Data Visualization #3–Cartograms as an alternative to standard area-based electoral maps

In my first post of this series I explained at length why basic geographically-based electoral maps are not very good at conveying the phenomena of interest (see that post for more detail), and alluded to the increased use of political geographers, and political scientists, of alternative methods of “mapping” the required information that were more clear about the message(s) contained in the data.

Let’s examine this further using the map above. This map shows the results of the Canadian federal (national) election of October 2019.The respective proportions of total area “won” by each political party as depicted in the map above are not easily translated into either the relative vote share of the parties, or the relative number of seats won. Someone ignorant about Canadian federal politics would see a relatively similar total amount of red, blue, and orange, and assume that these parties had relatively equal support across the country. The sizes (land mass), and populations of, federal electoral districts in Canada vary drastically and, as a result, these maps are not a good gauge of voter support for political parties.

Since this problem is widespread political scientists, and political geographers, have attempted to find solutions to this problem. One increasingly-common approach has been to use what are called cartograms. Cartograms are maps in which the elements (in this case, electoral districts) are usually transformed in such as way as to maintain their connections to neighbours (contiguous cartograms), but to either increase or decrease the area of the specific electoral district in order to match it to a common variable. A variable often used in the transformation of electoral maps is population size. Thus, in a completed cartogram, the size of the electoral districts is not the actual land mass of the electoral district, but is proportional to the population of the electoral district (sometimes the number of voters, or the size of the electorate is used instead of population). It’s no surprise, then, that cartograms are also called “value-by-area” maps.

Cartograms are used by geographers and social scientists to depict a wide variety of phenomena. Here are some examples. The first one is a global cartogram for which the size of the area in each country is equivalent to total public health spending by that country. We can easily see that most of the world’s spending on public health occurs in the rich countries of the global north.

Here’s one more, depicting the global share of organic agriculture, by country.

Below, I have created a cartogram that has transformed the standard electoral map of the 2019 Canadian federal election into one in which the size of the electoral districts is mostly proportional to their populations. By “mostly” I mean that they’re not perfectly proportional, since the difference in sizes between the largest and smallest districts is so large the algorithm eventually stabilizes without creating completely equal-sized electoral districts.

This map more accurately conveys the nature of political partisan support (at least as it relates to the winning of electoral districts) across the country during the 2019 election, and provides visual evidence for the reality of an election in which the Liberal Party (red) won a plurality of the seats in the federal parliament (House of Commons). Because urban districts are much smaller than rural districts, the strength of Liberal Party support in Canada’s two largest cities–Toronto and Montreal–is obfuscated by the traditional area-based electoral map, but becomes evident in this cartogram.

The next map in this series will analyze another approach to geographically-based electoral maps–the hexagon map.

Here’s the R code for the cartogram above. Here, the original R-spatial data object–can_sf–is the base for the calculation of the cartogram data.

## Here is the code to generate the cartogram object:

can_carto_sf = cartogram_cont(can_sf, "Population_2016", itermax=50)

## Now, the map, using ggplot2

gg.can.can.carto <- ggplot(data = can_carto_sf) +
  geom_sf(aes(fill = partywinner_2019), col="black", lwd=0.075) + 
  scale_fill_manual(values=c("#33B2CC","#1A4782","#3D9B35","#D71920","#F37021","#2B2D2F"),name ="Party (2019)") +
  labs(title = "Cartogram of Canadian Federal Election Results \u2013 October 2019",
       subtitle = "(by Political Party and Electoral District)") +
  theme_void() + 
        legend.text = element_text(size = 16),
        plot.title = element_text(hjust = 0.5, size=20, vjust=2, face="bold"),
        plot.subtitle = element_text(hjust=0.5, size=18, vjust=2, face="bold"),
        legend.position = "bottom",
        plot.margin = margin(0.5, 0.5, 0.5, 0.5, "cm"), = margin(0,0,30,0),
        legend.key.size = unit(0.75, "cm"),
        panel.border = element_rect(colour = "black", fill=NA, size=1.5))

Data Visualization #2–Animations aid in Conveying Change

The first entry in my 30-day (it will actually be 30 posts over about 2 months) data visualization challenge argued that geographically-based electoral maps have many drawbacks as data visualization techniques. I demonstrated by using the results from the 2017 and 2020 British Columbia (BC) provincial elections as supporting evidence.

