Measuring the compactness of political districting plans

by Roland G. Fryer

Publisher: National Bureau of Economic Research in Cambridge, Mass

Written in English

Published: 2007 Pages: 33 Downloads: 981

Subjects:

Apportionment (Election law) -- United States,
Election districts -- United States

About the Edition

The United States Supreme Court has long recognized compactness as an important principle in assessing the constitutionality of political districting plans. We propose a measure of compactness based on the distance between voters within the same district relative to the minimum distance achievable -- which we coin the relative proximity index. We prove that any compactness measure which satisfies three desirable properties (anonymity of voters, efficient clustering, and invariance to scale, population density, and number of districts) ranks districting plans identically to our index. We then calculate the relative proximity index for the 106th Congress, requiring us to solve for each state"s maximal compactness; an NP-hard problem. Using two properties of maximally compact districts, we prove they are power diagrams and develop an algorithm based on these insights. The correlation between our index and the commonly-used measures of dispersion and perimeter is -.22 and -.06, respectively. We conclude by estimating seat-vote curves under maximally compact districts for several large states. The fraction of additional seats a party obtains when their average vote increases is significantly greater under maximally compact districting plans, relative to the existing plans.

Edition Notes

The Physical Object
Statement	Roland G. Fryer, Jr., Richard T. Holden.
Series	NBER working paper series -- working paper 13456., Working paper series (National Bureau of Economic Research) -- working paper no. 13456.
Contributions	Holden, Richard T., 1974-, National Bureau of Economic Research.
Pagination	33, [18] p. :
Number of Pages	33
ID Numbers
Open Library	OL17635537M
OCLC/WorldCa	179874790

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There are many mathematical ways to measure geometric compactness of districts that take the shape of formulas or equations, often named for their creators (e.g. Polsby-Popper, Boyce-Clark, Reock) or how they are measured (e.g. “convex hull,” “length/width ratio”). Part 1: Draw compact districts with a length/width ratio greater than Our method combines the geographic information from a political districting plan with election data to produce a persistence diagram. We are then able to visualize and analyze large ensembles of computer-generated districting plans of the type commonly used in . A substantial literature considers the problem of measuring district compactness. Young () and Niemi et al. () examine a wide variety of methods to measure compactness. Here, we seek to build on Altman (), which analyzes the historical compactness of districts in the context of districting principles and voting rights challenges. Redistricting in the United States is the process of drawing electoral district boundaries. A congressional act passed in requires that representatives be elected from single-member districts, except when a state has a single representative, in which case one state-wide at-large election be held.

number split. In the number of resulting fragments the citizen plans range from 7 to 18 while the political plans show a range of 38 to Compactness As in our examination of the plans at issue in Indiana, California and Pennsylvania, we chose the Goedicke Compactness Index as our measure of compactness. In this case we were. were used to describe various aspects of measuring compactness, convenient contiguous territory, The new districting plan shall not be used prior to the primary election of If a the political affiliations of registered voters, previous election results, or demographic. than necessary. By any common measure of compactness, the Act plan was significantly less compact than every single one of the simulated districting plans. By deviating very significantly from these traditional districting criteria of geographic compactness and preserving county boundaries, the Act plan also managed to create a total. were used to describe various aspects of measuring compactness, convenient contiguous territory, and the The new districting plan shall not be used prior to the primary election of If a selecting a proposed legislative redistricting plan and compactness was considered in selecting the second proposed legislative redistricting plan.

• Submitted plans must stand as a complete City -wide plan for districting i.e., is a mathematical compactness measure of a shape developed to quantify the degree ofgerrymandering of political districts. • The measurement is calculated as a ratio of the area of the district to. use of political and demographic data in the districting process and delegate the job to independent boards or even computer programmers with a mandate only to maximize compactness, contiguity, and respect for municipal boundaries, in many large, urban states this might lock in rather than. We also offer compactness data from our validated measure state legislative and congressional districts, “ A Unified Method of Evaluating Electoral Systems and Redistricting Plans.” American Journal of Political Science, 38, Pp. – Other Districting Systems. A districting plan can dilute minority voting Many different ways to measure compactness, but most common complaints come from appearances: relationships with political parties, incumbents or political candidates” 33 COI: Defined by Those Familiar with the.

