Gerrymandering

When politicians choose their voters

Last Time

1. An sf object is a data frame plus geometries.
2. Unary functions measure or reshape a geometry.
3. Binary predicates test how two geometries relate.
4. A spatial join matches rows by location.

Key Ideas for Today

1. Gerrymandering packs and cracks voters.
2. The mean-median score detects skew.
3. The efficiency gap compares wasted votes.
4. An ensemble shows what fair maps look like.

Concept Acquisition

1. House seats are apportioned to states by population after each census, and each state divides itself into districts that each elect one representative.
2. Whoever draws the map can pack the other party’s voters into a few districts and crack the rest across many, winning more seats with the same votes.
3. A wasted vote is one cast for a loser or for a winner beyond the number needed to win (50% + 1).
4. The mean-median score, the efficiency gap, and ensembles of random maps are three ways to measure partisan advantage, and none is a single test of fairness.
5. In Rucho v. Common Cause (2019), the Supreme Court held partisan gerrymandering nonjusticiable in federal court.

Tool Acquisition

1. No new functions: mutate() and summarize() compute each district’s vote share and the mean-median score.

Concept Application

1. Spread 275 Dem and 225 Rep voters across five districts to win as many seats as possible for one party.
2. Compute the mean-median score and the efficiency gap for a five-district election.
3. Frame the project’s question: does a new map increase partisan advantage relative to 2024?

district	D votes	R votes	Winner (D/R)
1
2
3
4
5
Total	275	225

Consider a state with 5 districts, each of which must have 100 voters and will elect a winner from its own Dem and Rep candidates. The total number of votes in the state who will vote for a Dem is 275 and the total for Rep is 225.

Question: How would you spread the voters out to ensure that Dems win as many districts as possible?

02:30

On the pinned board, draw five district columns and record a student map that wins 5 of 5 for D. Return after the packing activity and the efficiency gap.

Agenda

1. US Elections
2. Gerrymandering
3. Project

US Elections

Who do we vote for?

Federal

• President
• Representatives
• Senators

State

• Governor and other execs
• State Representatives
• State Senators
• Judges

Local

• County commissioners
• City councils
• School board members

Policies

• State Propositions
• City Measures

Congressional Districts

1. US House of Reps has 435 members allocated to states by population.
2. Each decade, a census is conducted to reapportion seats between states.
3. State legislatures determine map to divide state into districts.
4. Voters in each district vote only on their candidates.

Redistricting Rules

Source: https://districtr.org/california

Redistricting Rules

Source: https://districtr.org/california

Redistricting in CA

In CA, district maps are drawn by an independent commission.

• 14 members: 5 Dem, 5 Rep, 4 Ind.
• Commissioners
  • should be “independent from legislative influence and reasonably representative of the State’s diversity”
  • must have voted in 2/3 last elections and be registered (or not) for 5 years.
  • cannot be politically employed in past / future

Gerrymandering

Your Turn

Question: Back to our state of 275 D and 225 R voters. Spread the voters out so that Republicans win as many districts as possible.

02:00

Collect a map on the pinned board next to the opening answers. R can win 4 of 5: pack 79 D voters into one district, crack the rest at 49 per district.

Three Quantitative Approaches

1. Mean - Median Score (Grofman, 1983)
2. Efficiency Gap (Stephanopoulos and McGee, 2015)
3. Ensembles / Extreme Outliers

Mean-Median Score

The difference between the mean and the median of a party’s vote shares across districts:

\[ M = \textrm{mean}(\mathbf{v}) - \textrm{median}(\mathbf{v}) \]

Here \(\mathbf{v}\) is the vector of Republican vote shares across the \(N\) districts.

On the board, dot-plot the five R shares; mark mean (.45) and median (.51). Point out how the packed D district drags the mean down.

# A tibble: 5 × 4
  district `D votes` `R votes` Result
     <int>     <dbl>     <dbl> <chr> 
1        1        75        25 D wins
2        2        60        40 D wins
3        3        43        57 R wins
4        4        48        52 R wins
5        5        49        51 R wins

df |>
  mutate(v = `R votes` / (`R votes` + `D votes`))

# A tibble: 5 × 5
  district `D votes` `R votes` Result     v
     <int>     <dbl>     <dbl> <chr>  <dbl>
1        1        75        25 D wins  0.25
2        2        60        40 D wins  0.4 
3        3        43        57 R wins  0.57
4        4        48        52 R wins  0.52
5        5        49        51 R wins  0.51

df |>
  mutate(v = `R votes` / (`R votes` + `D votes`)) |>
  summarize(mean(v),
            median(v))

# A tibble: 1 × 2
  `mean(v)` `median(v)`
      <dbl>       <dbl>
1      0.45        0.51

df |>
  mutate(v = `R votes` / (`R votes` + `D votes`)) |>
  summarize(mean_v = mean(v),
            med_v = median(v)) |>
  mutate(mean_v - med_v)

# A tibble: 1 × 3
  mean_v med_v `mean_v - med_v`
   <dbl> <dbl>            <dbl>
1   0.45  0.51            -0.06

Mean-Median Score

The difference between the mean and the median of a party’s vote shares across districts:

\[ M = \textrm{mean}(\mathbf{v}) - \textrm{median}(\mathbf{v}) \]

Here \(\mathbf{v}\) is the vector of Republican vote shares across the \(N\) districts.