Although there were some significant political changes over the course of the two elections, these were poorly-represented by these maps. Only when we zoomed into the population centres of southwestern BC were we able to partially convey the changes that had occurred. We could have made our effort to convey the underlying movement in political party support between 2017 and 2020 a bit more obvious by using animated maps, rather than the static ones that were used.

When it comes to representing change over time, animated graphs can be very useful (as long as they aren’t too complicated and busy) and are advantageous to static maps.

Below we can find the maps in the original animated to more clearly show the changes over time. Here’s the map of the whole province:

The change between 2017 and 2020 is made clear by a jarring change in the map, where a bit more NDP-orange shows up, replacing the BCLP-blue (see the previous post for descriptions of the two parties). Otherwise, there doesn’t seem to be much change in the province overall.

We know, however, that the drastic changes that took place did so in the very tiniest southwestern corner of the BC mainland. Let’s zoom in there to have a look.

We can now more clearly see the change in results (in terms of electoral districts won) between 2017 and 2020 in this populous region. Not only did the NDP (orange) win many seats in the eastern Vancouver suburbs that had not only been won by the BCLP in 2017 but had been a bastion of support for the right-wing vote over many decades, but the NDP candidate in the Victoria-area district of Oak Bay-Gordon Head won a seat that had previously been held by the former leader of BC Green Party, Andrew Weaver (it’s the small piece of green, that changes to orange, in the eastern part of the lower orange horizontal band on the lower-left of the map) . Are these changes the harbinger of a sea-change in BC provincial politics, or are they just an anomalous blip?

Going back to my original point about these types of maps being poor representations of the underlying change in voters’ preferences, we don’t know much about the level of support for the respective parties in any of these electoral districts. All that we do know, based on the “first-past-the-post” electoral system used by BC at the provincial level, is the party whose candidate finished with the most votes in each of these electoral districts. We don’t know if a district newly-won by the NDP candidate was by one vote, or by 10,000 votes. In future posts, I’ll present graphs that will allow us to answer this question visually.

Our next posts will focus on alternatives to the basic electoral geographic maps that we’ve used in these first two posts.

Data Visualization #1–Electoral Results Map

The data visualization with which I begin my 30-day challenge is a standard electoral map of the recently-completed British Columbia provincial election, the result of which is a solid (57 of 87 seats) majority government for the New Democratic Party, led by Premier John Horgan.

It’s a bit ironic that I begin with this type of map since, for a few reasons, I consider them to be poor representations of data. First, because electoral districts are mapped on the basis of territory (geography) they misrepresent and distort what they are purportedly meant to gauge–electoral support (by actual voters, not acreage) for political parties.

Though there are other pitfalls with basic electoral maps I’ll highlight what I believe to be the second major issue with them. They take what is a multinomial concept–voter support for each of a number of political parties in a specific electoral district–and summarize them into a single data point–which of the many parties in that electoral district has “won” that district. Most of these maps provide no information about either a) the relative size of the winning party’s victory in that district, or b) how many other parties competed in that district and how well each of these parties did in that district.

Although the standard electoral map provides some basic electoral information about the electoral outcome (and it is undeniable that in terms of determining who wins and runs government, it is the single most important piece of information), they are “information-poor” and in future posts I’ll show how researchers have tried to make their electoral maps more information-rich.

But, first, here are some standard electoral maps for the last two provincial elections in British Columbia (BC)–May 2017 and October 2020. Like many jurisdictions in North America, BC is comprised of relatively densely-populated urban areas–the Lower Mainland and southern Vancouver Island–combined with sparsely-populated hinterlands–forests, mountains, and deserts. Moreover, there is a strong partisan split between these areas–with the conservative BC Liberal Party (BCLP–the story of why the provincial Liberal Party in BC is actually the home of BC’s conservatives is too long for this post) dominating in the hinterlands while the left-centre New Democratic Party (NDP) generally runs more strongly in the urban southeast of the province. In Canada, electoral districts are often referred to as “ridings”, or “constituencies.”

