Do Open Wards increase turnout?

I’m a committeeperson in the 24th Ward, which serves West Philly’s Mantua, Parkside, and Powelton neighborhoods. In May 2022, we voted to become an Open Ward. What does that mean? There’s no single definition, and each Open Ward establishes its own bylaws. But at a high level, being “Open” means that Committeepeople vote on which candidates to endorse and on other Ward operations, rather than simply following the Ward Leader. In addition to being more democratic, we also hope that by empowering committeepeople in this way, we can increase participation and Ward capacity for Get Out the Vote and other efforts.

Many of these benefits are fuzzy, but an increase in voter participation should be measurable. So, do we have any evidence that this works? Do Open Wards increase turnout? A number of wards have been open for years (some even for decades). Today, I’m doing some statistical analyses to measure if that’s true.

First, what wards are “Open”? As I said, there’s no single definition. But for this analysis, I’m using the set of Wards that have bylaws allowing committeepeople to vote on endorsements. Those I’m considering Open are:

Ward Year Opened
1 2018
2 2018
5 60s or 70s
8 60s or 70s
9 60s or 70s
15 2022
18 2018
24 2022
27 60s or 70s
30 1998
39a 2022

(If you want to contest these definitions or years, my email is open.)

View code
library(sf)
library(dplyr)
library(tidyr)
library(ggplot2)
source("../../admin_scripts/theme_sixtysix.R")
source("../../admin_scripts/util.R")
asnum <- function(x) as.numeric(as.character(x))

divs <- st_read("../../data/gis/warddivs/202011/Political_Divisions.shp")ward_from_div <- function(warddiv){
  ward <- substr(warddiv, 1, 2)
  div <- substr(warddiv, 4,5) 
  ward <- case_when(
    ward == "39" & asnum(div) >= 25 ~ "39a",
    ward == "39" & asnum(div) < 25 ~ "39b",
    TRUE ~ ward
  )
  return(ward)
}

divs <- divs |>
  mutate(
    warddiv = pretty_div(DIVISION_N),
    ward = ward_from_div(warddiv)
  )

wards <- divs |> group_by(ward) |> summarise() |> st_make_valid()

open_wards <- tribble(
  ~ward, ~year_opened,
  "01", "2018",
  "02", "2018",
  "05", "60s or 70s",
  "08", "60s or 70s",
  "09", "60s or 70s",
  "15", "2022",
  "18", "2018",
  "24", "2022",
  "27", "60s or 70s",
  "30", "1998",
  "39a", "2022"
)

wards <- wards |> mutate(
  is_open = ward %in% open_wards$ward,
  is_open_pre_22 = ward %in% (
    open_wards |> filter(year_opened != "2022") |> with(ward)
  )
)

ggplot(wards) + 
  geom_sf(aes(fill = is_open)) +
  scale_fill_manual(
    values=c(`TRUE` = light_blue, `FALSE` = light_grey),
    guide=FALSE
  ) +
  geom_text(
    data = wards |> filter(is_open) |> 
      mutate(
        x = st_coordinates(st_centroid(geometry))[,"X"],
        y = st_coordinates(st_centroid(geometry))[,"Y"]
      ),
    aes(
      x = x,
      y = y,
      label = ward
    ), 
    size = 3
) +
  theme_map_sixtysix() +
  labs(
    title="Philadelphia's Open Wards"
  )

The first thing you’ll notice is that these wards cluster around Center City. As such, they tend to be wealthier and whiter than the city as a whole; the same demographics that have seen a generalized surge in turnout since 2016. That makes the causality here difficult to measure: does the openness of a ward increase turnout, or did these wards become open thanks to local political engagement, and turnout there would have increased regardless?

There’s another complication in answering the question: how should we define turnout? I don’t love the usual measure, votes cast divided by registered voters; that number will be alarmingly low because of inactive voters still on the rolls, and the denominator moves for all sorts of reasons, including slow cleaning of the voter rolls or registration drives (I’ve called this the Turnout Funnel). And wards might have very different populations with different propensities to vote, or even be eligible to vote, which we want to control for.

I’ll use my favorite metric: turnout in an off-year election as a percentage of Presidential turnout. Off-year turnout is more malleable to local GOTV efforts: there’s more need just to remind people when Election Day is, and people get less communication about the election from other channels. A division’s Presidential turnout gives a ceiling on plausible off-year turnout. In this case, I’ll measure turnout in November 2022 divided by turnout in November 2020.

