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).

## Competitiveness

### Talismanic Compactness

This is a measure which offers a balance between competitiveness
across the state and competitiveness within individual districts.

Formally, this can be written as:

\[\textrm{Talismanic Competitiveness} =
T_p (1 + \alpha T_e)\beta\]

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

```
compet_talisman(plans = nh$r_2020, shp = nh, rvote = nrv, dvote = ndv)
#> [1] 0.04953732 0.04953732
```

where `nrv`

and `ndv`

are averages of votes.
(In general, you want to compute these scores over many elections and
average them.)

## Segregation

### Dissimilarity

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 \(d\), \(g_d\), total population in district \(d\), \(t_d\), a group population proportion in a
state \(G\), and total population in
the state \(T\).

Dissimilarity can be computed with:

```
seg_dissim(plans = nh$r_2020, shp = nh, group_pop = pop_black, total_pop = pop)
#> [1] 0.0273714 0.0273714
```

## Incumbents

### Incumbent Pairings

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.

```
fake_inc <- rep(FALSE, nrow(nh))
fake_inc[c(1, 2)] <- TRUE
```

This would indicate that there are only incumbents in the first two
rows of the data.

Incumbent pairings can be computed with:

```
inc_pairs(plans = nh$r_2020, shp = nh, inc = fake_inc)
#> [1] 1 1
```