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Measuring the compactness of political districting plans by Roland G. Fryer Download PDF EPUB FB2

Measuring the Compactness of Political Districting Plans Roland G. Fryer, Jr and Richard T. Holden NBER Working Paper No. October JEL No. H70,K19 ABSTRACT The United States Supreme Court has long recognized compactness as an important principle in assessing the constitutionality of political districting plans.

Abstract We develop a measure of compactness based on the distance between voters within the same district relative to the minimum distance achievable, which we coin the relative proximity index.

Any compactness measure that satisfies three desirable properties (anonymity of voters, efficient clustering, and invariance to scale, population density, and number of districts) ranks districting Cited by: Measuring the Compactness of Political Districting Plans ,d University Richard Holden University of New South Wales Abstract We develop a measure of compactness based on the distance between voters within the same district relative to the minimum distance achievable, which we coin the relative proximity index.

Any compactness measure that satisfies three desirable properties (anonymity of voters, efficient clustering, and invariance to scale, population density, and number of districts) ranks districting plans identically to our by: The United States Supreme Court has long recognized compactness as an important principle in assessing the constitutionality of political districting plans.

We propose a measure of compactness based on the distance between voters within the same district relative to the minimum distance achievable -- which we coin the relative proximity by: Roland G. Fryer Jr. & Richard Holden, "Measuring the Compactness of Political Districting Plans," Journal of Law and Economics, University of Chicago Press, vol.

54(3), pages - Cited by: Fryer R, Holden R. Measuring the Compactness of Political Districting Plans. Journal of Law and Economics. Cited by: Citation Fryer, Roland Gerhard, and Richard Holden.

"Measuring the Compactness of Political Districting Plans." Journal of Law and Economics 54 (3): – Measuring the Compactness of Political Districting Plans. By Roland G. Fryer and Richard Holden.

Get PDF ( KB) Cite. BibTex; Full citation Publisher: University of Chicago Press. Year: DOI identifier: / OAI identifier: Provided by: MUCC. Measuring the Compactness of Political Districting Plans. By Jr. Roland G. Fryer and Richard Holden. Abstract. We develop a measure of compactness based on the distance between voters within the same district relative to the minimum distance achievable – which we coin the relative proximity index.

Any compactness measure which satisfies. The United States Supreme Court has long recognized compactness as an important principle in assessing the constitutionality of political districting plans. We propose a measure of compactness. Get this from a library.

Measuring the compactness of political districting plans. [Roland G Fryer; Richard T Holden; National Bureau of Economic Research.] -- The United States Supreme Court has long recognized compactness as an important principle in assessing the constitutionality of political districting plans.

We propose a measure of compactness based. "Measuring the Compactness of Political Districting Plans," Scholarly ArticlesHarvard University Department of Economics.

Roland G. Fryer, Jr & Richard T. Holden, "Measuring the Compactness of Political Districting Plans," NBER Working PapersNational Bureau of Economic Research, Inc. Measuring Compactness and the Role of a Compactness Standard in a Test for Partisan and Racial Gerrymandering for creating districting plans (whether for political redistricting or for other.

Downloadable. The United States Supreme Court has long recognized compactness as an important principle in assessing the constitutionality of political districting plans.

We propose a measure of compactness based on the distance between voters within the same district relative to the minimum distance achievable -- which we coin the relative proximity index.

Measuring the Compactness of Political Districting Plans. Any compactness measure that satisfies three desirable properties (anonymity of voters, efficient clustering, and invariance to scale, population density, and number of districts) ranks districting plans identically to our index.

We then calculate the relative proximity index for the. The idea is to measure the compactness of a districting plan in a state using the average squared distance between voters within districts.

