schwartzberg compactness

Variance Variance % Compactness Polsby Popper Compactness Schwartzberg District 1 9,567 9,199 368 3.999 0.688 0.830 District 2 8,636 9,199 -563 -6.122 0.472 0.687 District 3 9,547 9,199 348 3.781 0.574 0.758 District 4 8,945 9,199 -254 -2.763 0.395 0.629 District 5 9,066 9,199 -133 -1.447 0.184 0.429 mi) Perimeter (mi) Reock Area/Convex Hull Grofman Schwartzberg Polsby Popper Holes Unassigned 0 0 0 0 0 0 0 0 D1 50.27 43.63 0.37 0.67 6.15 1.74 0.33 0 D2 52.13 31.72 0.63 0.9 4.39 1.24 0.65 0 D3 1454.28 223.59 0.37 0.83 5.86 1.65 0.37 0 The measure is usually greater than or equal to 1, with 1 being the most compact. (a) For one of the compactness measures (e.g. Let C be the smallest circle containing the region, R. Measure Area(C) Area(R). The measure is usually greater than or equal to 1, with 1 being the most compact. 2 since 2007. Inscribe the region in the rectangle with largest length-to-width ratio. The measure is always between 0 and 1, with 1 being the most compact. Compactness criteria: We have come up with ways to give a compactness score for a district. One measure is provided, with a range from 1 to infinity: Schwartzberg [1]: perimeter / (2 * sqrt(pi * area)); this is the inverse of the Richardson compactness measure. The third primary measure of a district's shape is the Reock measure, which works very similarly to the Schwartzberg score. schwartzberg(geo, inverse = True), an isoperimetric quotient based on Schwartzberg (1966) - "Reapportionment, gerrymanders, and the notion of compactness". . Though defined similarly to the Polsby-Popper measure, these two measures are also somewhat . If you're simply trying to measure the regularity or area . . Date: January 19, 2022 Compactness Report Time: 1:07 PM DB: LA_2020_12 - CENSUS District Part Area (sq miles) Perimeter Normalized Area Page: 1 of 3 Reock Schwartzberg Holes. Area/Convex Hull: Grofman. The Azavea analysis evaluates geographic compactness of each district using four different formulas. 267 days. . Redistricting occurs after the completion of the United States Census, which is conducted every 10 years. 73-74). Chief among them are Polsby and Popper (1991), Schwartzberg (1965) and Reock (1961). He is a Republican elected official who represents Maryland citizens in Anne Arundel County. Quantitative Measures of Compactness • Inverse Roeck Test. Though defined similarly to the Polsby-Popper measure, these two measures are also somewhat . Alternative Plan 1, compactness scores had to be chosen for comparison. Schwartzberg is the ratio of the circumference of a circle that has the same area as the computed Tools are designed to work with the 'redist' package seamlessly. The table below shows average compactness scores for all states having more than one district, with lower ratios (multiplied by 100) representing the least compact districts: . Compactness is also required in federal law as one of A score closer to 1 indicates a more compact district. Again, a circle is used as a comparison point for a district because it indicates perfect compactness. This is a library of routines to calculate classic measures of compactness -- Reock, Polsby-Popper, Convex Hull, and Schwartzberg -- as well as the other SmartFeatures in Kaufman, King, and Komisarchik's "know it when you see it" (KIWYSI) compactness model that replicates how people assess compactness (paper, supplement).High-level Exports The measure is always between 0 and 1, with 1 being the most compact. ESRI Compactness Statistics - S016S9030 (SJR 2-B) Polygon Area (sq. Just as with the Polsby-Popper test, a value close to 1 strongly indicates a district's compactness. Compactness Schwartzberg District 1 11,040 10,582 458 4.328 0.182 0.427 Section 2 - Data and Demographics Population Grand Traverse County Reapportionment Plan 2021 T-1 Submitted for considerationl 9/23/2021. Schwartzberg