An Objective Numerical Compactness Analysis

ofCommittee Plan 12B vs. Public

Plan EBy: Douglas J. De Clue

10 October, 2011

Compactness is a Redistricting Requirement

• Districts created in the redistricting process are required to be compact and have equal population.

• Equal population is well understood, but compactness has not been explained to the committee in objective numeric terms.

• The more geographically compact a shape is the more area it will contain for a given perimeter length.

• The most compact geometric shape is a perfect circle.

• Any real world districts should be evaluated relative to this ideal shape.

Definition of Compactness

• In the case of redistricting, if one measures the perimeter around a district, one can compare the area of that district to the area of a perfect circle having the same perimeter length. A district shaped as a perfect circle has a iso-perimetric ratio of 1.

• The ratio of the perfect circle area divided by the actual district area is known as the iso-perimetric ratio. It is the best way to numerically quantify the degree of compactness of a given district.

Iso-perimetric Ratio

• It is possible to use SHP (Shape) files of the plans available from the Orange County Growth Management, Decision Support Department to perform an iso-perimetric ratio analysis on each to mathematically determine which is the most compact.

Analysis of Competing Plans 12B and E

Analysis of Competing Plans E and 12B

• Using the iso-perimetric analysis technique, Public Plan E is geometrically more compact with an overall root mean square statistical scoring across all districts of 2.70 vs. 2.95 for Committee Plan 12B.

• If we were fencing off the districts, Public Plan E requires only 92.25% of the interior fence length of Commitee Plan 12B and is clearly more compact with twenty fewer miles of fenceline.

Analysis Results