8.13. Political Redistricting Based on the new census information, it is time to redraw the boundaries...

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8.13. Political Redistricting Based on the new census information, it is time to redraw the boundaries of the political districts in the state of Idazona. Each district will have one representative in the next Congress, and Idazona has been allocated four representatives based on its share of the national population. The state is made up of nine counties, with populations (in thousands) shown in the table. (See the state map in Figure 8.20.) The main requirement in the formation of districts is that they produce equal popu- lations, or as close to equal as possible. Furthermore, the districts must be composed of adjacent counties without splitting any county between two or more districts. Officials in Idazona interpret the requirement to mean that if a district is created from two counties, then those two counties must share a border. Furthermore, if a district is created from three counties, then at least one of the counties must be adjacent to the other two. No dis- trict is permitted to have exactly one county or more than three counties. Mathematically, officials are seeking a districting plan for which the maximum deviation between a district population and the average district population will be as small as possible. What assignment of counties to districts will satisfy the desired conditions? County Population 1 1 2 Figure 8.20. State map of Idazona. 3 4 5 6 7 8 9 25 23 29 20 22 37 34 21 34 2 8 9 8.13. Political Redistricting Based on the new census information, it is time to redraw the boundaries of the political districts in the state of Idazona. Each district will have one representative in the next Congress, and Idazona has been allocated four representatives based on its share of the national population. The state is made up of nine counties, with populations (in thousands) shown in the table. (See the state map in Figure 8.20.) The main requirement in the formation of districts is that they produce equal popu- lations, or as close to equal as possible. Furthermore, the districts must be composed of adjacent counties without splitting any county between two or more districts. Officials in Idazona interpret the requirement to mean that if a district is created from two counties, then those two counties must share a border. Furthermore, if a district is created from three counties, then at least one of the counties must be adjacent to the other two. No dis- trict is permitted to have exactly one county or more than three counties. Mathematically, officials are seeking a districting plan for which the maximum deviation between a district population and the average district population will be as small as possible. What assignment of counties to districts will satisfy the desired conditions? County Population 1 1 2 Figure 8.20. State map of Idazona. 3 4 5 6 7 8 9 25 23 29 20 22 37 34 21 34 2 8 9

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District 1 County 1 25000 County 6 23000 County 2 5000 District 2 County 8 34000 County 21 9000 Dist... View the full answer