state needs 5 districts with 5 voting blocks, a piece. Draw the districts (labeled with A, B, C, D, and E) so that the specified party wins the most districts, and then (in both cases) provide the Polsby-Popper compactness score for all 5 districts.
state needs 5 districts with 5 voting blocks, a piece. Draw the districts (labeled with A, B, C, D, and E) so that the specified party wins the most districts, and then (in both cases) provide the Polsby-Popper compactness score for all 5 districts.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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1.
![**Redistricting and the Polsby-Popper Compactness Score**
Below are two copies of the same state, each divided into a 7x7 grid of voting blocks. Each colored square represents a voting block: red for one political party and blue for another. The state requires 5 districts, and each district consists of 5 voting blocks. The goal is to draw the districts such that the specified party wins the most districts and to then calculate the Polsby-Popper compactness score for each district.
### (a) RED WINS!
![Diagram (a)]
In this scenario, the districts are drawn such that the red party wins the most districts.
**Polsby-Popper Scores Calculation**:
\[ C(A) = \]
\[ C(B) = \]
\[ C(C) = \]
\[ C(D) = \]
\[ C(E) = \]
### (b) BLUE WINS!
![Diagram (b)]
In this scenario, the districts are drawn such that the blue party wins the most districts.
**Polsby-Popper Scores Calculation**:
\[ C(A) = \]
\[ C(B) = \]
\[ C(C) = \]
\[ C(D) = \]
\[ C(E) = \]
**Explanation of the Polsby-Popper Score**:
The Polsby-Popper score is a measure of the compactness of a given district. It is calculated using the formula:
\[ C(P) = \frac{4\pi \times \text{Area}}{(\text{Perimeter})^2} \]
where:
- **Area**: The total area of the district.
- **Perimeter**: The total perimeter of the district.
This score ranges from 0 to 1, where a score closer to 1 indicates a more compact district.
In each grid:
- The red and blue squares are intermingled.
- The challenge is to draw the districts, labeled A, B, C, D, and E, in such a way that the specified party (red or blue) wins the most districts.
- After drawing the districts, compute each district's Polsby-Popper score to evaluate the compactness of the districts.
**Observation**:
- It's possible to manipulate district boundaries (a process known as "gerrymandering") to favor one party over another, even with the same distribution of voters.
- Compactness scores help to indicate how](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffeeb79a1-23ea-4f54-b610-a8910f30c066%2Fc754c391-43a1-45b6-96f4-c2048eb2ce10%2F4ca3vci_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Redistricting and the Polsby-Popper Compactness Score**
Below are two copies of the same state, each divided into a 7x7 grid of voting blocks. Each colored square represents a voting block: red for one political party and blue for another. The state requires 5 districts, and each district consists of 5 voting blocks. The goal is to draw the districts such that the specified party wins the most districts and to then calculate the Polsby-Popper compactness score for each district.
### (a) RED WINS!
![Diagram (a)]
In this scenario, the districts are drawn such that the red party wins the most districts.
**Polsby-Popper Scores Calculation**:
\[ C(A) = \]
\[ C(B) = \]
\[ C(C) = \]
\[ C(D) = \]
\[ C(E) = \]
### (b) BLUE WINS!
![Diagram (b)]
In this scenario, the districts are drawn such that the blue party wins the most districts.
**Polsby-Popper Scores Calculation**:
\[ C(A) = \]
\[ C(B) = \]
\[ C(C) = \]
\[ C(D) = \]
\[ C(E) = \]
**Explanation of the Polsby-Popper Score**:
The Polsby-Popper score is a measure of the compactness of a given district. It is calculated using the formula:
\[ C(P) = \frac{4\pi \times \text{Area}}{(\text{Perimeter})^2} \]
where:
- **Area**: The total area of the district.
- **Perimeter**: The total perimeter of the district.
This score ranges from 0 to 1, where a score closer to 1 indicates a more compact district.
In each grid:
- The red and blue squares are intermingled.
- The challenge is to draw the districts, labeled A, B, C, D, and E, in such a way that the specified party (red or blue) wins the most districts.
- After drawing the districts, compute each district's Polsby-Popper score to evaluate the compactness of the districts.
**Observation**:
- It's possible to manipulate district boundaries (a process known as "gerrymandering") to favor one party over another, even with the same distribution of voters.
- Compactness scores help to indicate how
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Step 1: the polsby-popper score for the districts in the state,assuming that the red party wins
VIEWStep 2: the polsby-popper score for the districts in the state,assuming that the blue party wins
VIEWStep 3: the polsby popper compactness scores for the district are as follows
VIEWStep 4: therefore the blue party wins the state with a total score of 3
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