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An Objective Numerical Compactness Analysis of Committee Plan 12B vs. Public Plan E

An Objective Numerical Compactness Analysis of Committee Plan 12B vs. Public Plan E. By: Douglas J. De Clue 10 October , 2011. Compactness is a Redistricting Requirement. Districts created in the r edistricting process are required to be compact and have equal population.

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An Objective Numerical Compactness Analysis of Committee Plan 12B vs. Public Plan E

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  1. An Objective NumericalCompactnessAnalysisofCommittee Plan 12B vs. Public Plan E By: Douglas J. De Clue 10 October, 2011

  2. Compactnessis a RedistrictingRequirement • Districts created in the redistrictingprocess are required to becompact and have equal population. • Equalpopulation iswellunderstood, but compactnesshas not been explained to the committeein objective numericterms.

  3. Definition of Compactness • The more geographically compact a shapeis the more area itwillcontain for a givenperimeterlength. • The most compact geometricshapeis a perfectcircle. • Any real world districts shouldbeevaluated relative to thisidealshape.

  4. Iso-perimetric Ratio • In the case of redistricting, if one measures the perimeteraround a district, one can compare the area of that district to the area of a perfectcirclehaving the sameperimeterlength. A district shaped as a perfectcircle has a iso-perimetric ratio of 1. • The ratio of the perfectcircle area divided by the actual district area isknown as the iso-perimetric ratio. It is the best way to numericallyquantify the degree of compactness of a given district.

  5. Analysis of Competing Plans 12B and E • It is possible to use SHP (Shape) files of the plans availablefrom the Orange CountyGrowth Management, Decision Support Department to perform an iso-perimetric ratio analysis on each to mathematicallydeterminewhichis the most compact.

  6. Analysis of Competing Plans E and 12B

  7. AnalysisResults • Using the iso-perimetricanalysis technique, Public Plan E isgeometrically more compact with an overallrootmean square statisticalscoringacross all districts of 2.70 vs. 2.95 for Committee Plan 12B. • If wewerefencing off the districts, Public Plan E requiresonly 92.25% of the interiorfencelength of Commitee Plan 12B and isclearly more compact withtwentyfewer miles of fenceline.

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