# Community Demographics and the 2012 Presidential Election

Earlier this month I was fighting a pretty bad cold. While I probably should have been doing “real” work during the sinusy waking hours at home, I decided instead to finish season two of The Walking Dead and scratch an itch regarding the 2012 presidential election. I feel like I’ve seen some sloppy journalism and “data porn” floating around in the wake of the election: simple mash-ups of data and ill-drawn conclusions about how race, poverty, religion, and historical baggage (e.g., slavery) influenced the vote.

So I threw together some data, too, to try and understand these thing for myself (and you, if you care). In short, I built a statistical computer model that predicts the vote distribution between Obama and Romney at the U.S. county level, using some demographic info about each county as evidence. Here is a quick summary of what the data seems to say:

• Obama-leaning communities tend to: live in more multi-unit housing, have more businesses owned by women and minorities, be more educated, and have an economy driven by manufacturing. (Some weak associations include: population density, retail or food & service economies, and percentage speaking a language other than English at home).
• Romney-leaning communities tend to: be more White or Hispanic, have more children, and own their own homes. (Some weak associations include: a wholesale-trade economy, percent of residents who were foreign-born, and whether the county was part of a former slave state or territory).
• Apparently irrelevant features include: income level or poverty rate, household size, and presence of a voter ID law.

Juicy details below. Note that these findings are correlations, and correlation does not imply causality. Also, these are results for counties, not individuals. For example, the percent of the population under 18 years of age is a predictive feature of pro-Romney counties. Clearly, these children were not voting for Romney (they are too young!), so it must have been the adults in counties with more children. We should be similarly cautious about drawing hasty conclusions about people described by other demographic features. (There is an interesting result regarding Hispanic populations that I discuss below.) Sometimes such conclusions are reasonable, but you have to be careful, and what sets my little study apart from most of the mash-ups I have seen is that these different demographic features are all taken into account. In other words, we’re considering the role of, say, voter ID laws in the context of everything else.

Before we dive in, a caveat: I am not a political scientist. I am a computer scientist with a background in machine learning and natural language processing. I am learning more social science, but my methods and interpretations do not benefit from a ton of social theory or training (yet).

## The Data Set

The core of the data is a mash-up of two sources: county-level election results taken from this Google Fusion table made available by The Guardian newspaper on November 7, 2012, and U.S. Census data downloaded from the State & County QuickFacts repository. The latter represents most of the demographic features I used. I only focused on Obama vs. Romney and ignored third-party candidates, as there were simply too few votes for a meaningful analysis. Besides, I didn’t study up on the other candidates’ positions, so I wouldn’t even be sure how to interpret the results.

For each county I a few additional features to test two hypotheses. First, there has been some speculation that voter ID laws hurt President Obama in some way. To test this, I added binary variables with a value of one to counties in states that (1) required photo ID, (2) requested photo ID, or (3) required non-photo ID. Second, this juxtaposition circulated widely on the Interwebs, comparing an 1860 map of free vs. slave territories to the 2012 election results; the suggestion being that regions where slavery was legal back then are anti-Obama today. To test this, I added a binary variable with value of one if the county was part of an 1860 slave region, and zero otherwise.

In summary, the data set consists of 3,077 counties with both vote (outcome) and demographic (evidence) information, and there are 55 demographic variables used to try and predict each county’s vote distribution.

## The Model

To my non-machine-learning friends: I’ve tried to write this section clearly with you in mind, but it uses a little pro-level math jargon and notation. I won’t be offended if you just skip to the figures and such below.

The model is a kind of logistic regression (LR), which is a pretty common method for observational studies in social science. That is, I make the simple assumption that each feature (“percent under age 18,” “percent in poverty,” etc.) makes an additive contribution to whether the county as a whole swings toward Obama vs. Romney. For the equation-lovers out there, the predicted proportion of votes that go to Obama $\tilde{p}_\beta(o|\mathbf{c})$ is given by:

$\tilde{p}_\beta(o|\mathbf{c}) = f(-\sum_k \beta_k \times \mathbf{c}_k)$

where $\beta$ is a vector of model weights, $\mathbf{c}$ is a vector of demographic features for a particular county, and $f(\cdot)$ is the logistic function. So if $\mathbf{c}_k$ denotes the “percent in poverty,” $\beta_k$ is the corresponding weight for that feature: positive values are Obama-leaning, and negative values are Romney-leaning. Multiply these together, add up the products for all demographic features/weights, shove it through $f(\cdot)$, and out comes the predicted proportion of votes that go to Obama. The trick is to pick the right weights in $\beta$ to make accurate predictions and understand how each of these demographics may affect voting habits.