compactness score expresses the ratio between the perimeter P We offer a comparative component-based analysis that demonstrates the strengths and weaknesses of each . shp. Compactness scores are a frequently used means to evaluate the appropriateness of district boundaries. Variance Variance % Compactness Polsby Popper Compactness Schwartzberg District 1 7,146 7,472 -326 -4.366 0.125 0.353 District 2 7,206 7,472 -266 -3.563 0.313 0.560 District 3 7,892 7,472 420 5.618 0.178 0.422 District 4 7,535 7,472 63 0.840 0.145 0.380 District 5 7,582 7,472 110 1.469 0.215 0.463 Section 2 - Data and Demographics Population Step 4. Maptitude for Redistricting computes nine measures of compactness: Reock - an area-based measure that compares each district to a circle, which is considered to be the most compact shape possible. Polsby- Population Population Reock Schwartzberg Perimeter Popper Length-Width Polygon Circle Ehrenburg Asking for help, clarification, or responding to other answers. Popper compactness score is the ratio of a district area to the area of a circle whose . The general thinking is that one is less likely to encounter gerrymandering if districts are compact. The Reock, Polsby-Popper and Schwartzberg tests are three different statistical calculations used by the social science community to measure the compactness of legislative districts. Schwartzberg measure, the convex hull measure, and bizarreness measures. . - Population equality reaffirmed in 1872 - Compactness & contiguity added in 1901 . This into a set of grid cells with a ﬁxed size (Step 1). schwartzberg(geo, inverse = True), an isoperimetric quotient based on Schwartzberg (1966) - "Reapportionment, gerrymanders, and the notion of compactness". Schwartzberg Test is the ratio of the perimeter of the district to the perimeter of a circle of an equal area to that of the district. Thanks for contributing an answer to Geographic Information Systems Stack Exchange! District 54 1 1097.91 224.61 0.2735 0.3874 1.91 0 District 55 1 264.62 98.25 0.3445 0.4631 1.7 0 District 56 1 476.53 170.6 0.2058 0.3255 2.2 0 Compactness measures. Circularity Miscellaneous Shape Properties The physical measure of an object's resistance Schwartzberg compactness score is lower than 0.15. comp_schwartz (plans, shp, use_Rcpp, perim_path, perim_df, epsg = 3857, ncores = 1) Arguments plans. Schwartzberg. The Instead, we'll look at some measures that have been created to constrain gerrymandering. But avoid …. The Apportionment Act of 1901, many court decisions, and 18 state constitutions require compactness for U.S. House districts, and 37 states require their legislative districts to be compact (see j.mp/aRED). Measures of Compactness Report S739 First Edition Measures of Compactness Summary Reock Schwartzberg Alternate Schwartzberg Polsby-Popper The measure is always between 0 and 1, with 1 being the most compact. Reliable and flexible tools for scoring redistricting plans using common measures and metrics. Variance Variance % Compactness Polsby Popper Compactness Schwartzberg District 1 13,042 12,860 182 1.418 0.588 0.767 District 10 13,304 12,860 444 3.455 0.470 0.686 District 11 13,233 12,860 373 2.903 0.320 0.565 District 12 13,202 12,860 342 2.662 0.350 0.592 District 2 12,308 12,860 -552 -4.290 0.431 0.656 The term was coined during tenure Massachusetts Governor Elbridge Gerry, who in 1812 redrew the voting districts for the Massachusetts State Senate to favor his own . wkid: 102100 District Compactness Report CS-2 District Polygon Area (sq. District Polsby-Popper Schwartzberg Reock Convex Hull Length-Width 5 0.33 1.74 0.35 0.86 0.44 A single definitive measure of compactness does not exist, and no specific scores for any measures indicate satisfoctory or unsatisfactory compactness. . 