View code
df_major <- readRDS("../../data/processed_data/df_major_20230116.Rds")

turnout <- df_major |> filter(is_topline_office, ward != "99") |>
  group_by(warddiv, year, election_type) |>
  summarise(votes=sum(votes))

turnout <- turnout |> left_join(
  divs |> as.data.frame() |> select(warddiv, ward),
  by="warddiv"
) |>
  left_join(
    wards |> as.data.frame() |> select(ward, is_open, is_open_pre_22),
    by="ward"
  )

div_turnout <- turnout |>
  pivot_wider(
    names_from=c("election_type", "year"),
    values_from = "votes"
  )

ward_turnout <- turnout |> 
  group_by(ward, year, election_type, is_open, is_open_pre_22) |>
  summarise(votes=sum(votes)) |>
  pivot_wider(names_from=c("election_type", "year"), values_from="votes")

ward_turnout |>
  mutate(row = case_when(is_open ~ ward, TRUE ~ "Closed Wards")) |>
  group_by(is_open) |>
  summarise(votes_20 = sum(general_2020), votes_22 = sum(general_2022, na.rm=T)) |>
  mutate(ratio = votes_22 / votes_20)
View code
ggplot(wards |> left_join(ward_turnout, by="ward", suffix=c("", "_w"))) + 
  geom_sf(aes(fill = general_2022 / general_2020)) +
  geom_sf(aes(color=is_open), fill = NA, lwd=1) +
  scale_color_manual(guide=FALSE, values=c(`TRUE` = "white", `FALSE` = alpha("white", 0))) +
  scale_fill_viridis_c() +
  theme_map_sixtysix() %+replace%
  theme(legend.position = "right") +
  labs(
    title="Turnout in 2022 vs 2020",
    subtitle="Open Wards are outlined.",
    fill = "Votes cast \n2022 / 2020"
  )

Overall, the Open Wards (including those that only became Open later) cast 148,000 votes for President in 2020, and then 118,000 for Governor in 2022, an 80% rate. The other wards cast 594,000 and 380,000, a 64% rate. That’s a 16 percentage point difference!

But it might not be causal. We need to control for the ways Open Wards are systematically difference from Closed ones. We could do this by adding a bunch of control variables to a regression, but I prefer a stronger approach: using spatial boundary discontinuities. We can look at neighboring divisions on opposite sides of a ward boundary, one in a closed ward and one in an Open Ward) and compare the differences. By using only neighboring divisions, we create a useful apples-to-apples comparison; we assume that any systematic differences between these divisions is the effect of Open Wards. (I did a similar analysis in 2019, measuring the power of ward endorsements.)

For this analysis, I’ll limit to wards that were only Open before 2022 (sadly excluding my own 24). I filter down so each division is only in a single pair, and control for the proportions Black and Hispanic in the divisions (the pairing of divisions across boundaries should mean these proportions are not that different, but this will control for any lingering differences that do exist).

View code
block_data <- readr::read_csv(
  "../../data/census/decennial_2020_poprace_phila_blocks/DECENNIALPL2020.P4_data_with_overlays_2021-09-22T083940.csv",
  skip=1
)
block_shp <- sf::st_read(
  "../../data/gis/census/tl_2020_42101_tabblock/tl_2020_42_tabblock20.shp"
)block_shp <- st_transform(block_shp, st_crs(wards))
block_cents <- block_shp |> st_centroid()

st_contains_df <- function(shp1, shp2, id1, id2){
  raw <- st_contains(shp1, shp2)
  res <- list()
  for(i in 1:length(id1)){
    res[[i]] <- data.frame(
      id1 = id1[i],
      idx2 = raw[[i]],
      id2 = id2[raw[[i]]]
    )
  }
  return(bind_rows(res))
}

blocks_to_wards <- st_contains_df(wards, block_cents, wards$ward, block_cents$GEOID20) |>
  rename(ward = id1, block_i = idx2, geoid = id2)

res <- list()
for(ward in unique(blocks_to_wards$ward)){
  blocks_w <- block_cents[
    blocks_to_wards |> filter(ward == !!ward) |> with(block_i),
  ]
  divs_w <- divs |> filter(ward == !!ward)
  blocks_to_divs <- st_contains_df(divs_w, blocks_w, divs_w$warddiv, blocks_w$GEOID20) |>
    select(-idx2) |>
    rename(warddiv = id1,  geoid = id2)
  res[[ward]] <- blocks_to_divs
}
blocks_to_divs <- bind_rows(res)

div_pops <- blocks_to_divs |>
  inner_join(block_data |> mutate(geoid = substr(id, 10,24)), by="geoid") |>
  group_by(warddiv) |>
  summarise(
    pop = sum(`!!Total:`),
    hisp = sum(`!!Total:!!Hispanic or Latino`),
    nhw =  sum(`!!Total:!!Not Hispanic or Latino:!!Population of one race:!!White alone`),                                                                            
	nhb = sum(`!!Total:!!Not Hispanic or Latino:!!Population of one race:!!Black or African American alone`),  
    nha = sum(`!!Total:!!Not Hispanic or Latino:!!Population of one race:!!Asian alone`)
  )
neighboring_wards <- st_touches(wards)
neighboring_wards <- neighboring_wards |>
  lapply(as.data.frame) |>
  bind_rows(.id = "id0") |>
  mutate(id0 = asnum(id0)) |>
  rename(id1 = `X[[i]]`) |>
  filter(id0 < id1) |>
  mutate(ward0 = wards$ward[id0], ward1 = wards$ward[id1])

