The listed compactness measures have inherent biases with certain types of districts. Measures that compare perimeter to area do poorly with wiggly natural boundaries like coastlines and rivers. Measures that compare district area to the area of a regular shape like a circle do better with natural features but fail with intrinsic shapes like the WV panhandles. They also don't catch districts that are gerrymandered with a cut out area since they can mimic natural boundary shapes.
District State Area Perimeter Polsby-Popper Schwartzberg Convex Hull Reock Polsby-Popper Z Score Schwartzberg Z-Score Convex Hull Z-Score Reock Z-Score Average Z-Score Polsby-Popper Rank Schwartzberg Rank Convex Hull Rank Reock Rank
HI-1 Area 541.1 Perimeter 256.6
Polsby-Popper 0.103 -1.124 61 (raw value, Z-score, and rank).
Schwartzberg 0.321 -0.705 61 (raw value, Z-score, and rank)
Convex Hull 0.609 -1.124 98 (raw value, Z-score, and rank)
Reock 0.279 -0.705 84 (raw value, Z-score, and rank)
Average Z-score -0.914
HI-2 Area 16040.5 Perimeter 1723
Polsby-Popper 0.068 -1.361 21 (raw value, Z-score, and rank).
Schwartzberg 0.261 -1.613 21 (raw value, Z-score, and rank)
Convex Hull 0.836 1.131 381 (raw value, Z-score, and rank)
Reock 0.458 0.759 326 (raw value, Z-score, and rank)
Average Z-score -0.271
Since both districts fare badly under the perimeter-based measure, it must be due to the coastline, though HI-1 is also going to be hurt for following mountain ridges - and possibly Pearl Harbor.
HI-2 does very well on Reock and Convex Hull. Area outside the state but within the convex hull or circumscribing circle must be excluded from the calculation.
Are there alternatives to using a Z-score, I suspect that most of the measures are not very linear?
Trivia question:
Which are the districts which are most compact?
Hint 1: One district is best under two different measurements.
Hint 2: At-large districts are not included, so AK, MT,WY, ND, SD, DE, and VT are excluded.
