A new kind of election map

by Andy Woodruff on November 8, 2008

Update, Dec. 22: A few variations of the map technique are posted here.

2008 election results with population

We spent some of our spare time last week exploring data from the 2008 presidential election and thinking of some interesting ways to visualize it. Above is one map we put together.

One thing we sought to do was present an alternative to cartograms, which are becoming increasingly popular as post-election maps. Cartograms are typically offered as an alternative to the common red and blue maps showing which states or counties were won by each candidate, wherein one color (presently, red) dominates the map because of the more expansive—but less populated—area won by one candidate. Election cartograms such as the popular set by Mark Newman distort areas to reflect population and give a more accurate picture of the actual distribution of votes. A drawback of cartograms that we’re very aware of, however, is that in distorting sizes, shapes and positions are necessarily distorted, sometimes to the point of making the geography virtually unrecognizable.

Our map is one suggestion of a different way to weight election results on the map while maintaining correct geography. What we’ve done is start with a simple red and blue map showing which candidate (Republican and Democrat, respectively) won each county in the lower 48 states. Then, to account for the population of those counties (or, the approximate distribution of votes), we’ve adjusted opacity. High-population counties are fully opaque while those with the lowest population are nearly invisible. Against the black background, the highest concentrations of votes stand out as the brightest.

We’ll let viewers be the judge of its cartographic effectiveness, but we hope you’ll at least agree that it looks pretty cool!

Click on the image at the top of the post to view a larger version, or see it in a Zoomify viewer, or download the full size (suitable for printing).

There are 24 comments in this article:

  1. November 10, 2008Anthony Robinson says:

    Beautiful map, and clever idea for symbolization. Your other work on tag clouds for campaign speeches is also way cool.

  2. November 10, 2008An intensity cartogram of 2008 US presidential election at Resilience Science says:

    […] From Axis Maps […]

  3. November 10, 2008Celebrity Paycut - Encouraging celebrities all over the world to save us from global warming by taking a paycut. says:

    […] From Axis Maps […]

  4. November 11, 2008Tom Albright says:

    Cool! I wonder if it might be more appropriate to link opacity to population density rather than raw population?

  5. November 11, 2008andy says:

    We did throw one together with population density, too. I think which is superior may be debatable, as they both have their merits and drawbacks when it comes to being understandable and presenting an accurate picture. With population density it certainly looks good visually, though:
    Election results with population density

  6. November 13, 2008Alternative to Cartograms Using Transparency | FlowingData says:

    […] is near impossible. They’re more of a pretty picture than an analytical tool. Axis Maps proposes an alternative to cartograms, and the example of course uses presidential election […]

  7. November 13, 2008Jon Peltier says:

    I agree that the shape distortion in a cartogram takes a bit to get used to. You sure couldn’t use one for navigation.

    But that’s not their purpose. They are intended to show information on a different demographic basis than merely geographic area. For this I find them rather effective.

    The intensity based system is also interesting, but I feel it’s less effective. For one thing, using colors, or shades of colors, is less effective than most other means of representing quantitative data. Red and blue are clear, since the electoral college makes presidential elections an all-or-nothing proposition.

  8. November 13, 2008andy says:


    Concerning the purpose of a cartogram, certainly we can’t expect to understand accurate spatial relationships from it. But I think the purpose of a cartogram has got to be a bit more than just showing data on a different basis, or else you’re probably better off with some sort of chart. If we complain about cartograms here, we’re mostly talking about a certain type of cartogram, namely those using the Gastner and Newman method because those maps by Mark Newman are probably the most widely-circulated election cartograms. (I complained about these recently on my personal site.) Some cartograms are better than others at showing the data while maintaining reasonably understandable geography.

    It’s somewhat a matter of taste and other personal factors, of course, but for simply ordinal comparisons I’d take this intensity map over a cartogram. Brightness is relatively easier to compare, as opposed to area, which I believe people are generally known to be pretty terrible at estimating. Different hues make it a bit difficult, of course, but that’s the reason we chose to only use two (red and blue) rather than the purple color scheme you sometimes see.