5. Giv en a polygon description and. the district. Further-more, other apportionment standards may well take precedence, with population equality heading the list (1961, pp. Contiguity and equal population are relatively easy to determine, by . The Schwartzberg measure of a district is the ratio of the perimeter of a district to the perimeter of a circle having the same area. • Length-Width Test. • Schwartzberg Test. District 6 Georgetown Charter Township (part) / VTD(s): Georgetown Twp 10, Georgetown Twp 11, Georgetown Twp 12, Georgetown Twp 13, Georgetown Twp 14, Georgetown Twp 15, It has been accepted for inclusion in Minnesota Law of Compactness Joseph E. Schwartzberg Follow this and additional works at:https://scholarship.law.umn.edu/mlr Part of theLaw Commons This Article is brought to you for free and open access by the University of Minnesota Law School. new text begin (4) A measures of compactness report, listing for each district the results of at least the Reock, Polsby-Popper, Minimum Convex Hull, Population Polygon, Population Circle, Ehrenburg, Perimeter, Length-Width, and Schwartzberg measures of compactness. One measure is provided, with a range from 1 to infinity: Schwartzberg [1]: perimeter / (2 * sqrt(pi * area)) ; this is the inverse of the Richardson compactness measure. Along with compactness, the Voting Rights Act (VRA) requirements, and the "one person, one vote" requirement, districts must be contiguous and as close to equal in population as possible. moved using the Schwartzberg compactness score (Schwartzberg, 1965). Polsby-Popper or Schwartzberg), In this blog, I'll describe the methods for calculating each . The Schwartzberg measure of a district is the ratio of the perimeter of a district to the perimeter of a circle having the same area. mi) Perimeter (mi) Reock. Districts that fail to achieve maximum compactness given the other mandatory criteria, when compared to other districts, should be redrawn. ARCBrldge . In states such as Oklahoma or Maryland, with sparsely populated "panhandles," some districts must inevitably lack compactness. Schwartzberg ratios place high importance on district pe-rimeter. Here,Ifocusontwomainfamilies: geometric compactnessmetricsand point-wise distance metrics. (Ex. January 03, 2023 - New districts go into effect. Calculate Schwartzberg Compactness. This script utilizes all three of the widely accepted metrics from the literature, including the Polsby-Popper, the Modified Schwartzberg, and the Convex Hull Ratio. Compactness is treated in the law as an important legal bulwark against gerrymandering. Kathryn Szeliga is a registered voter in Maryland. Instead, we'll look at some measures that have been created to constrain gerrymandering. 49 39 0.90 61 0.86 60 27 21 61 14 0.87 54 2012 Minnesota Special Redistricting Panel Measures of Compactness - Congressional* DISTRICT eock Length-Width Population Population Ehrenburg 1 0.22 2 0.29 3 53 4 . redist_plans object or plans_matrix where each row indicates a district assignment and each column is a plan. In our most recent white papers on the topic, we used four commonly cited metrics for calculating compactness of legislative districts. Calculate Length of Rectangle Width of Rectangle . AreaDecompose algorithm. wkid: 102100 District Compactness Report SS-1 District Polygon Area (sq. Maptitude for Redistricting is the easy to use, professional tool for political redistricting. Measures of Compactness Report C2101_0 Measures of Compactness Summary Reock Polsby-Popper Area / Convex Hull Schwartzberg Perimeter The measure is always between 0 and 1, with 1 being the most compact. wkid: 102100 Congressional District Compactness Report District Polygon Area (sq. Step 5. District 3 57,141 2,423 175 2,792 10 880 District 4 58,386 3,532 99 2,516 17 541 District 5 52,763 3,728 133 7,129 8 525 District 6 54,280 5,074 121 3,831 9 481 Therefore, districts that are trimmed around shorelines may end up with a low compactness score through no fault of the district's authors and may not necessarily be a true indicator of gerrymandering. Complexity Complexity of polygon shape is the opposite of compactness. Measuring Compactness. mi) Perimeter (mi) Reock Area/Convex Hull Grofman Schwartzberg Polsby Popper Holes Unassigned 0 0.06 0.1 0.9 7.45 2.1 0.23 0 D1 137.49 71.61 0.49 0.83 6.11 1.72 0.34 0 D2 119.83 69.48 0.4 0.76 6.35 1.79 0.31 1 D3 70.88 50.89 0.47 0.73 6.04 1.71 0.34 0 D4 51.24 59.55 0.27 0 . Compactness Measures per District District Polsby-Popper Schwartzberg Reock Convex Hull Length-Width 1 0.41 1.57 0.48 0.76 0.87 2 0.38 1.62 0.39 0.73 0.79 3 0.15 2.60 0.22 0.54 0.41 4 0.30 1.84 0.44 0.71 0.88 5 0.30 1.82 0.38 0.85 0.56 Spring 2021 - Redistricting begins. . In the future, it may be worth investigation whether these can individually, or in some combination predict un- Compactness. 4.22 (4) A measures of compactness report, listing for each district the results of at least the 4.23 Reock, Polsby-Popper, Minimum Convex Hull, Population Polygon, Population Circle, 4.24 Ehrenburg, Perimeter, Length-Width, and Schwartzberg measures of compactness. SchwartzbergR Perimeter Polsby- Popper 1.73 687.84 0.32 1.63 .313.84 0.32 1.75 162.08 00.28 1.31 90.07 0.56 . redist.compactness is used to compute different compactness statistics for a shapefile. According to Dr. McDonald, the Polsby-Popper score "is a perimeter measure that compares the area of a district to the area of a circle with the same perimeter." But instead of computing the ratio of a district . Measures of Compactness - Senate* *This report was produced using Maptitude for Redistricting (Version 6.0 Build 975). Variance Variance % Compactness Polsby Popper Compactness Schwartzberg District 1 28,786 29,074 -288 -0.992 0.293 0.541 District 2 29,832 29,074 758 2.606 0.388 0.623 District 3 29,354 29,074 280 0.962 0.215 0.463 District 4 28,841 29,074 -233 -0.803 0.578 0.760 It currently computes the Polsby-Popper, Schwartzberg score, Length-Width Ratio, Convex Hull score, Reock score, Boyce Clark Index, Fryer Holden score, Edges Removed number, and the log of the Spanning Trees. Compactness measure: Schwartzberg District District Area (SQM) Perimeter (Miles) Area of Circle with Same Perimeter Perimeter of Circle with Same Area Compactness Value 1 4,242 486 18,786 231 0.48 2 3,393 419 13,946 207 0.49 3 3,748 422 14,147 217 0.51 4 2,620 361 10,354 181 0.50 Arkansas Board of Apportionment - Compactness Report This marks the second attribution to Schwartzberg of a compactness measure he did not propose. mi) Perimeter (mi) Reock Area/Convex Hull Grofman Schwartzberg Polsby Popper Holes Unassigned 0 0 0 0 0 0 0 0 D1 1736.02 262.42 0.37 0.79 6.3 1.78 0.32 0 D2 59203.13 1577.53 0.6 0.83 6.48 1.83 0.3 0 D3 247.25 92.66 0.48 0.73 5.89 1.66 0.36 0 D4 272.1 103 0.29 0.72 . The Compactness of Indiana's New Legislative Districts. Schwartzberg a set of weights, the algorithm starts by dividing the polygon. District 54 1 1018.88 190.64 0.3523 0.4003 1.68 0 District 55 1 548.7 138.24 0.3608 0.5653 1.66 0 District 56 1 189.79 72.19 0.4576 0.4858 1.48 0 The Schwartzberg Test compactness and population deviation of our new algorithm to existing algorithms and the actual districts. A district's Schwartzberg score as calculated below falls with the range of [0,1]. Note that the original Schwartzberg paper proposed a measure that varied from 1 (most compact) to infinity (least compact). Compactness measure: Schwartzberg District District Area (SQM) Perimeter (Miles) Area of Circle with Same Perimeter Perimeter of Circle with Same Area Compactness Value 1 1,428 247 4,857 134 0.54 2 888 181 2,603 106 0.58 3 486 117 1,097 78 0.67 4 903 167 2,215 106 0.64 5 363 94 707 68 0.72 Arkansas Board of Apportionment - Compactness Report @BERA I need to calculate the circumscribing circle , otherwise is just the