There are a few differences between the way I estimate these weights and a standard LR analysis. First, one usually predicts a true/false variable (like “did Obama get the most votes?”), and picks weights that minimize a loss function $\ell(\beta)$ like the “log-loss” of the actual observed true/false outcomes. With this data set, though, the outcomes are not true/false but distributions (i.e., the proportion of votes that go to Obama or to Romney). So instead, I pick weights that minimize the KL-divergence between the actual vote distribution $p(o|\mathbf{c})$ and the predicted distribution $\tilde{p}_\beta(o|\mathbf{c})$:

$\ell(\beta) = \sum_{\mathbf{c}} D_{\mathrm{KL}}\big(~ p(o|\mathbf{c}) ~\|~ \tilde{p}_\beta(o|\mathbf{c}) ~\big) + \alpha \sum_k |\beta_k|$

If you are familiar with regression analysis, the standard LR is just a special case of this: $p(o|\mathbf{c})$ is either zero or one, and the equation above reduces to the log-loss function. The second summation in the equation is an “L1 regularization” prior on the weights (a.k.a. the LASSO). This does two things: (1) it penalizes large weights and makes better predictions by not overfitting, and (2) it encourages a sparser, more easily interpretable model by “throwing away” demographic features that seem to be statistically irrelevant, by driving those weights toward zero. The $\alpha$ parameter controls the regularization level, and after a little tuning I picked a value of 50.

(Insert obligatory “the loss function is convex and can be minimized using an orthant-wise limited-memory quasi-Newton optimization method” statement here. Also, I guess you could do an ordinary least-squares regression — I haven’t tried that — but this approach guarantees that predictions are properly probabilistic.)

If this is all new to you, this method basically just tries to pick model weights $\beta$ whose predictions are as similar as possible to actual vote distributions. The only other minor modeling note is that features exhibiting long-tail distributions were log-tempered: $\mathbf{c}_k = \log(1 + \mathbf{c}_k)$. This is a pretty common adjustment and leads to better predictions, too.

### So How Accurate is This Model?

I tried a few ways of fitting the weights, and the KL-divergence approach described above seems to work best. Here’s a comparison of that vs. a standard true/false logistic regression, both using the L1 regularization:

The scatter plots show the actual vs. predicted proportion of votes going to Obama (all predictions pooled over ten folds using cross-validation). Each dot represents a county: blue dots are correctly predicted as majority Obama, red dots correctly predict majority Romney, and grey dots are misclassifications. The standard LR (right) has a little bit better classification accuracy, but it gets the vote distributions waaaaay off: by 25.7% on average. The KL-divergence LR (left) is only off by 8.9%, which is significantly better (p<.00001, paired 2-tailed t-test). For comparison, guessing 50/50 for every county would be off by 15.5% on average. Furthermore, you can see the straight “diagonal line” type relationship between the two axes in the left plot (as opposed to the “S” shape on the right), which is sort of the goal. So KL-divergence LR it is.

To better visualize what’s going on, here are some maps:

In broad strokes, the demographic model’s predictions (top) capture a lot of the trends in the actual vote distributions (middle; similar maps elsewhere). However, the model errs toward a 50/50 split; it doesn’t predict the really polarized counties as well (this is possibly due to weight shrinkage from the L1 term). The difference map (bottom) shows the model’s errors: bluer regions are actually more pro-Obama than predicted, redder regions are more pro-Romney, and whiter regions are spot-on. (Note that a few counties are greyed out in all the maps… this is because there I had no voter data for these counties).