    In the end, either map—this or a cartogram—is really going to tell you little more than things like “there’s more blue in this area than that area.” It’s not easy to extract a precise quantitative value in either case.

  9. November 13, 2008Jon Peltier says:

    Andy –

    I am not saying I don’t appreciate your attempts. It’s an intriguing approach, and maybe I need to think on it. I don’t find it easy to compare geographically separated brightnesses. Unless the two regions are abutting, the surrounding shades affect one’s perception of the particular region.

    Seeing a different density of color makes me think at first of density of population, or perhaps strength of the vote in favor on one or the other candidate. Using the brightness to indicate population goes one step beyond, integrating the area I can see with the population density. This is not at all a fault of your approach, it is merely the interpretation which has been ingrained by the thousands of maps which precede yours.

    You make two points that I can agree with completely (paraphrased):

    1. It’s a matter of taste and other personal factors.

    2. In the end, neither map is really going to provide observations more qualitative that “there’s more blue in this area than that area.”

  10. November 13, 2008bill raynor says:

    On my monitor the graphic is essentially black. Not much differentiation

  11. November 13, 2008Robert Roth says:

    I think this is a really intriguing solution to Dorling’s mantra of mapping natural/physical phenomena in natural/physical spaces and human/social phenomena in human/social spaces. While cartograms may work when the number of enumeration units is small and their shapes/topological relations are well known, I can assure you that they do not work at the US county-level.

    I can think of two ways in which this view could be extremely useful for map-centered exploration and hypothesis generation:

    (1) Visualizing a dataset in conjunction with its certainty/quality (here opacity=certainty). Unlike almost all other representations techniques for uncertainty, this would actually emphasize areas that are more certain. The eye would be drawn to locations of high certainty, with the darkening effect disguising those values that are of low certainty (and so therefore probably should not be seen).

    (2) The domain of epidemiology, where the nature of rare diseases provide unreliable rates in areas of small populations (opacity=population or SMR significance). This technique could allow epidemiologists and health service managers a representation that stresses high- and low-risk rates that are known to be reliable.

    Simple and effective.

  12. November 14, 2008An Undistorted Election Results Map | PTS Blog says:

    […] an approach Axis Maps has developed which does not distort the geographical geometry of the map, in A new kind of election map and also in I hate your favorite election map in his personal blog. This visualization approach […]

  13. November 14, 2008Jon Peltier says:

    As I ruminate on these maps and compare them to the cartograms they would supplant, I am gaining a better ability to internalize their data.

    Take the ink used to color the cartogram-distorted state, and spread it (dilute it?) over the state’s undistorted area. Okay, I have the paradigm in my head now, and the maps work.

    I can think of two improvements, or at least two variations I’d like to see that would aid in comprehension. 1 – use a white background instead of black, and 2 – show state boundaries to give some context to the maps drawn at county level.

  14. November 14, 2008Stephen Mercer says:

    The most useful maps would be ones that showed “this portion of people in this region voted for Obama and this other portion in this same region voted for McCain”. I keep visualizing maps like a Google Earth map of a city, with very tall sky scrapers around Los Angeles (high population density) and some flat houses out in Montana. I think seeing a blue tower next to a red tower would let you see simultaneously who won the county and where the geographic regions most worth targeting are.

    I’d also like to see you try to put together a topographical map of the United States, where regions that voted for Obama are represented as peaks and regions that voted for McCain are represented as valleys, with ties as sea level. The further from sea level, the more people voted for that candidate in that region. That way if a region like Los Angeles was essentially a dead tie, it would remain flat, despite its gigantic population. But if it all voted in one direction, it would tower above the rest of the map. The value of this map would be that it would show who would’ve won a popular election, where are the big geographical social divides (there would be lots of topo lines between Travis and Williamson counties in Texas, for example), and it shows the regions most worth targeting — the flat areas. Areas that are closest to ties are the most ripe for campaigning because they can A) be swung the other direction most easily which matters in our winner-take-all system and B) people tend to vote in groups and a tie means no strong consensus has been established or that there are two disjoint groups in the area. If it is the former then it is an area worth targeting for campaigns.