neighboring_divs <- vector(mode="list", length=nrow(neighboring_wards))
for(row in 1:nrow(neighboring_wards)){
  ward0 <- neighboring_wards$ward0[row]
  ward1 <- neighboring_wards$ward1[row]
  
  divs0 <- divs |> filter(ward == ward0)
  divs1 <- divs |> filter(ward == ward1)
  touches <- st_touches(divs0, divs1) |>
    lapply(as.data.frame) |>
    bind_rows(.id = "id0") |>
    mutate(id0 = asnum(id0)) |>
    rename(id1 = `X[[i]]`) |>
    mutate(div0 = divs0$warddiv[id0], div1 = divs1$warddiv[id1])
  neighboring_divs[[row]] <- touches |> select(div0, div1)
}
neighboring_divs <- bind_rows(neighboring_divs)

neighboring_divs <- neighboring_divs |>
  left_join(
    div_turnout, by=c("div0"="warddiv")
  ) |>
  left_join(
    div_turnout, by=c("div1"="warddiv"),
    suffix=c("_0", "_1")
  ) |>
  left_join(
    div_pops, by=c("div0" = "warddiv")
  )|>
  left_join(
    div_pops, by=c("div1" = "warddiv"),
    suffix=c("_0", "_1")
  )

neighboring_divs <- neighboring_divs |>
  mutate(
    prop_22_over_20_0 = general_2022_0 / general_2020_0,
    prop_22_over_20_1 = general_2022_1 / general_2020_1,
    signed_is_open = is_open_1 - is_open_0,
    signed_is_open_pre_22 = is_open_pre_22_1 - is_open_pre_22_0
  )

# Grab arbitrary unique pairs
set.seed(215)
neighboring_divs_lm <- neighboring_divs |>
  group_by(div0) |>
  filter(sample.int(n()) == 1) |>
  group_by(div1) |>
  filter(sample.int(n()) == 1)

form <- as.formula(
  "prop_22_over_20_1 - prop_22_over_20_0 ~ -1 + signed_is_open_pre_22 + I(hisp_1 / pop_1 - hisp_0 / pop_0) + I(nhb_1 / pop_1 - nhb_0 / pop_0)"
)
fit <- lm(form, data = neighboring_divs_lm) 
summary(fit)
## 
## Call:
## lm(formula = form, data = neighboring_divs_lm)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.31756 -0.05978 -0.00070  0.04634  0.32425 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## signed_is_open_pre_22           0.01738    0.01503   1.156    0.248    
## I(hisp_1/pop_1 - hisp_0/pop_0) -0.26663    0.06638  -4.017 7.38e-05 ***
## I(nhb_1/pop_1 - nhb_0/pop_0)   -0.24061    0.03274  -7.349 1.72e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09265 on 316 degrees of freedom
## Multiple R-squared:  0.1924, Adjusted R-squared:  0.1847 
## F-statistic:  25.1 on 3 and 316 DF,  p-value: 1.37e-14

The result: divisions in Open Wards had 1.7pp stronger turnout than divisions just across the boundary, but this result has a p-value of 0.25 and is not statistically significant (meaning we don’t have enough data to be confident it’s different from zero). This provides a confidence interval of (-1pp, 5pp).

A few notes about this analysis:

  • The result was much bigger (about 5pp) when I didn’t control for race! This means that even when comparing only division across boundaries, there are racial differences between the divisions in Open Wards and those not.
  • I’m only using one election comparison (2022 vs 2020), and we obviously have a lot more. I’ll think about ways to compellingly use more elections without introducing complications. Quick checks using 2018 vs 2016 did not substantively change the results.

So, what does this mean? Our best estimate for Open Wards’ change in turnout is a small, positive effect, but we don’t have enough data to be confident this is different from zero. Open Wards of course have other claims to benefits than just turnout: more democratic decision-making, for example. And a 2 percentage point increase in Philadelphia’s turnout, if it existed, wouldn’t be nothing: if scaled across the city, it would have meant 4,000 votes in 2019’s Superior Court election, which was decided by 17,000.

Turnout didn’t decide the election. Preferences did.

Ahead of the election, I was chatting with a reporter. They mentioned that everyone was talking about turnout. Philadelphia had seen weak relative turnout in the last two years, they pointed out, and that would decide this race.