This seems like a great idea in that the measure is precisely defined and depends on where people live. I’m not quite sure how compactness would be balanced against other concerns, though.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The United States Supreme Court has long recognized compactness as an important principle in assessing the constitutionality of political districting plans.

We propose a measure of com-pactness based on the distance between voters within the same district relative to the minimum distance achievable which. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The United States Supreme Court has long recognized compactness as an important principle in assessing the constitutionality of political districting plans.

We propose a measure of compactness based on the distance between voters within the same district relative to the minimum distance achievable – which. This is the fourth comparative study of compactness measures, as applied to political districting.

We review the studies of Manninen, Young and Niemi and consolidate their listings into a single, more refined taxonomy that includes additional measures. We critique certain measures and conclude, with Niemi, that no single measure is perfect. IN SUMMARY zCompactness Measures (cont.): – – Only cause trouble in racial gerrymandering unless a very specific state test is mandated – – Still allow plenty of room for political and racial gerrymandering – – Are one of the Expert Witnesses’ ’ best friends – – Should, nonetheless, be included in viable software packages – – Deserve yet another round through the.

Political Districting, the problem of partitioning a geographical region into sub-regions as electoral districts for political seat assignment, has been widely studied by researchers of both social and mathematical sciences. Compactness on the other hand pertains to the shape of the area, is difficult to rigorously define, and can be.

“ Measuring the Compactness of Political Districting Plans.” The Journal of Law and Economics 54 (3): – doi: / Glover, F. By Roland G. Fryer Jr. and Richard T. Holden, Published on 08/01/ This book will prepare readers for the redistricting of congressional, state legislative, and local collegial bodies that will follow the Census.

Almost every state legislature will devote extensive time to redrawing its own districts along with the state's congressional districts during Chapters 2 through 5 cover the major factors involved in drawing the new maps.5/5(1). A Cluster-Theoretic Approach to Political Districting Febru Abstract Political districting has been one of the most contentious issues within American politics over the last two centuries.

Since the landmark case of Baker v. Carr, in which the United States Supreme Court ruled that the. ing standards for fair districting. Four Characteristics of Districting Plans Our ultimate goal is the normative one of proposing standards against which the quality of districting plans for political units can be judged.

Even apart from the widely accepted standards of compactness, contiguity, and equal size, a large number of other standards. Political districting: Garfinkel and Nemhauser () Compactness: dj = distance between the units of j for district j which are farthest apart.

dj = (dj measures the “range ” of the district) A(j) = area of district j is a dimensionless measure of the shape compactness of district j District j is feasible only if. A MATHEMATICAL MODEL FOR POLITICAL DISTRICTING WITH COMPACTNESS CONSIDERATION AND AN APPLICATION TO KENTUCKY SENATE DISTRICTING BY KEVIN T.

PATRICK THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Science in Agricultural and Consumer Economics in the Graduate College of the. concluded “either the Cox or Goedicke area/perimeter-squared” measure is the best way to specify compactness in a districting procedure.

By the Goedicke measure the compactness index = C.I. = pA/P2 where A is the area of a district in units of square measure and P is the perimeter of the district in the same units of linear measure.

proportional representation. Such a gerrymandered plan would have a near perfect measure of compactness using the convexity definition of compactness. Figure 9 A tenth counter-example shows why simple area-to-perimeter measures, or their inverses, do not reliably measures area compactness due to their sensitivity to size variation of districts.Compactness of a congressional district is a traditional principle in adjudicating gerrymandering claims in political redistricting.

During the last decade, many states have used compactness as an important criterion to constrain the presence of gerrymandering in the redistricting process. Analysis of partisan bias in the districting plans.Compactness of Political Districting Plans, 54 J.

LAW & ECON. () (introducing a measure of compactness of entire districting plans instead of isolated districts and taking an axiomatic approach); Clemens Puppe & Attila Tasnádi, Axiomatic Districting, 44 SOC. CHOICE & WELFARE 31 () (defin-ing normative principles that a measure of.