11. Consider the weighted voting system [q: 8, 4, 2, 1]. Enter your answers as percentages to two decimal places. Find the Banzhaf Power Distribution of this weighted voting system whena) q = 831B2B334b) q = 931B2B3B4c) q = 10B1323B4d) q = 14B1B23B4

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Answered: 11. Consider the weighted voting system…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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A small country consists of four states. The population of State A is 44,800, the population of State B is 52,200, the population of State C is 49,200, and the population of State D is 53,800. The total number of seats in the legislature is 100. Using a divisor of D = 1950, the modified quotas (to two decimal places) are State A: 22.97 seats, State B: 26.77 seats, State C: 25.23 seats, State D: 27.59 seats.
recall the country composed of four states, A, B, C, and D as shown in the table below. According to the country's constitution, the Congress will have 30 seats, divided among the four states according to their respective populations. Use Jefferson's method with d = 52 to apportion the seats for states A and C. Preference Table State A В D Population 220 333 415 712 (in thousands) 4 and 7 5 and 8 O 7 and 4 4 and 8
Consider two weighted voting systems: System A (50 players) and System B (48 players).The number of sequential coalitions for System A divided by the number of sequential coalitions for System B equals 2450 50 49 2500
Apportionment
The of voters who will Vote for partg candidate A, B and C is given percentage in the following table. A- 13 C No of voters Area 1 60 20 20 25000 45 30 25 60 00 Areg 2
i) A public opinion surveyed a simple random sample of 1000 voters. Respondents were classified by gender (male or female) and by voting preference (Average, Good, or Excellent). Results are shown in the contingency Table 4 below. Voting Preferences Total Average Good Excellent Male 210 120 70 400 Female 200 350 50 600 Total 410 470 120 1000 Make a clustered bar chart to show all the possibilities of voting preferences when gender is known. NOTE: DO NOT SOLVE ON EXCEL AND CLASSIFY EACH STEPS
A small country has 30 seats in congress, divided among the states according to their respective populations. The table show the populations after a 1990 census. 1.) Complete the table using Hamilton's method to apportion the seats for the populations after 1990. Round all standard quotas and the divisor to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Find the divisor. Enter your answer in the space provided below. Divisor: State Initial Quotas Final Quotas Population 1990 29,081 49,016 121,913 200,010 Standard Quotas A B C Total
Consider the weighted voting system [5: 3, 2, 1, 1], what is the weight of the coalition formed by P1 and P2? 5 3 7 4
*Contemporary Mathematics*
Consider the weighted voting system [q: 11, 8, 7, 5, 2] a. What is the total weight of the system? 33 b. What is the smallest value that the quota q can take? 18 c. What is the largest value that the quota q can take? 33 d. What is the weight of the coalition formed by P₁ and P3? 18 e. For what values of the quota q is the coalition formed by P₁ and P2 a winning coalition? Enter values in increasing order separated by a comma but no spaces. |
Alabama Paradox There are 3 states and 20 seats. In 20 years, the number of seats was increased to 21. Suppose the years are 2000 and 2020. 1.) Complete the table using Hamilton's method to apportion the 20 seats for the populations after 2000 and the 21 seats after 2020. Round all standard quotas and the divisor to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Fill in every cell. 20 seats 21 seats State Population 2000 Standard Initial Final Standard Initial Final Quotas Quotas Quotas Quotas Quotas Quotas A 5,222 В 9,677 15,821 30,720 C Total 2.) What are the two divisors? Enter your answer in the space provided below. Divisor for 20 seats: Divisor for 21 seats: 3.) Did an Alabama paradox occur? Explain your answer. Write your response below:
A panel, composed of members of 3 political parties, has 60 Democrats, 64 Republicans, and 8 Greens. A committee is chosen from the panel that is proportional to the party members and relatively prime. If a two-person leadership team is chosen randomly from the committee, how many different pairs could be selected such that both members of the team are from the same party?

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11. Consider the weighted voting system [g: 8, 4, 2, 1]. Enter your answers as percentages to two decimal places. Find the Banzhaf Power Distribution of this weighted voting system when a) q = 8 81 B2 B3 B4 b) g = 9 B1 B2 83 B4 c) q = 10 B1 B2 B3 B4 d) g = 14 B1