District compactness

Polsby-Popper 4 pi A / P^2, Schwartzberg P / (2 sqrt(pi A)), convex-hull ratio and Reock (area over the minimum enclosing circle, by Welzl's incremental algorithm on the hull vertices) of a simple polygon.

Usage

DistrictCompactness(polygon)

Arguments

polygon

Two-column vertex matrix (no repeated closing vertex).

Value

List.

References

Polsby, D. D. and Popper, R. D. (1991). The third criterion: compactness as a procedural safeguard against partisan gerrymandering. Yale Law and Policy Review 9, 301-353.

Reock, E. C. (1961). A note: measuring compactness as a requirement of legislative apportionment. Midwest Journal of Political Science 5, 70-74.

Examples

DistrictCompactness(rbind(c(0, 0), c(1, 0), c(1, 1), c(0, 1)))$reock
#> [1] 0.6366198