Redistricting is problem with
many, many dimensions. This vignette introduces some useful measures
related to redistricting, but with smaller categories. See the vignette
“Using redistmetrics” for the bare-bones of the
package.
We first load the redistmetrics package and data from
New Hampshire. For any function, the shp argument can be
swapped out for your data, rvote and dvote for
any two party votes, pop_black for any group population,
pop for the total population, and the plans
argument can be swapped out for your redistricting plans (be it a single
plan, a matrix of plans, or a redist_plans object).
This is a measure which offers a balance between competitiveness across the state and competitiveness within individual districts.
Formally, this can be written as:
Talismanic Competitiveness = Tp(1 + αTe)β
where
$$ T_p = \frac{1}{n_d} * \sum_{k=1}^{n_\textrm{dists}} \big|\frac12 - \textrm{voteshare}_D\big|$$ $$ T_e = |\frac{n_\textrm{dists} - Seats_D}{n_\textrm{dists}}-\frac12| $$
Talismanic Compactness can be computed with
where nrv and ndv are averages of votes.
(In general, you want to compute these scores over many elections and
average them.)
Dissimilarity describes how similar the demographic proportions in districts are to the total state population’s demographics.
Formally, this can be written as:
$$ \textrm{Dissimilarity} = \sum_{i = 1}^{n_\textrm{dists}} \frac{(t_d |g_d - G|)}{2T*G(1 - G)}$$
for a group population proportion in district d, gd, total population in district d, td, a group population proportion in a state G, and total population in the state T.
Dissimilarity can be computed with:
We compute incumbent pairings as the number of incumbents who are placed into a district with other incumbents beyond those allowed. Formally, this is:
$$\textrm{Inc. Pairs} = \sum_{d = 1}^{\textrm{ndists}}\max(0, ~n^{(d)}_{inc} - 1)$$
We do not have incumbent data included for New Hampshire. As such, we create fake incumbent data.
This would indicate that there are only incumbents in the first two rows of the data.
Incumbent pairings can be computed with: