represent the party affiliation, beliefs, or voting patterns of each person in the county. The data are aggregated to the county level and are classified differently than the data in the map on the right. This sort of aggregation and classification is useful because it allows us to distinguish between voting patterns in different parts of the country—rural/urban variations, for instance. The map on the right is still lying of course—not all residents in the US voted, and those who did were not necessarily voting for the endorsed Republican or Democratic candidate—but it is trying to provide a more accurate picture of the data. Both maps lie in order to give a picture of the election outcome in particular parts of the country.

Consider the cartogram version of the election map, below. The cartogram distorts area based on county-level election returns, so counties with larger populations appear bigger. The cartogram lies by distorting area, but in some ways, it gives us a clearer picture of election results. In the standard county aggregation map above it appears that the US voted strongly Republican; but the cartogram shows that many Republican-leaning counties have relatively small populations, while counties with larger populations mainly voted for the Democratic candidate.

A cartogram map of the US elections in 2012, it is extremely distorted in an array of blue, purple and red.
Election cartogram. This cartogram of election results distorts apparent county area by the number of returns, so counties with larger populations appear bigger. [9]

5.1.6 Aggregation and Zonation

We have looked at how data are aggregated to larger areas and how this process of aggregation can affect how data are interpreted, such as causing the potential for the ecological fallacy. In addition to aggregating data, we can also zone it differently, which is another way of saying we can draw an almost infinite array of differing boundaries for any given aggregation. We often use county boundaries in our analyses, for example, but the boundaries of counties are arbitrary. They were drawn over time according to a range of different principles, such as where a river flowed or where settlement was being encouraged. Population data is often aggregated and reported by county but they could be (and often are) reported via other zonations, such as zip codes, phone-number area codes, school districts, or watershed boundaries.

Importantly, the way in which data are aggregated and where the boundaries of zones are drawn can easily change data patterns and analysis outcomes. Depending on the scale at which you look at a geographic pattern, you can derive completely different results from the exact same underlying data. This is called the modifiable areal unit problem. For example, consider the rate of a disease in a population. Individuals at specific locations become sick, but health officials often want to know the broader trends of diseases. For this reason – and to protect the privacy of patients – they may count the number of cases by block, zip code, or another zonation. But artificially breaking up space into these larger areas can change the apparent patterns of disease. The figure below illustrates this for deaths from respiratory problems in Ottawa, Canada. Each map uses the same underlying data but groups or zones cases differently: by a health department aggregation, by neighborhood, and by census tract. Each classes spatial units into quartiles, or in other words, divides the areas into four equal groups by how many people are dying in those areas. Note that these three maps all use the same exact underlying data and are just using different ways of zoning the groups. Nonetheless, these maps look very different, highlighting the challenge of the modifiable areal unit problem.

Three maps calculating disease spread using the same data, however each map looks very different.
Health and zonation. These maps all show data on where people die from respiratory problems in Ottawa, Canada. Each map uses the same underlying data but groups or zones cases differently. Each categorizes spatial units into quartiles. [10]

In addition to zoning, the modifiable areal unit problem can result from aggregation. Consider the figures below of solar potential in the lower 48 United States. Solar potential refers to the suitability of a particular place to develop solar power. These data are from the National Renewable Energy Laboratory and these maps were created by Anthony Robinson (2010). The first map shows the average annual solar potential by state. In other words, these data are aggregated by state. You can see right away that some states look better than others.

A map of the U.S., aggregated by state, showing sola potential.
Solar potential by state. Annual solar potential by state, which measures the suitability of a particular place to develop solar power. [11]

The same underlying data aggregated to counties instead makes it look like a lot of states that were shown in one color at the state level actually include several categories of solar potential when you look at the data by county.

A map of the U.S., aggregated by county, showing sola potential.
Solar potential by county. Annual solar potential by county, which measures the suitability of a particular place to develop solar power. [12]

The third map shows the original underlying data on which the other two maps were based. These original data calculate solar potential in 10-kilometer grid cells. You can see how the state and county boundaries compare to the raw data and how aggregation changes the apparent distribution of phenomena.

A map of the U.S., aggregated by 10 kilometer grid cells, showing solar potential.
Solar potential by grid cell. Annual solar potential given by the original data, which used a 10km grid cell. [13]

 


  1. CC BY-SA 3.0. Adapted from Daniel R. Strebe - Own work.nhttps://commons.wikimedia.org/w/index.php?curid=16115307 https://commons.wikimedia.org/w/index.php?curid=16115242.
  2. CC BY-NC-SA 4.0. Steven M. Manson, 2015
  3. CC BY-NC-ND 4.0. Benjamin D. Hennig Worldmapper.org
  4. CC BY-NC-SA 4.0. Steven Manson 2005 Data from SocialExplorer and US Census
  5. CC BY-NC-SA 4.0. Steven Manson 2005. Data from SocialExplorer and US Census
  6. CC BY-NC-SA 4.0. Steven Manson 2005 Data from SocialExplorer and US Census
  7. CC BY-NC-SA 4.0. Sara Nelson 2015
  8. CC BY 2.0. M.E.J. Newman. 2012 Maps of the 2012 US presidential election results. http://www-personal.umich.edu/~mejn/election/2012/
  9. CC BY 2.0. M.E.J. Newman. 2012 Maps of the 2012 US presidential election results. http://www-personal.umich.edu/~mejn/election/2012/
  10. CC BY 2.0. Parenteau, M. P., & Sawada, M. C. (2011). The modifiable areal unit problem (MAUP) in the relationship between exposure to NO 2 and respiratory health. International journal of health geographics, 10(1), 58. https://ij-healthgeographics.biomedcentral.com/articles/10.1186/1476-072X-10-58
  11. CC BY-SA 3.0. Adapted from Anthony C. Robinson. Maps and the Geospatial Revolution https://www.e-education.psu.edu/maps/l4_p4.html
  12. CC BY-SA 3.0. Adapted from Anthony C. Robinson Maps and the Geospatial Revolution. https://www.e-education.psu.edu/maps/l4_p4.html
  13. CC BY-SA 3.0. Adapted from Anthony C. Robinson. Maps and the Geospatial Revolution. https://www.e-education.psu.edu/maps/l4_p4.html
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5.1 Little lies Copyright © 2020 by Eric Deluca and Sara Nelson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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