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Political Redistricting By Saad Padela
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Political Redistricting By Saad Padela. The American Political System Legislative bicameralism Number of seats in lower house is proportional to population.

Jan 16, 2016

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  • Political Redistricting By Saad Padela

  • The American Political SystemLegislative bicameralismNumber of seats in lower house is proportional to populationSingle-member districtsFirst-past-the-post (or plurality) votingOne man, one vote

  • The Case for RedistrictingNew Census data every 10 years# of Representatives = * Population0 < < 1# of Representatives = # of DistrictsPopulation rises => More seatsDistricts must be redrawn

  • Gerrymandering

  • Types of GerrymanderingPartisanDemocrats vs. RepublicansBipartisanIncumbents vs. ChallengersRacial and ethnicMajority vs. Minority groupsBenignIn favor of minority groups

  • Gerrymandering StrategiesDifferent election objectivesTo win a single districtTo win a majority of many districtsPartisanOwn votesWin districts by the smallest margin possibleMinimize wasted votes in losing districtsOpponent's votesFragment them into different districtsConcentrate them into a single district

  • Gerrymandering StrategiesBipartisanMaximize number of safe districtsRacial and ethnicFragment supporters of minority candidatesBenignMaximize chances of minority representation by concentrating them into single districts

  • A Linear Programming Formulation?Easy to seeSmall scholarly literatureThose who are involved in it like to keep their work secret

  • Detection of GerrymanderingA rich literatureHess, S.W. 1965. Nonpartisan Political Redistricting by Computer. Operations Research, 13 (6), 998-1006.

  • Good Districts are...Equally populousContiguousCompact

  • Equal populationEasy to write as a constraint

  • ContiguityHighly intuitiveSometimes tedious to code

  • CompactnessAmbiguousDifficult to measureNiemi 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)DispersionPerimeterPopulation

  • A Typology of Compactness Measures: DispersionDistrict Area Compared with Area of Compact FigureDis7 = ratio of the district area to the area of the minimum circumscribing circleDis8 = ratio of the district area to the area of the minimum circumscribing regular hexagonDis9 = ratio of the district area to the area of the minimum convex figure that completely contains the districtDis10 = ratio of the district area to the area of the circle with diameter equal to the district's longest axis

  • A Typology of Compactness Measures: DispersionDistrict Area Compared with Area of Compact FigureDis7 = ratio of the district area to the area of the minimum circumscribing circleDis8 = ratio of the district area to the area of the minimum circumscribing regular hexagonDis9 = ratio of the district area to the area of the minimum convex figure that completely contains the districtDis10 = ratio of the district area to the area of the circle with diameter equal to the district's longest axis

  • A Typology of Compactness Measures: DispersionMoment-of-inertiaDis11 = 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 1Dis12 = average distance from the district's areal center to the point on the district perimeter reached by a set of equally spaced radial lines

  • A Typology of Compactness Measures: PerimeterPerimeter-onlyPer1 = sum of the district perimetersPerimeter-Area ComparisonsPer2 = ratio of the district area to the area of a circle with the same perimeterPer4 = ratio of the perimeter of the district to the perimeter of a circle with an equal areaPer5 = perimeter of a district as a percentage of the minimum perimeter enclosing that area

  • A Typology of Compactness Measures: PopulationDistrict Population Compared with Population of Compact FigurePop1 = ratio of the district population to the population of the minimum convex figure that completely contains the districtPop2 = ratio of the district population to the population in the minimum circumscribing circleMoment-of-inertiaPop3 = population moment of inertia, normalized from 0 to 1

  • Warehouse Location modelHess, 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

  • Heuristic MethodsHess, 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.

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

  • Criticisms of CompactnessAltman, 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 compactnessContext-dependent, and purely relativeAsymmetrical effects on different political groupsCompactness can also disadvantage geographically concentrated minorities

  • More Sophisticated MeasuresNiemi, R. and J. Deegan. 1978. A Theory of Political Districting. American Political Science Review, 72 (4), 1304-1323.Neutralityv% of the popular vote results in s% of the seatsRange of Responsiveness% range of the total popular vote over which seats change from one party to the otherConstant Swing Ratiorate at which a party gains seats per increment in votesCompetitiveness% of districts in which the normal vote is close to 50%

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