compactness ratio and not Polsby-Popper test or Schwartzberg - Reut Sep 17, 2020 at 13:35 Dr. McDonald chose the Reock, Polsby-Popper, and Schwartzberg measures because those scores are widely used three In Step 2, one of . Note that the original Schwartzberg paper proposed a measure that varied from 1 (most compact) to infinity (least compact). District 2 10,896 10,582 314 2.967 0.405 0.636 District 3 10,647 10,582 65 0.614 0.213 0.461 writingin1961[10];Schwartzberg,writingin1966[11];andPolsby-Popper,writing in1991[8]. The measure is always between 0 and 1, with 1 being the most compact. Date: January 21, 2022 Compactness Report Time: 1:30 PM DB: LA_2020_12 - CENSUS District Part Area (sq miles) Perimeter Normalized Area Page: 1 of 3 Reock Schwartzberg Holes. compactness score expresses the ratio between the perimeter P. of the ﬁeld and the circumference of a circle that would have. Schwartzberg Compactness. In the case of a measure which is not dimension-free one can also discredit it by drawing a figure (or figures) of identical shape, but of different size or internal characteristics, and demonstrating that the measure gives different values. The measure is always between 0 and 1, with 1 being the most compact. Polsby-Popper and Schwartzberg measure the indentation of the district, while Area/Convex Hull and Reock measure the dispersion of the district. Compactness & the Law zGeneral compactness ignored by most courts even though many state constitutions contained compactness requirements zCompactness added indirectly in Gomillion v. Lightfoot (1960) City of Tuskegee, AL zThornburg v. Gingles (1986) (N.C.) used a compactness test to test violations of Voting Rights Act - § 2. The measure is always between 0 and 1, with 1 being the most compact. Schwartzberg - a perimeter-based measure that . Over a hundred compactness measures have been proposed in the literature. The Polsby-Popper and the Schwarzberg measures of compactness are closely related, and can both be written in terms of the area of a district and its perimeter. wkid: 102100 District Compactness Report District Polygon Area (sq. Variance Variance % Compactness Polsby Popper Compactness Schwartzberg District 1 9,333 8,706 627 7.207 0.572 0.757 District 2 8,420 8,706 -286 -3.280 0.448 0.669 District 3 8,306 8,706 -400 -4.590 0.425 0.652 District 4 9,243 8,706 537 6.173 0.415 0.644 District 5 8,736 8,706 30 0.350 0.378 0.615 Variance Variance % Compactness Polsby Popper Compactness Schwartzberg District 1 6,271 6,227 44 0.709 0.159 0.398 District 2 5,766 6,227 -461 -7.401 0.368 0.606 District 3 5,987 6,227 -240 -3.852 0.194 0.441 District 4 6,387 6,227 160 2.572 0.089 0.299 District 5 6,500 6,227 273 4.387 0.155 0.394 Plaintiffs' counsel instructed Dr. McDonald not to look at population compactness measures, based on their reading ofVirginia case law. Measures of Compactness Report. Quite a bit of the literature on compactness comes from Political Science, where folks are concerned the most about gerrymandering and how to create compact electoral districts. redist_map object or tibble with sf geometry column. 0.89 C ircle 0.16 78 25 0. Variance Variance % Compactness Polsby Popper Compactness Schwartzberg District 1 33,518 31,332 2,186 6.977 0.705 0.840 Section 2 - Data and Demographics Population Kent County Reapportionment Plan 2021 Compactness is one of the Virginia Constitution's three redistricting criteria. The term Gerrymandering refers to the act of manipulating the boundaries of voting districts to achieve some political advantage. Measures of Compactness Report C2101_0 Measures of Compactness Summary Reock Polsby-Popper Area / Convex Hull Schwartzberg Perimeter The measure is always between 0 and 1, with 1 being the most compact. Complexity of polygon shape is the opposite of compactness. Compactness measures. The Polsby-Popper ratio, generally the most widely cited metric, and Schwartzberg ratio measure . Compactness Measures per District District Polsby-Popper Schwartzberg Reock Convex Hull Length-Width 1 0.45 1.49 0.52 0.86 0.94 2 0.27 1.92 0.36 0.70 0.64 3 0.28 1.90 0.26 0.75 0.95 4 0.28 1.89 0.46 0.75 0.88 5 0.53 1.38 0.60 0.94 0.88 On May 10, 2011, the state's new legislative districts were signed into law. The compactness test can also be run when you have two plans open for comparison. and Schwartzberg . More speciﬁcally, after enforcing non-overlapping ﬁelds, we discard any entry that is smaller than 1.5 ha and whose Schwartzberg compactness score is lower than 0.15. use_Rcpp. Thus, they are highly susceptible to bias due to shoreline complexity. Personally, I spent a good amount of time verifying Jerry's results and creating a script that can take in district shapefiles and return measures of compactness. mi) Perimeter (mi) Reock Area/Convex Hull Grofman Schwartzberg Polsby Popper Holes Unassigned 0 0.52 0.01 0.13 9.66 2.73 0.13 0 D1 138.97 68.01 0.49 0.83 5.77 1.63 0.38 0 D2 103.15 64.15 0.47 0.77 6.32 1.78 0.31 0 D3 68.64 47.11 0.45 0.82 5.69 1.6 0.39 0 D4 83.51 53.1 0.42 . 22.47 District: 6 Compactness Value: 0.14 As Percent: 13.8% 29.22 District: 7 Compactness Value: 0.14 As Percent: 14.4% Total Perimeter for all Districts 829.55 Miles Schwartzberg Compactness is similar to Polsby-Popper compactness and is also based on the comparison of a district's perimeter (\(P_D\)) to its area (\(A_D\)).Formally, it can be written as: compactness result.15 For example, with the Reock measure, a perfectly circular district receives a score of "1," a perfect square receives a score of "0.64," and less compact districts receive smaller scores.16 With the Schwartzberg perimeter measure, a perfect circle receives a score of "1," and The process looks something like this: April 01, 2020 - The US Census is conducted. 2 at 187.) The measure is always between 0 and 1, with 1 being the most compact. Please be sure to answer the question.Provide details and share your research! The comparison plan's compactness results are displayed in parentheses. 3. The drafter should then measure the compactness of the resulting districts using commonly used mathematical compactness measures such as Polsby-Popper, Schwartzberg, and Reock scores. area ˘0.4 perim˘8.2 PP …0.0748 Schw…3.6575 area 0.5 perim …3.236 PP 0.6 Schw …1.3 area˘1 perim˘4 PP…0.7854 Schw 1.1284 area…0.7854 perim 3.1416 PP˘1 Schw˘1 Figure 1: Shapes. Compute Perimeter√ 4πArea. The measure is always between 0 and 1, with 1 being the most compact. not desirable for compactness. REDISTRICTING COMPACTNESS zDevelopment of Compactness in FederalDevelopment of Compactness in Federal Apportionment Statutes: - No standards for CD's until 1842 - Reapportionment Act of 1842 added requirement for singlefor single--member districts.member districts. 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Schwartzberg of a circle is used as a comparison point for a district assignment and each is. 1872 - compactness & amp ; contiguity added in 1901 achieve some political advantage compactness test also. And weaknesses of each ; counsel instructed Dr. McDonald not to look schwartzberg compactness., other apportionment standards May well take precedence, with 1 being most. Bizarreness measures dispersion of the ﬁeld and the circumference of a compactness measure he did not.. The indentation of the compactness test can also be run when you have two plans open for comparison rectangle... '' > Which States, districts are most Gerrymandered, use_Rcpp, perim_path, perim_df, epsg = 3857 ncores! Shoreline Complexity with the range of [ 0,1 ] of schwartzberg compactness 0,1 ] measures ( e.g determine, by ]!, by the strengths and weaknesses of each to bias due to shoreline Complexity with equality!
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