  15. November 14, 2008andy says:

    Stephen, the topographic map would be an interesting approach, though I’m skeptical of how effective 3D (or I guess we technically call that 2.5-dimensional) maps are for something like that. We don’t really have the free time right now to work on something like that, or else I’d at least try to make some isolines.

    I don’t recall seeing maps exactly like you describe, where they actually go below “sea level” in addition to above, but in general it made me think of this population map from Time. A couple of 3D election examples I’ve seen are by Robert Vanderbei (2004) and the Washington Post. Usually it’s counties protruding into the air, but it would be interesting to see it as a smooth surface, possibly with a finer level of detail.

  16. November 16, 2008Blah! › Analyzing the Election says:

    […] Another population analysis where the brightness of each county is determined by population. […]

  17. November 19, 2008Zach says:

    Stephen and Andy,

    While it’s not exactly what you described, we have attempted some 3D (or 2.5-dimensional) maps that may be of interest.


    As with the Axis election map experiment, which I like btw, we’ll leave the assessment of the analytical merit up to you. In general I find that I learn most by seeing different perspectives and by sorting data multiple ways.

  18. November 22, 2008James Wheeler says:

    I suggest brightness mapped to population density, and saturation mapped to margin. This would yield gray areas on the map where the vote is near 50-50.

  19. December 4, 2008miked98 says:

    Very cool map. In theory, of course, you could use color to encode up to three dimensions (RGB, HSV, Lab, depending on your choice of basis vectors in the color space) — but in practice even two is tricky.

    Among the challenges in the HSV space: (i) hue is not independent of value (yellows are brighter than reds), and (ii) as you reduce brightness, your range of expression narrows (the narrowing of the color cone).

    Finally, HSV is not a perceptually uniform color space: which is to say, we are much better at detecting differences in reds than in blues (which is visually apparent in your map).

    Ross Ihaka (one of the originators of the R language) has several excellent lectures on color spaces at: http://www.stat.auckland.ac.nz/~ihaka/120/ – and recently came out with an R package — colorspace — with some useful features.

    And of course, Colin Ware’s book ”Information Visualization” has a great chapter on color.

  20. January 19, 2009indiemaps.com/blog » political cartography: voting with our pocketbooks says:

    […] election maps adapt the technique of encoding uncertainty information in transparency initially suggested by Alan […]

  21. April 1, 2010What I did to your data « Geography 970 says:

    […] possible solution, which I have not looked at yet: Value by alpha or something like that. Go bivariate — one variable is TPP, the other is an indicator of data […]

  22. June 14, 2010Value-by-alpha maps | Visualization for Discovery says:

    […] are ugly and unreadable election results cartograms, I worked with my Axis Maps dudes to create a 2008 U.S. election map that used transparency rather than size to vary the visual impact of map units, thinking that […]

  23. June 16, 2010Flavius says:


    I am not an expert on maps or anything, I just like maps and occasionally create maps as a hobby.

    I must say that the mapping technique (Value-by-Alpha Map) that I read about here is very interesting.

    However I would like to point out one suggestion. The map (2008 US elections) shows only 2 aspects out of 3, which I think are the most important here.

    The aspects shown on the map are obviously the winning party (represented by red or blue) and the population of the county (represented by the brightness of the color).

    A 3rd, and important aspect which I think is omitted is the amount of votes for each party.
    I mean, it’s not the same to label as blue or red a 51% vs 49% win and also a 95% vs 5% win.

    This aspect could be shown on the map by gradients between 100 percent blue and 100 percent red instead of just plain red or blue.

    For example if blue had 75% and red 25% then it would be a shade of purple, closer to blue than to red. This color would then be affected by the population layer, which would change its brightness.

    It would be interesting to see if such a map is easier to read and understand or it’s just too cluttered and therefore hard to read.

    Of course there might be other factors, such as only a fraction of the population of a county voted, which might be taken into account.

    What do you think?

  24. October 24, 2011Isarithmic Maps of Public Opinion Data « David B. Sparks says:

    […] scale to encode mean values, and a transparency/alpha parameter to encode local density (similar to this approach for choropleth maps). Thus, in the northwestern U.S., from which relatively few responses were […]