So the model isn’t perfect, but it’s pretty darn good, especially considering it only uses demographic features as evidence and no explicit vote history or geography information (which should improve predictions, but is tangential to my interest in the demographics). It predicts voting proportions within 8.9% on average, explains nearly half the variance among those proportions, and correctly picks the county winner 85.4% of the time. Awesome!

(Update: Larry Wasserman indirectly pointed out over email that counties are not weighted by population or voter turnout here. This might affect the model.)

## Some Findings

Now let’s have a look at the model weights and what they tell us about voting patterns in different kinds of communities. Here’s a figure illustrating the learned weights (or download a more detailed PDF version):

Pro-Obama features are typeset in blue, pro-Romney features are in red, and features with zero weight (those “thrown away” as irrelevant) are in black. The features I added are highlighted with yellow. The colored squares on the right indicate the magnitude of the weight: darker colors have more impact. As you can see, there are only about eleven pro-Obama and six pro-Romney features of much practical significance. Let’s dig in.

### Voter ID Laws and Slavery

Let’s begin by looking at the two “Internet hypotheses” I tried to test by adding new features.

First, voter ID laws have no discernible impact. It may be that at the individual level, these laws do reduce voter fraud and/or prevent disadvantaged citizens from voting, but at the county level the model simply threw these features away. I re-ran the analysis with all three variables collapsed into one (i.e., “any kind of ID law”) and got the same result. As a sanity check, I tried the model without the L1 regularization, and the ID law features did turn out to be negatively associated with Obama, but this alternative non-regularized model was also much worse at prediction for all the measures I considered.

So my model says that voter ID laws had zero effect on on Obama vs. Romney outcomes at the county level. Oh yeah? That isn’t the story implied by the news stories, or even by this figure showing violin plots of the data:

It looks like Obama took 44% of the vote in counties with no voter ID laws, compared to 34% in counties with any kind of law (pkinds of communities that were open to voter ID laws, which might also happen to prefer Romney to Obama to begin with. As evidence of this, the model takes these other demographic features into account, and since the ID laws do not help improve the predictions, they get ignored.

(Note: I didn’t throw any latent-variable models at the data and I’m not a causality expert, so all of these are best guesses as to what’s really going on.)

(Also: How did Obama win if he took only 34-44% of the vote, on average, in counties both with and without ID laws? These statistics aren’t normalized for population. Romney won more counties than Obama, but Obama won many of the more populous counties, thus winning both the overall popular and electoral votes.)

Second, being part of a historically slave state or territory does have a slightly negative effect on predicted Obama votes. It is statistically significant, and may indeed reflect racial prejudices that 152 years of progress in civil rights has yet to overcome. However, the weight isn’t too practically significant (the percent of the population under age 5 and percent of owner-occupied homes have even stronger effects). I suspect that the “former slave territory” feature is actually being used by the model as a proxy for geography. Note that the model’s errors (in the “difference” map above) are geographically systematic, and the free/slave state variable partially overlaps with these errors. It might be that with better geographic information, the model would ignore this feature, but then again maybe not. Besides, it’s hard to tease things like this apart, since associations with slavery are partially encoded in present-day racial demographics as well.

### Race and Ethnicity

Not surprisingly, whiter communities lean strongly toward Romney and blacker communities lean strongly toward Obama. This doesn’t mean that all (or even most) Whites voted for Romney, but people who live in mostly White communities did. Likewise for Blacks and people (regardless of color) who live in mostly Black communities. For example, my White friends who live in Pittsburgh’s Hill District tend to support Obama. Asian presence leans slightly toward Obama as well. Native Hawaiian and Pacific Islander presence has no discernible impact. Perhaps the most interesting observation has to do with the presence of a Hispanic community. The percent of residents who are of Hispanic (or Latino) origin strongly predicts more Romney votes, but the percent of Hispanic-owned businesses strongly predicts more Obama votes. For the other non-White groups, the percent of population and percent of business ownership lean in the same direction, but not with Hispanics. Why?