If one were completely ignorant about BC’s provincial politics one would assume, simply from a quick perusal of the map above, that the “blue” party–the BC Liberal Party–was the dominant party in BC. In addition, it would seem that there was very little change in partisan support and electoral outcomes across the electoral districts over the course of the two elections. In fact, the BCLP lost 15 districts, all of which were won by the NDP. (The Green Party lost one of the districts it had won to the NDP as well, for a total NDP gain of 16 districts (seats on the provincial legislature) between 2017 and 2020. This factual story of a substantial increase in NDP seats in the legislature is poorly conveyed by the maps above because the maps match partisanship to area and not to voters.

To repeat, in future posts I will demonstrate some methods researchers have used to mitigate the problem of area-based electoral maps, but for now I’ll show that once we zoom into the southwest corner of the province (where most of the population resides) a simple electoral map does do a better job of conveying the change in electoral fortunes of the BCLP and NDP over the last two elections This is because there is a stronger link between area and population (voters) in these districts than in BC as a whole.

You can more easily see the orange NDP wave overtaking the population centres of the Lower Mainland (greater Vancouver area–upper left part of each map) and, to a lesser extent, southern Vancouver Island. Data visualization #2 will demonstrate how to create animated maps of the above, which more appropriately convey the nature of the change in each of the electoral districts over the two elections.

Here’s the R code that I used to create the two images in my post, using the ggplot2 package.

## Once you have created a sf_object in R (which I have named bc_final_sf, the following commands will create the image above.

## First plot--2017
gg.ed.1 <- ggplot(bc_final_sf) +
  geom_sf(aes(fill = Winner_2017), col="black", lwd=0.025) + 
  scale_fill_manual(values=c("#295AB1","#26B44F","#ED8200")) +
  labs(title = "May 2017") +
  theme_void() + 
        plot.title = element_text(hjust = 0.5, size=12, face="bold"),
        legend.position = "none")

## Second plot--2020
gg.ed.2 <- ggplot(bc_final_final) +
  geom_sf(aes(fill = Winner_2020), col="black", lwd=0.025) + 
  scale_fill_manual(values=c("#295AB1","#26B44F","#ED8200")) +
  labs(title = "October 2020") +
  theme_void() +
        plot.title = element_text(hjust = 0.5, size=12, face="bold"),
        legend.position = "bottom")

## Combine the plots and do some annotation <- gg.ed.1 + gg.ed.2 & theme(legend.position = "bottom") <- + plot_layout(guides = "collect") + 
  title = "British Columbia Election Results \u2013 by Riding",
  theme = theme(plot.title = element_text(size = 16, hjust=0.5, face="bold"))
  )    # to view the first image above

## For the maps of the Lower Mainland and southern Vancouver Island, the only difference is that we add the following line to each of the individual maps:

coord_sf(xlim = c(1140000,1300000), ylim = c(350000, 500000))  

## so, we get 

gg.ed.lmsvi.1 <- ggplot(bc_final_final) +
  geom_sf(aes(fill = Winner_2017), col="black", lwd=0.075) + 
  coord_sf(xlim = c(1140000,1300000), ylim = c(350000, 500000)) + 
  scale_fill_manual(values=c("#295AB1","#26B44F","#ED8200")) +
  labs(title = "May 2017") +
  theme_void() + 
        plot.title = element_text(hjust = 0.5, size=10, vjust=3),  
        legend.position = "none")

‘Controlling’ for confounding variables graphically

As we’ve learned (ad nauseum) basing causal claims on a simple bivariate relationship is fraught with potential roadblocks. Even though there may be a strong, and statistically significant, relationship between an independent and dependent variable, if we haven’t controlled for potentially confounding variables, we can not state with any measure of confidence that the putative relationship between the IV and DV is causal. We should always statistically control for any (and all) potentially confounding variables.

Additionally, it is often desirable to dig deeper into the data and find out if the units-of-analysis are fundamentally different on the basis of some other variable. Below you may find two plots–each of which shows the relationship between margin of victory and electoral turnout (by electoral district) for the 2017 British Columbia provincial election. The first graph plots a simple bivariate relationship, while the second plot breaks that initial relationship down by political party (which party won the electoral district). It could conceivably be the case that the relationship between turnout and margin of victory varies across the values of political party. That is, the relationship may hold in those electoral districts where party A won, but not hold in those in which party B won.

We can see here that there is little evidence to suggest a difference in the relationship based on which party won the electoral district. Can you think of another `third’ variable that may cause the relationship between turnout and margin of victory to be systematically different across different values of that variable? What about rural-versus-urban electoral districts?

Here are the plots: