Inequality correlation

For any given state there is a plan which has the minimum possible range of population. In this exercise the state is divided into districts based on the 2010 congressional apportionment. The districts must be made of whole geographic units which are usually counties or equivalents like parishes in Louisiana and independent cities in Virginia. In the New England states towns are used as geographic units.

Counties that are greater than the population quota have the population divided by the quota. The population of that county is reduced to the remainder, and the number of districts in that state is reduced by the quotient. The number of districts that remain represent the maximum number of apportionment regions for the state.

A heuristic approach has been taken to identify those plans for each state. The districts must satisfy contiguity (not including point contiguity) and population equality not exceeding a maximum deviation of 0.5% or range of 1%. A graph of the data showing the range as a function of the mean number of geographic units is presented below. The graph suggests a natural measure for comparing the relative inequality of two plans. Results for the states which meet the criteria are included at the end.

The data points are best fit to an exponential curve and the range is displayed as the logarithm (base 10) to provide a straight line fit. All points were initially used in a regression, and points exceeding one standard deviation in y were excluded. Those points are shaded in yellow. A final fit was made to the remaining points. The slope of the line is -0.101 +/- 0.010 and the y intercept is 4.41 +/- 0.31. The final fit line is shown on the graph in green.

State Data

Alabama

2010 population 4,779,736; 67 counties; 7 CDs at 682,819.

Deviations for 7 regions: -342/-359/+1682/+636/-234/-1438/+158; range 3120; average deviation 707.1. http://uselectionatlas.org/FORUM/GALLERY/256_01_10_13_7_53_18.jpeg

Arkansas

2010 population 2,915,918; 75 counties; 4 CDs at 728,980.

Deviations for 4 regions: -136/+137/+138/-139; range 337; average deviation 153.0. http://uselectionatlas.org/FORUM/GALLERY/256_31_03_12_5_17_33.jpg

Connecticut

2010 population 3,574,097; 169 towns; 5 CDs at 714,819.

Deviations for 5 regions: +1/+8/0/-5/-2; range 13; average deviation 3.3. http://uselectionatlas.org/FORUM/GALLERY/256_11_04_12_3_57_39.jpg

Georgia

2010 population 9,687,652; 159 counties; 14 CDs at 691,975.

Fulton has 228,606 more than 1 CD (CDs 5 and 6 are in one region). Gwinnett has 113,346 more than 1 CD (CDs 7 and 9 are in one region).

Deviations for 12 regions: +587/+677/+139/-82/(+140)/(+644)/+354/+573/+138/+22/+708/-3897; range 4605; average deviation 663.2. The deviation of -3897 is more than 0.5% and is due to a single county (Cobb) with slightly less than the quota, but the remaining districts have much smaller deviations and the range is well under 1%. http://uselectionatlas.org/FORUM/GALLERY/256_24_05_12_7_11_21.jpg

Idaho

2010 population 1,567,582; 44 counties; 2 CDs at 783,791.

Deviations for 2 regions +1/-1; range 2; average deviation 1. http://uselectionatlas.org/FORUM/GALLERY/256_06_04_12_7_49_31.jpg

Indiana

2010 population 6,483,802; 92 counties; 9 CDs at 720,422.

Marion has 182,971 more than 1 CD (CDs 5 and 7 are in one region).

Deviations for 8 regions: +124/-60/-131/+296/(+6)/-4/+60/-288; range 584, average deviation 121.2. http://uselectionatlas.org/FORUM/GALLERY/256_03_06_12_11_07_33.jpg

Iowa

2010 population 3,046,355; 99 counties; 4 CDs at 761,589.

Deviations for 4 regions: +17/+6/-15/-9; range 32; average deviation 11.8. http://uselectionatlas.org/FORUM/GALLERY/256_27_06_12_5_24_12.jpg

This plan provides for smaller deviations than the adopted plan for IA: -41/+35/+23/-18; range 76; average deviation 29.3.

Kansas

2010 population 2,853,118; 105 counties; 4 CDs at 713,280.

Deviations for 4 regions: +4/-6/-26/+26; range 52; average deviation 15.5. http://uselectionatlas.org/FORUM/GALLERY/256_18_06_13_6_40_27.jpeg

Kentucky

2010 population 4,339,367; 120 counties; 6 CDs at 723,228.

Jefferson has 17,868 more than 1 CD (CDs 2 and 3 are in one region).

Deviations for 5 regions: -33/(-32)/-54/+16/+102; range 156; average deviation 47.3. http://uselectionatlas.org/FORUM/GALLERY/256_12_06_13_9_13_29.jpeg

Louisiana

2010 population 4,533,372; 64 parishes; 6 CDs at 755,562.

Deviations for 6 regions: +1475/-1243/-346/+338/-1141/+917; range 2718; average deviation 910.0. http://uselectionatlas.org/FORUM/GALLERY/256_13_06_13_9_40_43.jpeg

Maine

2010 population 1,328,361; 533 towns; 2 CDs at 664,181.

Deviations for 2 regions: -1/0; range 1; average deviation 0.5. http://uselectionatlas.org/FORUM/GALLERY/256_24_06_13_4_09_38.jpeg

With such a large number of towns and only two districts there are many configurations that create exact equality. This plan maintains a compact shape for CD 1 that is 99% within whole counties.

Massachusetts

2010 population 6,547,629; 351 towns; 9 CDs at 727,514.

Deviations for 9 regions: +9/+4/+31/-23/-11/+23/-33/-20/+23; range 64; average deviation 19.6. http://uselectionatlas.org/FORUM/GALLERY/256_24_06_13_7_56_12.jpeg

Mississippi

2010 population 2,967,297; 82 counties; 4 CDs at 741,824.

Deviations for 4 regions: +176/-152/-68/+45; range 328; average deviation 110.3. http://uselectionatlas.org/FORUM/GALLERY/256_01_04_12_8_24_07.jpg

Missouri

2010 population 5,988,927; 115 counties; 8 CDs at 748,616.

St Louis County is 250,338 more than 1 CD (CDs 1 and 3 are in one region).

Deviations for 7 regions: (-27)/-77/+134/+51/+21/+10/-113; range 247; average deviation 61.9. http://uselectionatlas.org/FORUM/GALLERY/256_17_05_12_11_04_02.jpg

Nebraska

2010 population 1,826,341; 93 counties; 3 CDs at 608,780.

Deviations for 3 regions: -8/+12/-3; range 20; average deviation 7.7. http://uselectionatlas.org/FORUM/GALLERY/256_05_04_12_3_04_17.jpg

Nevada

2010 population 2,700,551; 17 counties; 4 CDs at 675,138.

Clark has 600,994 more than 2 CDs (CDs 1, 3 and 4 are in one region).

Deviations for 2 regions: (+234)/-234; range 467, average deviation 233.8. http://uselectionatlas.org/FORUM/GALLERY/256_13_05_12_1_46_29.png

New Hampshire

2010 population 1,316,470; 259 towns; 2 CDs at 658,235.

Deviations for 2 regions: 0/0; range 0; average deviation 0. http://uselectionatlas.org/FORUM/GALLERY/256_08_04_12_4_47_57.jpg

With such a large number of towns and only two districts there are many configurations that create exact equality.

New Mexico

2010 population 2,059,179; 33 counties; 3 CDs at 686,393.

Deviations for 3 regions: -737/+503/+234; range 1242; average deviation 491.3. http://uselectionatlas.org/FORUM/GALLERY/256_17_06_13_10_10_23.jpeg

North Carolina

2010 population 9,535,483; 100 counties; 13 CDs at 733,499.

Mecklenburg has 186,129 more than 1 CD (CDs 8 and 12 are in one region). Wake has 167,494 more than 1 CD (CDs 1 and 13 are in one region).

Deviations for 11 regions: (+2826)/-1257/+1351/-716/-1877/-319/+352/(+3279)/+191/+3695/-971; range 6974, average deviation 1510.2. The deviation of +3695 is just over 0.5%, but the range is still within 1%. http://uselectionatlas.org/FORUM/GALLERY/256_07_06_12_4_22_25.jpg

Oklahoma

2010 population 3,751,351; 77 counties; 5 CDs at 750,270.

Deviations for 5 regions: -2/-557/-849/-1227/+2636; range 3863; average deviation 1054.3. http://uselectionatlas.org/FORUM/GALLERY/256_04_04_12_8_01_05.jpg

Rhode Island

2010 population 1,052,567; 39 towns; 2 CDs at 526,284.

Deviations for 2 regions: +2/-3; range 5; average deviation 2.5. http://uselectionatlas.org/FORUM/GALLERY/256_04_01_14_8_58_55.jpeg

Texas

2010 population 25,145,561; 254 counties; 36 CDs at 698,488.

Harris has 600,020 more than 5 CDs (CDs 27-32 are in one region). Dallas has 272,676 more than 3 CDs and Collin has 83,853 more than 1 CD (CDs 20-24 are grouped together). Tarrant has 412,058 more than 2 CDs (CDs 16-18 in one region). Bexar has 317,797 more than 2 CDs (CDs 9-11 are in one region). Travis has 325,778 more than 1 CD (CDs 13-14 are in one region). El Paso has 102,159 more than 1 CD (CDs 1-2 are in one region). Hidalgo has 76,281 more than 1 CD (CDs 6-7 are in one region).

Deviations for 20 regions: (-70)/-245/-737/+701/(-459)/(+563)/-410/(-718)/+223/(-470)/+2563/(-248)/+1409/-834/(-242)/+810/-1716/-47/+48; range 4279; average deviation 629.8. http://uselectionatlas.org/FORUM/GALLERY/256_02_06_12_9_43_11.jpg

Utah

2010 population 2,763,885; 29 counties; 4 CDs at 690,971.

Salt Lake has 338,684 more than 1 CD (CDs 2 and 3 are in one region).

Deviations for 3 regions: +461/(-15)/-445; range 906; average deviation 307.2. http://uselectionatlas.org/FORUM/GALLERY/256_14_05_12_8_24_42.jpg

Virginia

2010 population 8,001,024; 95 counties, 39 independent cities; 11 CDs at 727,366.

Fairfax County has 354,360 more than 1 CD (CDs 8 and 11 are in one region).

Deviations for 10 regions: -1887/-1993/+724/-1576/-663/-1862/-1118/(+9484)/-373/-738; range 11,447; average deviation 2041.7. The deviation of the region containing 8 and 11 exceeds 0.5%, but if the region is split into two equal districts the overall range for the districts would be less than 1%. 19 of the independent cities are entirely within one county so they can't help form unique district boundaries. http://uselectionatlas.org/FORUM/GALLERY/256_18_06_12_10_49_03.jpg

West Virginia

2010 population 1,852,994; 55 counties; 3 CDs at 617,665.

Deviations for 3 regions: +113/+2/-116; range 229; average deviation 77.1. http://uselectionatlas.org/FORUM/GALLERY/256_31_03_12_3_52_57.jpg

This is the plan presented as the whole county plan with the lowest range in the case of Tennant v Jefferson County.

Wisconsin

2010 population 5,686,986; 72 counties; 8 CDs at 710,873.

Milwaukee has 236,562 more than 1 CD (CDs 4-5 are in one region).

Deviations for 7 regions: -2794/+38/-106/(+2275)/-155/+391/+353; range 5069; average deviation 873.1. http://uselectionatlas.org/FORUM/GALLERY/256_10_06_13_8_17_01.jpeg