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One of the ongoing debates in politics is whether elections are won by persuading swing voters to vote for your side or maximizing turnout among your base. We instinctively talk about campaigns as if they are battling for voters’ minds. Can Hillary win over Working Class Whites? Can Donald Trump limit his harm among racial minorities? This implies that the most important movement in elections is due to voters who are on the fence, changing their minds.

Recent push-back has argued that simply nobody changes their minds anymore, and the people who do probably aren’t all that likely to vote anyway. What really matters is energizing your base, and making sure they vote. There can be once-a-generation political realignments, but for the most part people just vote for their party. The difference between victories for one party or another is which party is more energized.

There are smarter people than me having this debate (my favorite recent book has been the eye-opening Democracy for Realists), but what I can do is look at the Philadelphia version. Where in Philadelphia does Turnout matter? Where does Persuasion?[1]

How to measure the difference between turnout and persuasion
One of the favorite tools of demographers is the decomposition. This is a (surprisingly simple) mathematical technique for breaking down the change in something into the relative importance of the change in its constituent parts. In the footnotes, I develop a formula that decomposes a the variability in a party’s win total (measured as the gap in votes between the winning party and the losing party) into variability of turnout plus variability of party preference. The equation boils down to

Variability in Gap = (Variability in Preferences) x (Average Turnout) + (Variability in Turnout) x (Average Preference)
= (Party Variability Component) + (Turnout Variability Component)

The equation reveals two campaign strategies, by maximizing each of the two addends:
(1) maximize the first component by persuading voters in divisions with variable preferences and high turnout.
(2) maximize the second component by turning out voters in divisions with highly variable turnout, where the average preference is strongly for your party.

These components boil down to obvious strategies, but the decomposition gives us a way to score divisions based on each. A division’s score along each component tells us what impact that division has changes in the citywide election.

Party variability measures the impact on the citywide Democrat-Republican gap that a division’s preference swings have. A division with a score of 0.02 means that when a division changes its party percentage by its average swing, the citywide vote total changes by 0.02 percentage points. This will depend on (1) how swing-y that division is, i.e. what constitutes its “average swing”, and (2) its typical turnout. Divisions that swing between Democrats and Republicans, and where everyone votes, will have high scores.

Turnout variability measures the impact on the gap that a division’s turnout swings have. A division with a score of 0.02 means that when a division increases its turnout by its average swing, the citywide vote total changes by 0.02 percentage points. This will depend on (1) how much turnout varies in that district, which determines its “average swing”, and (2) its typical party gap. Divisions where turnout varies wildly but which is strongly Democratic or Republican will have high scores.

(I use “relative turnout”, which is a division’s proportion of the citywide total, rather than vote counts. Thus, large swings for a Presidential election aren’t considered a swing unless the division votes disproportionately more than other divisions in that year. This also means that citywide turnout efforts won’t affect the score, only localized ones.)

Overall, it appears that persuasion has a larger impact on Philadelphia’s vote gap than turnout. The longer tail in the top facet means that many divisions have high scores along this dimension. This is largely because turnout doesn’t vary much between divisions–a division that represents 1% of the city’s votes will do so in most elections. The total votes for the city as a whole fluctuates dramatically, but divisions’ share within a given year doesn’t.

I expect this result to reverse when we zoom out to the state level; relative turnout variability is likely much higher between the city and the rest of the state than it is within the city.

Where Turnout Matters
Turnout will matter in divisions where the percentage of voters varies from year to year, and where voter preferences are overwhelmingly Democratic or Republican. The map below colors divisions by the turnout component score, with the hue representing whether Republicans or Democrats benefit from an increase in turnout. The Northeast and Manayunk have low scores–they are too split between parties for turnout to help one party more than another. West Philly also has surprisingly low scores: turnout there is simply too stable for turnout efforts to have an effect (except for in University City). Interestingly, the predominately-Hispanic section of North Philly has very high scores: voters turn out for Presidential elections and not for other elections, and they vote overwhelmingly Democratic.

Where Persuasion Matters
Persuasion campaigns will have an impact in divisions where the party preferences vary from election to election, and where turnout is always high. The map below colors divisions by their party preference score. The Northeast, Manayunk, and Port Richmond now light up: these are all neighborhoods where people vote at high rates, and swing between Democrats and Republicans. North Philly and West Philly are simply too consistent in party preferences–Democrats win with 99% of the vote–for convincing to matter.

What does this mean for the state?
Our most important upcoming election is the 2018 race for Governor. In a future post, I will replicate this analysis at the state level. What counties can be persuaded? What counties need to be mobilized? I expect that the state results could be very different than for within Philadelphia. Stay tuned!

Footnotes
[1] Of course, strategies for convincing and strategies for turnout are not so separable. There are probably a lot of campaign actions that achieve both.

