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Racial Redistricting and Minority Representation
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| | Unformatted Document Text:
4
ANALYSIS
19
π
BD
π
W D
π
R
n
1BD
n
1W D
n
1R
n
2BD
n
2W D
n
2R
n
3BD
n
3W D
n
3R
V (D)
Util.
1
3
1
75%
0%
25%
0%
76%
24%
0%
44%
56%
75%
0.25
2
3
1
44%
0%
56%
31%
20%
49%
0%
100%
0%
44%
0.32
3
3
1
0%
100%
0%
39%
0%
61%
36%
20%
44%
39%
0.39
4
3
1
0%
100%
0%
38%
0%
62%
37%
20%
43%
38%
0.43
5
3
1
30%
0%
70%
15%
85%
0%
30%
35%
35%
15%
0.48
1
3
2
0%
20%
80%
75%
0%
25%
0%
100%
0%
75%
0.20
2
3
2
75%
0%
25%
0%
37%
63%
0%
83%
17%
75%
0.25
3
3
2
42%
0%
58%
33%
20%
47%
0%
100%
0%
42%
0.30
4
3
2
35%
0%
65%
11%
89%
0%
29%
31%
40%
24%
0.35
5
3
2
30%
0%
70%
19%
81%
0%
26%
39%
35%
11%
0.40
1
3
3
0%
20%
80%
0%
100%
0%
75%
0%
25%
75%
0.17
2
3
3
0%
40%
60%
75%
0%
25%
0%
80%
20%
75%
0.22
3
3
3
15%
1%
85%
30%
61%
9%
30%
58%
12%
15%
0.25
4
3
3
25%
69%
6%
25%
48%
27%
25%
3%
72%
0%
0.31
5
3
3
25%
55%
20%
25%
33%
42%
25%
32%
43%
0%
0.36
1
3
4
0%
45%
55%
75%
25%
0%
0%
50%
50%
75%
0.17
2
3
4
0%
76%
24%
75%
25%
0%
0%
19%
81%
75%
0.22
3
3
4
0%
0%
100%
0%
95%
5%
75%
25%
0%
75%
0.25
4
3
4
39%
61%
0%
36%
59%
5%
0%
0%
100%
39%
0.29
5
3
4
7%
0%
93%
33%
55%
12%
35%
65%
0%
28%
0.33
1
3
5
0%
11%
89%
0%
84%
16%
75%
25%
0%
75%
0.17
2
3
5
0%
46%
54%
0%
49%
51%
75%
25%
0%
75%
0.22
3
3
5
0%
70%
30%
0%
25%
75%
75%
25%
0%
75%
0.25
4
3
5
0%
0%
100%
40%
60%
0%
35%
60%
5%
40%
0.29
5
3
5
38%
62%
0%
0%
0%
100%
37%
58%
5%
38%
0.33
Table 3: Districting plans that maximize minority voters’ utility, under the
assumptions: N
BD
= 25%, N
W D
= 40%, N
R
= 35%, X
BDBD
= 0.1, X
W DBD
=
0.3, X
RBD
= 0, χ
1W D
= 20%, χ
2W D
= χ
3W D
= 50%
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4
ANALYSIS
19
π
BD
π
W D
π
R
n
1
BD
n
1
W D
n
1
R
n
2
BD
n
2
W D
n
2
R
n
3
BD
n
3
W D
n
3
R
V (D)
Util.
1
3
1
75%
0%
25%
0%
76%
24%
0%
44%
56%
75%
0.25
2
3
1
44%
0%
56%
31%
20%
49%
0%
100%
0%
44%
0.32
3
3
1
0%
100%
0%
39%
0%
61%
36%
20%
44%
39%
0.39
4
3
1
0%
100%
0%
38%
0%
62%
37%
20%
43%
38%
0.43
5
3
1
30%
0%
70%
15%
85%
0%
30%
35%
35%
15%
0.48
1
3
2
0%
20%
80%
75%
0%
25%
0%
100%
0%
75%
0.20
2
3
2
75%
0%
25%
0%
37%
63%
0%
83%
17%
75%
0.25
3
3
2
42%
0%
58%
33%
20%
47%
0%
100%
0%
42%
0.30
4
3
2
35%
0%
65%
11%
89%
0%
29%
31%
40%
24%
0.35
5
3
2
30%
0%
70%
19%
81%
0%
26%
39%
35%
11%
0.40
1
3
3
0%
20%
80%
0%
100%
0%
75%
0%
25%
75%
0.17
2
3
3
0%
40%
60%
75%
0%
25%
0%
80%
20%
75%
0.22
3
3
3
15%
1%
85%
30%
61%
9%
30%
58%
12%
15%
0.25
4
3
3
25%
69%
6%
25%
48%
27%
25%
3%
72%
0%
0.31
5
3
3
25%
55%
20%
25%
33%
42%
25%
32%
43%
0%
0.36
1
3
4
0%
45%
55%
75%
25%
0%
0%
50%
50%
75%
0.17
2
3
4
0%
76%
24%
75%
25%
0%
0%
19%
81%
75%
0.22
3
3
4
0%
0%
100%
0%
95%
5%
75%
25%
0%
75%
0.25
4
3
4
39%
61%
0%
36%
59%
5%
0%
0%
100%
39%
0.29
5
3
4
7%
0%
93%
33%
55%
12%
35%
65%
0%
28%
0.33
1
3
5
0%
11%
89%
0%
84%
16%
75%
25%
0%
75%
0.17
2
3
5
0%
46%
54%
0%
49%
51%
75%
25%
0%
75%
0.22
3
3
5
0%
70%
30%
0%
25%
75%
75%
25%
0%
75%
0.25
4
3
5
0%
0%
100%
40%
60%
0%
35%
60%
5%
40%
0.29
5
3
5
38%
62%
0%
0%
0%
100%
37%
58%
5%
38%
0.33
Table 3: Districting plans that maximize minority voters’ utility, under the
assumptions: N
BD
= 25%, N
W D
= 40%, N
R
= 35%, X
BD
BD
= 0.1, X
W D
BD
=
0.3, X
R
BD
= 0, χ
1
W D
= 20%, χ
2
W D
= χ
3
W D
= 50%
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