We can “poke the box” a little bit to try and get a sense of what’s going on. By that I mean let the model make predictions both with and without these features, and see how they differ. Here is a map that visualizes the effects:

Redder regions are predicted to be more pro-Romney if the model takes Hispanic population and Hispanic business features into account. Bluer regions are similarly more pro-Obama. Whiter regions are unaffected, either because they do not have as many Hispanics around, or the opposite effects just cancel each other out (as in Las Vegas and Phoenix, apparently). As a sanity check, the counties that seem most affected in either direction are located in Florida or near the Mexican border, so that makes sense.

I surmise that what’s going on here has something to do with a balance of power. Consider the scene: counties with more Hispanics tend to vote for Romney, unless there are more Hispanic-owned businesses. Well, some of the Hispanics in these places are immigrants (both legal and illegal), and thus probably cannot vote. Perhaps these aliens are migrant workers, which in turn might stir up resentment among native non-Hispanic citizens who vote for Republicans in support of tougher immigration laws. West Texas might be that kind of place, for example (not that I would really know, that just fits with my own preconceptions). On the flipside, Hispanic citizens with voting rights might be more likely to own businesses, create jobs, rise to positions of leadership, and also vote Democrat. Florida, Southern California, and New Mexico might be places with a Hispanic population more like this.

The National Election Pool (NEP) (as summarized by The New York Times) says that Obama won among all non-White ethnic groups — including Hispanics — at the individual voter level. So the model of county-level voting behavior here suggests that where more non-voting Hispanics are present, the voting community might actually swing the other way. This is just my speculation, but I something like that might really be happening. Another lesson in correlation vs. causality: we shouldn’t simply conclude from a single statistical association which way Hispanics are actually voting.

(Update: See Steve Sailer’s interpretation in the comments below.)

### Housing

The strongest predictor of Obama votes is the percent of housing units that are in multi-dwelling structures. My first guess is that these buildings are (1) apartments and (2) projects, which are more common in urban areas that tend to be more left-leaning, and also indicate renters rather than home-owners. This is in contrast to the percent of homes that are owner-occupied (more common in rural and suburban areas), which is a predictor of Romney votes.

Another possibility is that the Obama campaign was just more well-mobilized in getting out to canvass these multi-dwelling units, which had an impact on voter turnout. In 2008, my wife and I lived in a four-unit urban complex in Madison, Wis., and we had a lot of Obama folks come by. In Pittsburgh for this election, we had one Obama campaigner darken the door of our rented row house. We never had a single McCain or Romney supporter either time.

### Economy and Wealth

The value of goods from manufacturing firms is another top-five predictor of Obama votes. The other economic sectors are tossups, with most leaning Obama except wholesale. However, the data set I used lacks any information on universities, military presence, farms, and other interesting economic drivers. I suspect these would have greatly improved the predictive power of the model, and would have been interesting to inspect as well. (All that info exists in the full Census report, but that data is messy and this isn’t a real research project…)

Also, I felt that during this election, Romney supporters were (unfairly) stereotyped as rich and out-of-touch while Obama supporters were seen as poor and government-dependent (given comments like “the 47 percent“). So I was particularly interested in features that directly describe a community’s distribution of wealth (percent in poverty, median household income, per capita income, etc.). They were all thrown away by the model. The general wealth of a community (or lack thereof) appears to have no substantial impact. There might be interesting interactions (e.g., communities that have both high education and high income, rather than treating these variables independently), but I poked around a little bit and couldn’t find any interesting or sensible ones (and they all seemed to hurt the model’s predictive power, too).

(Update: Andrew Gelman pointed out over email that affluence really does appear related at the individual level. I’m in the process of reading his popular book about the 2008 election, Red State Blue State.)

### Education, Gender, and Age

Communities with more education definitely voted for Obama: the association with college degrees is even stronger than high school degrees. This doesn’t necessarily mean that “smarter people voted Obama,” though. Counties with a concentration of educated people are probably urban centers or university towns, which tend to be more left-leaning. Note that the aforementioned NEP pool found that individuals with college degrees (though not post-graduate degrees) leaned slightly toward Romney, and that Obama won among individuals who didn’t finish high school by a 29% margin.

