1. An Objective Numerical Compactness Analysis of Committee Plan 12B vs. Public Plan E By: Douglas J. De Clue 10 October, 2011

2. 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.

3. 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

4. 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

5. 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

6. Analysis of Competing Plans E and 12B

7. 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