Appendix: The Decomposition
First, I’ll motivate demographers’ common decomposition in the case of only two years, then I’ll expand it to a multi-year version. (Apologies for the hideous math, I haven’t been able to figure out how to typeset math in this blog yet.)

Suppose we have a value G that is the product of two numbers, P and T. In the current case, G is the citywide vote gap between Democrats and Republicans, defined as the total votes for Democrats minus the total votes for Republicans. P is the percentage gap between Democrats and Republicans, and T is the total turnout in votes. Notice that

    G = P * T

Consider the case where we observe these values in two time periods, 0 and 1. We are interested in what caused the gap G to change between year 0 and year 1. It could be changes in the percentage P (call this persuasion) or changes in turnout T (call this mobilization). That is, we are interested in G_1 – G_0. We can write
    G_1 – G_0 = (P_1 * T_1) – (P_0 * T_0)
A little bit of algebra can show that:
    G_1 – G_0 = (P_1 – P_0) * Avg(T) + (T_1 – T_0) * Avg(P)
These two addends are our components. The first addend can be interpreted as the change in the vote gap due to the changes in the proportion voting for the Democrat, scaled by the average number of voters.  The second is the change in the gap due to changes in the total people voting, scaled by the average party preference.

A simple picture helps build intuition for this decomposition. Below, we are interested in the difference of the areas of the two rectangles, G_1 and G_0. Notice that the area of each can be written as base times height, or P * T. The area from G_0 to G_1 changes both because P changes and T changes. But how much of the change was due to P, and how much due to T?

One way to decompose the area is to draw the diagonal between the top right corners. The total difference between G_1 and G_0 is then the sum of the areas of the two trapezoids.

Remembering the 8th grade formula for the area of a trapezoid (area = height * avg(base lengths)) gives us the decomposition from above. Notice that the trapezoid on the right is the first component, and the trapezoid on the top is the second.

We aren’t limited to doing this for only the city as a whole. We can calculate this decomposition for each division. The total gap in the city is the sum of the gaps in each precinct. The total state gap is given by summing over each precinct i:
    G_1 – G_0 = SUM(G_i1 – G_i0)
= SUM(P_i1 * T_i1 – P_i0 * T _i0)
= SUM( (P_i1 – P_i0) * Avg(T_i) + (T_i1 – T_i0) * Avg(P_i) )
= SUM( Preference_Component_i + Turnout_Component_i)

We can thus calculate each precinct’s two scores, and then the total change in the city-wide gap between year 0 and year 1 as the sum of both scores for all precincts.

Thus far we’ve only been using two years. However, we want to be able to incorporate all of the elections at once.

The absolute value of the first term can be written as
    |(P_i1 – P_i0) * Avg(T_i)| = (|(P_i1 – Avg(P_i)| + |(P_i0 – Avg(P_i)|)  *  Avg(T_i),
(this relies on the fact that Avg(P_i) is between P_i0 and P_i1). This may look complicated, but it has a nice interpretation: it is the size of typical deviation of P_i from its average value, scaled by the average turnout.

We similarly write
    |(T_i1 – T_i0)| * Avg(P_i) = (|(T_i1 – Avg(T_i)| + |(T_i0 – Avg(T_i)|)  * Avg(P_i)
Where I’ve left P_i outside of the absolute value so the sign captures partisanship: positive values represent a Democratic gap, negative a Republican gap (signs are arbitrary).

This inspires a multi-year version of the decomposition:
    Decomposed Variability = Avg(|P_ij – Avg(P_i)|) * Avg(T_i) + Avg(|T_ij – Avg(T_i)|) * Avg(P_i)
= Preference Variability Component + Turnout Variability Component
Notice that the last term does not use the absolute value on P_i. This means that it will have the sign of the typical partisan gap, and thus the last term is capable of showing which party an increase in turnout will help.

(Statsy readers: Avg(|P_ij – Avg(P_i)|)  is like a linear version of the variance).

This allows us to score a county i based on whether its percent-Democrat varies more, or its turnout. It’s no longer an accounting identity, but it does simplify to the accounting identity above when you only consider two years.

We could be done here, but to really compare across years, I divide a precinct’s vote total by that year’s City vote total, T_j. This means that the left hand side can be interpreted as the percentage gap between Democrats and Republicans, rather than a raw vote count. For example, if the Republican won 52% to 48%, the gap would be 4 percentage points.
    Decomposed Pct Gap = Avg(|P_ij – Avg(P_i)|) * Avg(T_ij / T_j) + Avg(|T_ij/T_j – Avg(T_ij/T_j)|) * Avg(P_i)

Last week, I looked at Philadelphia’s turnout boom. What I didn’t talk about was the unmistakable race and class story in which neighborhoods saw surging turnout, and which didn’t. The neighborhoods surrounding Center City–University City, Fishtown, Passyunk–saw the greatest increases in turnout over the prior District Attorney election in 2013, with many divisions *tripling* their votes. Those neighborhoods are also where the most gentrification has recently occurred. However, turnout changed across the city, and the story is not as simple as “gentrification leads to more voting”.