The proportion of females did not appear to have a large impact either way (barely Romney-leaning), which is no surprise since most counties have a 50/50 gender split. However, the NEP pool also shows that Obama won by an 11% margin among women voters, and my model significantly associates more women-owned businesses with Obama.

I’m not sure what to conclude about age, though, in part because the data set only has a few age variables in it. As I mentioned at the beginning, the percent of the population under age 18 is a strong predictor of Romney votes (so is the percent under age 5). Since these young citizens are too young to vote, I assumed it must be their parents who were voting for Romney, but the NEP pool claims that Obama won parents of children under age 18 by a small margin. That confuses the story a bit. Another puzzler is the percent of the population over age 65, which is mildly associated with Obama in the model, whereas the NEP pool suggests that Romney won that group by 9%. There might be another “who is actually showing up to vote” story here (as with the presence of children and Hispanics), but I don’t know what it might be…

## In Conclusion

This was a fun little study, although it ended up being more involved than I intended… I needed the Thanksgiving weekend to finally write it up! There are some other observations one could make with the data, but these are the ones I found most interesting. I feel like the model dispels a couple of sloppy theories regarding voter behavior that I’ve heard (like voter ID laws and former slave states), and also uncovers some interesting trends (regarding ethnicity and wealth in particular). If you have any other thoughts or insights, please leave them in the comments below.

1. Steve Sailer says:

Thanks. Very impressive.

Regarding Hispanic voting, what happens is that Republican areas tend to be more favorable to low-end job creation (e.g., it’s easier to get a permit to put up a housing development in Texas than in Marin County). That jobs magnet brings low-skilled Hispanics into Republican areas. Over time, this influx plus their higher fertility brings Hispanics into demographic domination of an area, which boosts Democratic voting as they slowly acquire citizenship or their children reach voting age. But (leaving aside South Florida’s middle class Cuban refugee communities) growing Hispanic / Democratic dominance depresses economic dynamism. Outside of Florida, Hispanic entrepreneurs don’t create a lot of jobs and don’t push push the local economy into a higher level of higher paying jobs. The upper Rio Grande Valley in New Mexico would be an obvious example of where an ancient Hispanic community is economically stagnant. The lower Rio Grande Valley in Texas is another example of a poor, non-dynamic heavily Hispanic area with

The Inland Empire of Southern California is a classic example of a formerly Republican area that brought in huge numbers of Hispanics for construction and similar jobs, only to have it tilt increasingly Democratic due to Hispanic and other minority influx and have it economically collapse in 2007-2008 when large fractions of the newcomers proved unable to pay back their inflated mortgages.

1. burrsettles says:

Thanks, that’s an interesting explanation for the Hispanic disparities. However, Riverside, California still seems to lean left due in part to the number of Hispanic-owned businesses (according to the model-generated figure above)… the same is true for the upper and lower Rio Grande Valley regions.

On the other hand, the business-ownership statistics are from 2007, before the economic collapse. The percent population statistics are more current (2011).

2. You really want to check out Andrew Gelman’s book about the 2008 election, Red State, Blue State for the political/pop angle (though with lots of figures) or his and Jennifer Hill’s multilevel regression book, which goes through the multilevel models and post-stratifications used for the county-level and state-level predictions. The real solution to the problem isn’t L1 regularization, but a hierarchical model (you can make it L1 if you want, but Andrew used L2 because really, we don’t expect any of these effects to truly be zero). The Gelman and Hill book also has enough info in the later chapters to turn you into an expert on causality (Jennifer’s done some really neat work in this area in education).

Second, it’s pretty well known that you can train a logistic regression from probabilistically weighted data (you may remember me talking about this in San Diego in my talk, because you get these kind of probabilistic outputs from a Dawid-and-Skene-type annotation model). It’s not very common in machine learning where the (wrong) assumption is that the gold standard is perfect (i.e., no measurement error in the data).

(Now let’s hope the LaTeX plugin for WordPress is active here.)

