Conventional Cartographic Wisdom that I have Failed to Grasp

When I teach cartography, I am deliberate about not presenting my students with any rules. I do not want obedience to memorized maxims — instead, I simply tell them about practices that I think are good ideas, and then I offer an explanation of my reasoning. The students can choose to follow my advice, or not, based on how they feel about my rationale. It’s always been important to me to know, and to explain, why something is done a certain way.

But, there are certain cartographic conventions out there for which I don’t understand the logic. And that bothers me: I need to understand why. I do not suggest that these conventions are wrong; only that I lack a clear, intuitive rationale for following them, and so haven’t always incorporated them into my own practice. Maybe you can help explain them, or maybe you’re confused, too. I’m going out on a limb here, and basically making myself look potentially silly in public in order to dig up some clearer explanations. Let’s dive in.

1. Thematic maps should be on equal-area projections

This advice feels way too broad to me. If you were, for example, mapping population density, an equal-area projection is very sensible. When you want to show how many people there are per square kilometer, you want to make sure those square kilometers are all the same size on your map. But what about phenomena in which area isn’t a major factor? Here’s part of a map showing infrastructure: power plant capacity and fuel type, airport utilization, harbors, and undersea cables.

Now, this particular thematic map happens to be on an equal-area projection, but imagine for a moment I’d made it on a different projection, such as a conformal one. Would that be wrong? I think that many thematic datasets deal with area, and so equal-area projections will probably make sense most of the time. But presenting a hard-and-fast rule of “always put thematic maps on an equal-area projection” feels like too much to me. It’s unlikely that an equal-area projection would be a bad idea, so maybe that’s the thinking behind this convention? Is it simply a matter of “often it’s a good idea, and it’s rarely a bad one, so just do it all the time?” If so, fair enough, but it feels like it’s a broad default that discourages me from thinking about the particular needs of my dataset and symbology choices.

Again, maybe I’m missing something, and that’s what this post is here for: perhaps you can help me understand!

1a. Choropleth maps should be on equal-area projections

This is a more specific, and much more often-asserted version of item 1, so I want to give it its own section. At first it makes sense: choropleths use area-based symbology to show area-based data. Wouldn’t we want to keep those areas proportional to each other? Think for a moment, though, about a choropleth that uses a population cartogram as its base.

Here, an area’s color conveys one dataset, and its size conveys a related dataset that provides some useful context (what portion of the country’s population lives in those various income brackets). Our fallible human brains usually want us to interpret some meaning from variations in the size of areas (which is always a challenge with choropleths), so cartograms leverage that. We usually laud these heavily-distorted choropleths that are most assuredly not equal-area.

Now let’s think about non-cartogram choropleth on an equal area projection.

Here, color and size once again both convey data. But this time, size on the map simply communicates size on the earth. It doesn’t happen to provide any useful context to the main dataset about income. Is anything truly gained by ensuring that Rhode Island is seen in its proper proportion to South Dakota? The concept of “statewide average income” is already so abstracted that it doesn’t seem like readers should be thinking much about area anyway.

You can argue that “readers will assume that the size on the map relates to size on the earth, so let’s make that true to prevent mistakes.” And that’s very true, and a big problem in map interpretation generally. But it’s not specific to choropleths: that’s instead an argument for using equal-area projections for every map. And fair enough, if that’s what you believe! But, for this particular convention to make sense to me, I need to hear a rationale that is specific to the interpretation of choropleth maps.

So perhaps you can see my confusion. Why is there an emphasis on holding the areas of our enumeration units to exacting standards, if they are not communicating something that is important to understanding our primary dataset? Setting aside, of course, situations in which area is a related variable (such as a map of population density). It’s considered acceptable for me to make a basic world reference map in the Robinson projection (which is not equal-area), though it shows the size of countries inaccurately. If I instead choose to color those countries based on some statistical dataset, what has changed to make this projection no longer acceptable?

Again, I’m not saying that this convention is wrong. I’m out here admitting that I simply haven’t yet figured out a reason to adhere to it, based on the counterarguments that I’ve thought of.

2. Choropleths must show normalized data

This is, I think, another one of those situations where the convention is simply stated too broadly for my taste: it’s true most of the time, and I have no problem with that. Instead of mapping raw numbers, it’s usually wise to map some sort of rate. For example, we could tell people how many crimes happen in each state:

An old and hastily-created map that isn’t exactly up to my usual standards.

But, different states have different numbers of people, and so to put our states on equal footing and make comparisons more accurate, it would be better to show crime rate.

This happens all the time in scientific studies: researchers try to reduce the effect of confounding variables that might skew comparisons between groups. For example, in medical research, someone examining the effects of diet on cancer might mathematically account for differences in the age, sex, and occupation of people in different study groups.

I have no argument against the cartographic wisdom that says normalizing data is a good thing. Instead, I’m uncertain about the way this convention is phrased, as it does not fit my understanding of the situation. Why is it specific to choropleths; would this not be a useful convention for other sorts of symbology? If I were using proportional circles to show the number of pet cats that live in several in major cities, I feel like it would be best for my reader if I still normalized my data by population.

And yet, I was originally taught (and have since seen repeated by colleagues) that this advice is specific to choropleths. I was told, for example, that while it would be inappropriate to show a choropleth of raw, un-normalized crime data, it would be appropriate to show this same dataset with proportional circles. That’s never quite felt intuitive to me. Perhaps there’s an argument to be made about the different perceptual characteristics of these symbologies, and of how a reader interprets size changes vs. the changes in area colors? Perhaps changing symbol size, to many readers, feels like “more stuff” whereas changing colors feels like “greater concentration of stuff”? They feel different, so perhaps there’s potential there, but it feels subtle and difficult for me to express, if it’s true. Maybe you have a useful way of expressing it.

It’s also worth noting that I have made non-normalized choropleths before. Here’s one that shows the area codes of all the phone numbers in my contact list (and it’s not on an equal-area projection, either):

Those are raw counts, not normalized by the how many phone numbers are assigned to each area code). And honestly, I that feels fine to me. I could account for other variables, but I think those are less necessary here. Sometimes the raw numbers answer one question, and a normalized set of data answers another (though, in the case of “whose phone numbers does Daniel have?”, none of the answers are particularly interesting). In other cases, the raw numbers are misleading or confusing on their own. But this case doesn’t seem like one, and there are plenty of others. So, again, the convention feels overly broad to me.

Really, it seems to me that the better advice is to “account for any major confounding variables on your thematic maps.” But, that’s a little less pithy than “normalize your choropleth,” so I can see why it hasn’t caught on. Maybe one of you can suggest a more catchy phrasing.

---

Again, I offer these counter arguments not to suggest that the conventional wisdom is absolutely wrong (though conventional wisdom certainly can be). Only that I want to suggest that it’s not as obvious to me (and perhaps you?) as maybe it is to some people. I initially learned a lot of cartography as “this is the way it is,” and that never sat right with me. I have worked to learn the rationale behind a lot of the ways that maps are made, which helps me incorporate them into my own practices. But these particular bits and pieces are still stuck in the realm of “I don’t know why that’s stated as a rule.”

So if you’ve read this far, check out the comments; maybe someone has offered some interesting rationale. And maybe as time goes on I’ll edit this to reflect what I’ve learned, or refine my explanations to better convey the sticking points for me.

What about you? Are there any cartographic conventions that you’ve learned, but which you don’t see a reason to specifically follow?