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Understanding Political Redistricting: Strategies, Challenges, and Legal Implications

This article explores the complexities of political redistricting in the American political system, focusing on the impact of census data and the principles of legislative representation. It examines gerrymandering, including partisan, racial, and ethnic strategies, and provides insights into the detection of gerrymandering. The discussion includes the criteria for "good" districts such as population equality, contiguity, and compactness, as well as an overview of mathematical techniques used in optimizing district design.

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Understanding Political Redistricting: Strategies, Challenges, and Legal Implications

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  1. Political Redistricting By Saad Padela

  2. The American Political System • Legislative bicameralism • Number of seats in lower house is proportional to population • Single-member districts • First-past-the-post (or plurality) voting • “One man, one vote”

  3. The Case for Redistricting • New Census data every 10 years • # of Representatives = α * Population • 0 < α < 1 • # of Representatives = # of Districts • Population rises => More seats • Districts must be redrawn

  4. Gerrymandering

  5. Types of Gerrymandering • Partisan • Democrats vs. Republicans • Bipartisan • Incumbents vs. Challengers • Racial and ethnic • Majority vs. Minority groups • “Benign” • In favor of minority groups

  6. Gerrymandering Strategies • Different election objectives • To win a single district • To win a majority of many districts • Partisan • Own votes • Win districts by the smallest margin possible • Minimize wasted votes in losing districts • Opponent's votes • Fragment them into different districts • Concentrate them into a single district

  7. Gerrymandering Strategies • Bipartisan • Maximize number of “safe” districts • Racial and ethnic • Fragment supporters of minority candidates • “Benign” • Maximize chances of minority representation by concentrating them into single districts

  8. A Linear Programming Formulation? • Easy to see • Small scholarly literature • Those who are involved in it like to keep their work secret

  9. Detection of Gerrymandering • A rich literature • Hess, S.W. 1965. “Nonpartisan Political Redistricting by Computer.” Operations Research, 13 (6), 998-1006.

  10. Good Districts are... • Equally populous • Contiguous • Compact

  11. Equal population • Easy to write as a constraint

  12. Contiguity • Highly intuitive • Sometimes tedious to code

  13. Compactness • Ambiguous • Difficult to measure • Niemi et al. 1990. “Measuring Compactness and the Role of a Compactness Standard in a Test for Partisan and Racial Gerrymandering.” The Journal of Politics, 52 (4), 1155-1181. • “A Typology of Compactness Measures” (Table 1)‏ • Dispersion • Perimeter • Population

  14. A Typology of Compactness Measures: Dispersion • District Area Compared with Area of Compact Figure • Dis7 = ratio of the district area to the area of the minimum circumscribing circle • Dis8 = ratio of the district area to the area of the minimum circumscribing regular hexagon • Dis9 = ratio of the district area to the area of the minimum convex figure that completely contains the district • Dis10 = ratio of the district area to the area of the circle with diameter equal to the district's longest axis

  15. A Typology of Compactness Measures: Dispersion • District Area Compared with Area of Compact Figure • Dis7 = ratio of the district area to the area of the minimum circumscribing circle • Dis8 = ratio of the district area to the area of the minimum circumscribing regular hexagon • Dis9 = ratio of the district area to the area of the minimum convex figure that completely contains the district • Dis10 = ratio of the district area to the area of the circle with diameter equal to the district's longest axis

  16. A Typology of Compactness Measures: Dispersion • Moment-of-inertia • Dis11 = the variance of the distances from all points in the district to the district's areal center for gravity, adjusted to range from 0 to 1 • Dis12 = average distance from the district's areal center to the point on the district perimeter reached by a set of equally spaced radial lines

  17. A Typology of Compactness Measures: Perimeter • Perimeter-only • Per1 = sum of the district perimeters • Perimeter-Area Comparisons • Per2 = ratio of the district area to the area of a circle with the same perimeter • Per4 = ratio of the perimeter of the district to the perimeter of a circle with an equal area • Per5 = perimeter of a district as a percentage of the minimum perimeter enclosing that area

  18. A Typology of Compactness Measures: Population • District Population Compared with Population of Compact Figure • Pop1 = ratio of the district population to the population of the minimum convex figure that completely contains the district • Pop2 = ratio of the district population to the population in the minimum circumscribing circle • Moment-of-inertia • Pop3 = population moment of inertia, normalized from 0 to 1

  19. Warehouse Location model • Hess, S.W. 1965. “Nonpartisan Political Redistricting by Computer.” Operations Research, 13 (6), 998-1006. • Garfinkel, R.S. And G.L. Nemhauser. 1970. “Optimal Political Districting By Implicit Enumeration techniques.” Management Science, 16 (8). • Hojati, Mehran. 1996. “Optimal Political Districting.” Computers and Operations Research, 23 (12), 1147-1161. • All these formulations have class NP

  20. Heuristic Methods • Hess, S.W. 1965. • Garfinkel, R.S. And G.L. Nemhauser. 1970. • Hojati, Mehran. 1996. • Bozkaya, B., Erkut, E., and G. Laporte. 2003. “A tabu search heuristic and adaptive memory procedure for political districting.” European Journal of Operational Research, 144, 12-26.

  21. Statistical physics? • Chou, C. and S.P. Li. 2006. “Taming the Gerrymander – Statistical physics approach to Political Districting Problem.”

  22. Criticisms of Compactness • Altman, Micah. 1998. “Modeling the effect of mandatory district compactness on partisan gerrymanders.” Political Geography, 17 (8), 989-1012. • Nonlinear effects – “electoral manipulation is much more severely constrained by high compactness than by moderate compactness” • Context-dependent, and purely relative • Asymmetrical effects on different political groups • Compactness can also disadvantage geographically concentrated minorities

  23. More Sophisticated Measures • Niemi, R. and J. Deegan. 1978. “A Theory of Political Districting.” American Political Science Review, 72 (4), 1304-1323. • Neutrality • v% of the popular vote results in s% of the seats • Range of Responsiveness • % range of the total popular vote over which seats change from one party to the other • Constant Swing Ratio • rate at which a party gains seats per increment in votes • Competitiveness • % of districts in which the “normal” vote is close to 50%

  24. Balinksi, Michel. 2008. “Fair Majority Voting (or How to Eliminate Gerrymandering).” The American Mathematical Monthly, 115 (2), 97-114.

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