# Measures of Plan Distance

This vignette introduces some of the most common measures of some
basic measures of the distance between plans. This offers a quick look
at how similar or different a pair of plans are. 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, `pop`

for your 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).

```
library(redistmetrics)
data(nh)
```

Note that, when computing distance between plans, you always want to
provide more than one plan. For that reason, we will also load
`nh_m`

, a matrix of plans for New Hampshire.

```
data(nh_m)
nh_m <- nh_m[, 1:4]
```

We subset it to its first four columns (the first four plans).

## Hamming Distance

The Hamming distance is a simpler metric which just considers how
many units are assigned to different districts between pairs of
plans.

The Hamming distance can be computed with:

```
dist_ham(plans = nh_m)
#> [,1] [,2] [,3] [,4]
#> [1,] 0 76 190 211
#> [2,] 76 0 240 177
#> [3,] 190 240 0 233
#> [4,] 211 177 233 0
```

## Manhattan Distance

The Manhattan distance measures how many “blocks” you would need to
move to get between plans. This is most useful in MCMC contexts, rather
than general contexts.

The Manhattan distance can be computed with:

```
dist_man(plans = nh_m)
#> [,1] [,2] [,3] [,4]
#> [1,] 0 76 190 211
#> [2,] 76 0 240 177
#> [3,] 190 240 0 233
#> [4,] 211 177 233 0
```

## Euclidean Distance

The Euclidean distance measures the square root of the summed
distances you would need to move to get between plans. This is most
useful in MCMC contexts, rather than general contexts.

The Euclidean distance can be computed with:

```
dist_euc(plans = nh_m)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.000000 8.717798 13.78405 14.52584
#> [2,] 8.717798 0.000000 15.49193 13.30413
#> [3,] 13.784049 15.491933 0.00000 15.26434
#> [4,] 14.525839 13.304135 15.26434 0.00000
```