Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-15T15:28:45.713Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Shape Measure for Evaluating Electoral District Patterns

Published online by Cambridge University Press:  01 August 2014

Peter J. Taylor
Peter J. Taylor*
Affiliation:
University of Newcastle upon Tyne, England
Get access Rights & Permissions [Opens in a new window]

Abstract

The concept of shape is considered in abstract terms drawing on approaches outside the electoral districting literature. The concept is broken down into a series of four divergences from “compactness” relating to “elongation,” “indentation,” “separation,” and “puncturedness.” Given this conceptual framework, the use of shape measures in electoral districting is reconsidered and a new shape measure is proposed. This assesses the indentation of a district shape and is based on the internal angles within the shape. It is suggested that this measure may be particularly relevant to the evaluation of proposed new districting patterns. The technique is illustrated using proposed new Congressional Districts for Iowa.

Type
Articles
Information
American Political Science Review , Volume 67 , Issue 3 , September 1973 , pp. 947 - 950
Copyright
Copyright © American Political Science Association 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 Celler, Emanuel, “Congressional Apportionment—Past, Present and Future” in Symposium of 12 articles on “Legislative Reapportionment,” ed. Kramer, R., Law and Contemporary Problems, 17 (Spring, 1952)Google Scholar. Hacker, Andrew, Congressional Districting (Washington: The Brookings Institution, 1964)Google Scholar.

2 Roberts, Charles, “The Donkey, the Elephant and the Gerrymander,” The Reporter (September 12th. 1952) 30–4Google Scholar. Sickels, Robert J., “Dragons, Bacon Strips and Dumb-bells—Who's Afraid of Reapportionment?” Yale Law Journal, 75 (July, 1966), 1300–8CrossRefGoogle Scholar. Tyler, Gus and Wells, David “Camel Bites Dachshund,” New Republic, 145 (November 11th, 1961), 9–10 Google Scholar.

3 Reock, Ernest C. Jr., “Measuring Compactness as a Requirement of Legislative Apportionment,” Midwest Journal of Political Science, 5 (Feb. 1961), 70–74 CrossRefGoogle Scholar. Schwartzberg, Joseph E., “Reapportionment, Gerrymanders, and the Notion of Compactness,” Minnesota Law Review, 50 (January; 1966), 443–52Google Scholar.

4 See Hempel, Carl C., Fundamentals of Concept Formation in Empirical Science (Chicago: University of Chicago Press, 1952)Google Scholar.

5 See Lee, David R. and Sallee, T. Thomas, “A Method of Measuring Shape,” Geographical Review, 60 (Oct., 1970), 555–63CrossRefGoogle Scholar.

6 Reock, p. 73. Schwartzberg, p. 448. In other subjects this approach has been used by: Miller, V. C., “A Quantitative Geomorphic Study of Drainage Basin Characteristics in the Clinch Mountain Area, Virginia and Tennessee,” Office of Naval Research, Geography Branch, Project NR 389-042, Technical Report, 3 (1953)Google Scholar; Schumm, Stanley A., “The Evolution of Drainage Basins and Slopes in Badlands at Perth Amboy, New Jersey,” Bulletin of the Geological Society of America, 67 (May 1956), 597–646 CrossRefGoogle Scholar; Gibbs, Jack P., ed., Urban Research Methods (New York, 1961), pp. 99–106 Google Scholar, and Lee and Sallee, p. 557. A short review can be found in Haggett, Peter and Chorley, Richard J., Network Analysis in Geography (London: Arnold, 1969), pp. 70–78 Google Scholar.

7 Taylor, Peter J., “Distances within Shapes: an Introduction to a New Family of Finite Frequency Distributions,” Geografiska Annaler, 53B (July, 1971), 40–53 CrossRefGoogle Scholar.

8 Taylor, Figure 3.

9 For instance, the measures proposed by Reock, Schumm and Gibb.

10 For instance, the measures proposed by Schwartzberg and Miller.

11 For the use of such measures in political districting problems compare: Kaiser, Henry F., “An Objective Method for Establishing Legislative Districts,” Midwest Journal of Political Science, 10 (May, 1966), 200–23CrossRefGoogle Scholar. Weaver, James B. and Hess, Sidney W., “A Procedure for Non-partisan Districting: Development of Computer Techniques,” Yale Law Journal, 73 (December, 1963), 288–308 CrossRefGoogle Scholar. For the use of such measures in other problems, see: Boyce, Ronald B. and Clark, W. A. V., “The Concept of Shape in Geography,” Geographical Review, 54 (Oct. 1964), 561–72CrossRefGoogle Scholar; Blair, D. H. and Biss, T. H., “The Measurement of Shape in Geography: An Appraisal of Methods and Techniques,” Bulletin of quantitative data for geographers, 11 (University of Nottingham, 1967)Google Scholar.

12 This justification for considering shape in redistricting is more explicitly recognized in the British context where size and shape are related to problems of accessibility within a constituency; see Butler, David, “The Redistribution of Seats,” Public Administration, 33 (1955), p. 127 Google Scholar.

13 Schwartzberg (“Reapportionment,” p. 447) terms these points “trijunctions,” since the base area boundaries meet in threes.

14 This point is particularly well developed by Dixon, Robert G., Democratic Representation: Reapportionment in Law and Politics (London: Oxford University Press, 1968)Google Scholar, Chapter 18. See also Taylor, Peter J., “On Some Implications of the Spatial Organization of Elections,” Transactions, Institute of British Geographers (forthcoming, 1973)Google Scholar.

15 Dixon, p. 460.

16 Taper, Bernard, Gomillion versus Lightfoot: The Tuskegee Gerrymander Case (New York: McGraw Hill, 1962)Google Scholar.

Submit a response

Comments

No Comments have been published for this article.