I pushed back. Turnout is not the story here. We know basically what turnout will be. The big open question is preferences.

I wish I had gone on the record. I would have looked like a genius.

Put another way, as I explained on that Friday ahead of the election, if there were one piece of information that would help me predict the outcome, it would not be the relative turnouts of Voting Blocs. It would be Helen Gym’s performance in the Black Wards. If she gets 30%, she wins. If she gets 10%, she loses. Both seemed in play. She ended up at 14.

This brings up an important point about this Municipal Primary:

Preferences decided the election, not turnout

First, let’s be clear what I mean. It is trivially true that if zero of a candidate’s supporters turned out to vote, she would have lost. So in a completely uninteresting sense, turnout mattered.

A more useful statement is that the plausible range of turnouts in Voting Blocs had much less impact on the final result than the plausible range of preferences. The Black Voters Divisions were certainly going to represent between 35-45% of the City’s votes.

But with only limited polling, we had only a rough guess at voters’ preferences. Support for Cherelle Parker in those Divisions could have plausibly been anywhere from 30% to 60% in this crowded race. She ended up at 57.

The plausible range of turnouts in Black Voter Divisions could have swung the topline result +/- 2.5 percentage points. The plausible range of preferences in those Black Voter Divisions could have swung it +/- 6. Cherelle Parker won because she did extremely well among people we always expected to vote, and not by achieving an extreme turnout among her base.

Some Math

Let’s formalize this. A candidate’s overall proportion of the vote is the average of their proportions \(p_i\) in each geography \(i\), weighted by turnout \(t_i\).

\[ p = \frac{1}{\sum t_i} \sum t_i p_i \]

We can normalize turnout using \(\tilde{t}_i = \frac{t_i}{\sum t_i}\), so that \(\tilde{t}_i\) is each geography’s proportion of total turnout. Then

\[ p = \sum \tilde{t}_i p_i \]

Ahead of the election, we don’t know what each \(\tilde{t}_i\) and \(p_i\) is. Instead, we have priors with variances. The Law of Total Variance tells us

\[ Var(p) = E_p[Var( \sum \tilde{t}_i p_i) |\vec{p}] + Var_p(E[ \sum \tilde{t}_i p_i] |\vec{p}) \] where \(\vec{p}\) is the vector of all \(p_i\).

The expectations in the second term simply add. And we will assume that a candidate’s \(p_i\) is uncorrelated across geographies (that is, of course, the definition of my Voting Blocs).

\[\begin{align*} Var(p) &= E_p[Var( \sum \tilde{t}_i p_i) |\vec{p}] + Var_p( \sum E[\tilde{t}_i] p_i |\vec{p}) \\ &= E_p[Var( \sum \tilde{t}_i p_i) |\vec{p}] + \sum E[\tilde{t}_i] Var(p_i) \end{align*}\]

The variances in the first term are a little bit complicated, since the normalization of \(\tilde{t}\) means they will negatively covary across Divisions.

If we simplify to assuming only two geographies (for example, two Voting Blocs), then the Blocs will have a perfect -1 correlation in \(\tilde{t}\).

\[ Var(\tilde{t}) = \left[\begin{array}{rr} \sigma_t^2 & -\sigma_t^2 \\ -\sigma_t^2 & \sigma_t^2 \end{array}\right] \]

In this case, the uncertainty in the topline result reduces to

\[ Var(p) = \sigma_t^2 E[(p_1 – p_2)^2] + (E[\tilde{t}_1] Var(p_1) + E[\tilde{t}_2] Var(p_2)) \]

Which of these terms is bigger? In this past election, the second was much bigger than the first.

The standard deviation of uncertainty in turnout proportions (\(\sigma_t\)) was maybe 0.04, with expected performance differences between Blocs of maybe \(p_1 – p_2 \approx 0.4\), to be generous. That gives a contribution of \(0.04^2 \times 0.4^2 = 0.016^2\).

The standard deviation of uncertainty in candidate preferences (\(\sqrt{Var(p_i)}\)) was maybe 0.10. Since \(\sum{\tilde{t}} = 1\), that contributes the full \(0.10^2\).

The result: uncertainty in candidate’s performance in each Bloc contributed six times as much uncertainty as that of Blocs’ relative turnout!

So yeah, while it’s trivially true that with zero turnout, a candidate can’t win, it was Cherelle Parker’s high percentage among those who we expected to vote, and not a surprisingly high turnout among any group, that won the day.

A caveat

It’s important to note this analysis is for a municipal election with many candidates and sparse, uneven polling. Uncertainty in \(p\) was huge! In a Presidential election, comparatively, we know a lot more about \(p\). Uncertainty in \(t\) is probably more comparable in size to uncertainty in \(p\), though I doubt enough to actually become more important.