Other Measures

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.)

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

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