LULAC v. Perry (2006): Supreme Court declined to adopt a partisan-symmetry standard, similar to this one, for judging partisan gerrymanders.

Wasted Vote

A vote that doesn’t contribute to the election of a candidate. Two ways:

1. Votes cast for the candidate who loses.
2. Votes cast for the winning candidate beyond the number needed to win (50% + 1).

Premise: In partisan gerrymandering, the goal is to force the opposing party to waste as many votes as possible.

Efficiency Gap

The efficiency gap (EG) favoring party A over party B, for a given pattern of votes, is the difference in wasted votes divided by the total number of votes:

\[ EG = \frac{W_B - W_A}{T} \]

Where \(W_B\) is the number of wasted votes by Party B, \(W_A\) is the number of wasted votes by Party A, and \(T\) is the total votes cast.

Gill v. Whitford (2018): Supreme Court ruled the plaintiffs lacked standing and sent the case back, without deciding whether the efficiency gap is a valid test.

Your Turn

Task: Using the definition of a wasted vote, count the wasted D and R votes in each district, then compute the efficiency gap.

03:00

Debrief district by district; watch for students using 50 instead of 51 as the winning threshold.

\[ EG = \frac{173 - 72}{500} = .202 \]

Efficiency Gap

The efficiency gap (EG) favoring party A over party B, for a given pattern of votes, is the difference in wasted votes divided by the total number of votes:

\[ EG = \frac{W_B - W_A}{T} \]

Where \(W_B\) is the number of wasted votes by Party B, \(W_A\) is the number of wasted votes by Party A, and \(T\) is the total votes cast.

Gill v. Whitford (2018): Supreme Court ruled the plaintiffs lacked standing and sent the case back, without deciding whether the efficiency gap is a valid test.

Rucho v. Common Cause (2019)

But federal courts are not equipped to apportion political power as a matter of fairness, nor is there any basis for concluding that they were authorized to do so. … it is not even clear what fairness looks like in this context. … Deciding among just these different visions of fairness (you can imagine many others) poses basic questions that are political, not legal. There are no legal standards discernible in the Constitution for making such judgments… And it is only after determining how to define fairness that you can even begin to answer the determinative question: “How much is too much?”

Partisan gerrymandering is nonjusticiable: “outside the courts’ competence and therefore beyond the courts’ jurisdiction.”

Ensemble

A large collection of random district maps that all meet non-partisan criteria for a fair map. A proposed map whose partisan advantage is extreme compared to the ensemble is an extreme outlier.

Process:

1. Articulate non-partisan criteria for good maps, e.g. population equality, contiguity, compactness, and minimizing split counties.
2. Use a computer (MCMC) to generate many random maps that perform well on these criteria (the ensemble).
3. Compare the proposed map to the ensembles on measures of partisan advantage.

On the board, sketch a histogram of EG across ensemble maps; draw the proposed map as a line in the far tail. “Extreme outlier” = out here.

Words of Wisdom

Moon Duchin, from Political Geometry:

Things I Don’t Believe In

1. Presenting any single number as a metric of fairness
2. Especially any single number with a prescribed ideal
3. Redistricting as optimization

Things I Do Believe In

1. Using quantitative information to tell a qualitative story

Select items from “Political Geometry”, p. 25

Guess the Metaphor

A district map is like a walled city: whoever lays out the walls decides who lives inside them. Ring one party’s neighborhoods with a single wall and they’re packed; run a wall through the middle of a neighborhood and it’s cracked.

Project: Gerrymandering

Research Question

Will adoption of a new district map lead to an increase in partisan advantage?

If so, by how much?

Research Question

Will adoption of a new district map lead to an increase in partisan advantage relative to 2024?

If so, by how much?

Data needed to measure partisan advantage

• Election results
• District boundaries

2024 Election Results

Key Ideas for Today

1. Gerrymandering packs and cracks voters.
2. The mean-median score detects skew.
3. The efficiency gap compares wasted votes.
4. An ensemble shows what fair maps look like.

For Next Time

1. Sign up for Quiz 5 (11/2-11/3).
2. Finish PS 5, due 10/31.
3. Project Studio 4 is the week of 11/2.

References

• Political Geometry, Moon Duchin and Olivia Walch.
• A Citizen’s Guide to Redistricting, the Brennan Center for Justice.
• How the Efficiency Gap Standard Works, the Brennan Center for Justice.