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Political Redistricting

Political Redistricting. By Saad Padela. 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”. The Case for Redistricting.

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Political Redistricting

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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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