Philadelphian voters, by race and income
First, let’s look at the racial and class dynamics of voting in the 2017 election. We don’t have data on individual voters, so I map divisions to census tracts, and assign votes to racial/class groups based on their tract-level representation among the over-18 population. For example, a tract that was 60% Black would be apportioned 60% of the votes in that tract.[1] This will almost certainly understate the differences between groups: it assumes that groups within a tract vote at the same rates even if they vote at different rates across the city. All of the populations I use are five-year estimates from the American Community Survey (annually conducted by the Census Bureau), so the most recent data is from 2011 – 2015. First, let’s look at the number of voters of each race.

White non-Hispanic people make up more of the voting population than the overall over-18 population. The least represented are Hispanic voters. Some of this is likely eligibility to vote–I’m using the total population over 18 rather than registered voters, which I explained last week–but much of it isn’t: the gap was almost representative in the presidential election of 2016.

Class plays a role in these patterns. Below, I plot tracts’ turnout versus their median income. Wealthier tracts clearly vote at higher rates. The citywide rate was 15% (this is lower than the official turnout, which uses registered voters as the denominator). The turnout among tracts with median incomes over $50,000 was 22%. Among tracts with median incomes below $50,000, turnout was 13%.

However, the breakdown by race within this income plot is nuanced. Below is the same plot, with tracts colored by their predominant race (for example, a 60% Hispanic tract would be colored orange). Within racial groups, tracts with higher incomes vote at higher rates, but there are also differences across racial groups.

White tracts have the highest turnout overall, but among tracts with similar incomes, Black tracts have higher turnout. Hispanic tracts lag both.

Changes in turnout and race
These turnouts are not uniformly spread across the city. Among White tracts, there are large differences in turnout. Ditto among Black tracts Below maps the turnout of tracts in the city for 2017 and for 2009, where tracts have been colored by their predominant race.

Among Black tracts in 2017, Germantown, Stenton, and Point Breeze have the highest turnout rates.  University City, Mount Airy, and Center City have high rates among White tracts. The highest rate among Hispanic tracts is in Kensington, at the southern tip of Hispanic North Philly.

Between 2009 and 2017, citywide turnout increased from 9.6% of the over-18 population voting to 15.3%. Comparing the maps above makes clear that this increase did not happen uniformly, but instead by the rich getting richer: already-high-turnout tracts also had the largest increases in turnout. Below is a scatter plot of the same data. The x-axis is tracts’ turnout in 2009, while the y-axis is the change in turnout from 2009 to 2017. Points are colored by their predominant race in 2015.

The tracts that saw the greatest increase in turnout were predominately White tracts that were already voting at the highest rates in 2009. The slope among predominately-Black tracts is much shallower–all tracts saw turnout increase by about 5 percentage points–while the slope is non-existent among predominately Hispanic tracts. A note of caution: the background points show that these trends capture little of the variation among tracts.

Look back at the map. Notice that many of the highest turnout regions occur along racial boundaries. In past research, I’ve argued that these boundaries are where gentrification typically happens. Part of the high turnout along boundaries may be evidence that crudely shading tracts by the predominant race hides changing populations within them, and that the gentrifiers in University City, Brewerytown, and Kensington may be disproportionately voting. That certainly matches anecdotal evidence of who was energized by the Krasner/Rhynhart new blood in 2017. ​

There is certainly evidence that tracts with higher increases in income saw higher increases in turnout. The pattern is only weakly predictive, however. It wasn’t every newly-wealthy neighborhood that increased turnout. Cedar Park, Fishtown, Passyunk, and Brewerytown certainly did, but there are other tracts where incomes increased but voting didn’t; the tracts ringing Center City are different in type.

A certain group of Philadelphians is particularly engaged
The recent turnout surge occurred predominately among wealthier White tracts that already were voting at high rates. Black tracts in Philadelphia saw their votes increase at about similar rates to the city as a whole, while Hispanic votes fell disproportionately from 2016 highs.

The energy of 2017 is most extreme in the neighborhoods ringing Center City and in the Northwest. Philadelphia’s role in the 2018 Governor’s race may depend on energizing the *rest* of the city. More on that next week.

Questions? Comments? Ideas for future posts?
Leave a comment below!

Footnotes
[1] Assuming that e.g. higher voting in predominately Black wards implies that Black residents are more likely to vote suffers from the ecological fallacy. It may be instead true that the non-Black residents in those divisions are themselves more likely to vote. In fact, there may be good reason to suspect this in the predominately-Black, gentrifying neighborhoods. But this is the best data we have.