| district | D votes | R votes | Result |
|---|---|---|---|
| 1 | |||
| 2 | |||
| 3 | |||
| 4 | |||
| 5 | |||
| Total | 275 | 225 |
When politicians choose their voters
I’ve made printouts describing Prop 50 for you to peruse. There are 25 copies in the back corners of the lecture hall: help yourself.
| district | D votes | R votes | Result |
|---|---|---|---|
| 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.
How would you spread the voters out to ensure that Dems win as many districts as possible?
02:30





In CA, district maps are drawn by an independent commmision.
Suppose we observe an election where the vote share for Republicans in each of \(n\) districts is \(v_1, \ldots, v_N\).
The mean-median score is:
\[ M = \textrm{mean}(v_i) - \textrm{median}(v_i) \]
# 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
# A tibble: 5 × 5
district `D votes` `R votes` Result v_i
<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
# A tibble: 1 × 2
`mean(v_i)` `median(v_i)`
<dbl> <dbl>
1 0.45 0.51
# A tibble: 1 × 3
mean_v med_v `mean_v - med_v`
<dbl> <dbl> <dbl>
1 0.45 0.51 -0.06
Suppose we observe an election where the vote share for Republicans in each of \(n\) districts is \(v_1, \ldots, v_N\).
The mean-median score is:
\[ M = \textrm{mean}(v_i) - \textrm{median}(v_i) \]
LULAC v. Perry (2006): Supreme Court declined standards use a standard of partisan gerrymandering similar to this one.
Premise: In partisan gerrymandering, the goal is to force the opposing party to waste as many votes as possible.
Definition: A “wasted” vote doesn’t contribute to the election of a candidate. Two ways:
Suppose two parties, A and B. The efficiency gap (EG) favoring party A for a given pattern of votes, is defined as 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 did not issue an opinion; sent back to lower courts.
\[ EG = \frac{173 - 72}{500} = .202 \]
Suppose two parties, A and B. The efficiency gap (EG) favoring party A for a given pattern of votes, is defined as 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 did not issue an opinion; sent back to lower courts.
Federal courts are neither equipped nor authorized to apportion political power as a matter of fairness. It is not even clear what fairness looks like in this context. Deciding among… different visions of fairness 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 one can even begin to answer the determinative question: “How much is too much?”
Partisan gerrymandering is nonjusticiable: “outide the courts competence and therefore beyond the courts’ juristiction”.
General idea: Define what fair maps look like and then determine whether a proposed map is extreme in comparison.
Moon Duchin, from Political Geometry:
Things I Don’t Believe In
Things I Do Believe In
Will adoption of a new district map lead to an increase in partisan advantage?
If so, by how much?
Will adoption of a new district map lead to an increase in partisan advantage relative to 2024?
If so, by how much?