Typically you have data for a binary problem with outcomes $y_n \in \{ 0, 1 \}$ and predictor/covariate/feature vectors $x_n \in \mathbb{R}^K$. The model then fits a coefficient vector $\beta \in \mathbb{R}^K$. In the probabilistic case, the likelihood function is

$p(y|x,\beta) = \prod_{n=1}^N p(y_n|x_n,\beta)$

where

$p(y_n|x_n,\beta) = y_n \mbox{logit}^{-1}(y_n' \beta) + (1 - y_n) (1 - \mbox{logit}^{-1}(y_n' \beta))$.

If instead of assuming a binary $y_n \in \{ 0, 1 \}$, you let $y_n \in [0,1]$ to be the probability of a 1 outcome (or in the multi-logit case, a simplex), then the likelihood function doesn’t change.

Add whatever prior $p(\beta)$ you like, and then run a full Bayesian analysis to get samples representing the posterior distribution $p(\beta|y,x)$, use each sample for prediction, then you get full Bayesian predictive inference. This’ll solve your “paradox” with voter ID laws — you’ll get a negative estimate of the effect, but the uncertainty may extend into the positive range, and using proper Bayesian predictive inference will do the right thing (that is, if the uncertainty is large, it’s basically ignored, but without zero-ing the estimate). If you were a frequentist statistical political scientist, you’d probably run a hypothesis test on the relevant coefficient being positive rather than just zeroing it out with L1 regularization.

Or just optimize the product of the likelihood and the prior over $\beta$ for the max a posteriori estimate, but there’s really no reason to do that because the Bayesian model’s easy to fit in this case (for instance, you can use your new software Stan! we happen to be adding this capability to LingPipe at the moment, too, but I still wouldn’t recommend MAP point estimation unless your data is at too large a scale to permit Bayesian inference).

Next, you really really want to get interactions in there and fit a varying-slope model. It answers the question of “what’s wrong with Connecticut (vs. Mississippi). What you see is that income has a much more positive effect on Republican vote share in Mississippi than in Connecticut, which you can’t capture with a basic model. That is, the coefficient for the effect of income (i.e., a slope) varies from state to state.

And finally, I’d suggest not throwing rocks regarding conspiracy theories when you also put your model down and start engaging in what Andrew calls “story time.” You get your model’s fit and everything else is speculation!

P.S. You might also like Andrew’s raw data plots here:

http://themonkeycage.org/blog/2012/11/15/red-blue-maps-for-different-slices-of-the-population/

It shows you can go pretty far without any model at all.

1. burrsettles says:

Thanks, Bob.

1) I played around with L2 regularization in this model, too, but L1 gave (marginally) better predictions. That’s mostly why I went with it (with only 55 features sparsity wasn’t a huge concern).

2) I’m not surprised that people try to fit models to weighted dependent variables like the KL-divergence approach above. I’ve used it, e.g., in crowdsourcing settings where you get uncertain labels, and it seems to work well. But I don’t recall seeing it described in any machine learning/NLP papers. Do you have a proper citation/pointer to published work? I had a student here at CMU asking me about this the other day…

3) I don’t think I was throwing rocks. I tried to take care and only try drawing conclusions at the county (not individual) level, for which I thought there was some interesting evidence or counter-evidence. I also tried to be clear that the interpretation was all my speculation.

4) Thanks for the multitude of pointers… and you Bayesians sure know how to make a guy feel silly for using point estimates!

3. Buddy2U says:

My head is spinning trying to decipher all the statistical analysis. (Howbeit excellent) The bottom line for me is Conservatives did not get out and vote. Why? We did not have a conservative candidate.

1. Aaron P says:

The prevailing theory is that white men, unless otherwise behooved to partake in such an “uneventful” process, still find it insignificant, at this time, to hassle with it: (anymore nowadays, who has time to digest the precipitous rise of rancor sparked by all interested parties, especially when juxtaposed to available time this demo needs to discern the predilections between each party, to begin, and then to have that push to get out and ink a viable candidate lest their seemingly vapid lives take an ominous turn for the worst by their failure to act (to vote?)

So then, anything of great import should preclude the commonplace indolence observed by white men, with more emphasis on republicans who may not be so reticent anymore given the influx of insanity we’ve been seeing inundate our nation.