Coalition and Critical PlayersSolve the following problem.Consider the weighted voting system [75: 50, 46, 35, 20, 3]1. What is the smallest quota?Look at the following different coalitions. Determine if any player is critical. If any player iscritical, explain why they are critical.2. {p2, p3, p4} or [46, 35, 20].Write your response below:3. {p1, р 2, р3, р4} or [50, 46, 35, 20].Write your response below:

Given the weighted voting system 75: 50, 46, 35, 20, 3

Answered: Coalition and Critical Players Solve…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose a nation has 5 states, with populations shown in the chart below. The representative body had 150 seats. Find: the standard divisor, the modified divisor, and the distribution of representatives to each state. Then complete the table. Round all standard and modified quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator
Write your answer on your own sheet of paper and either scan it or take a picture of it and upload it or type your answers into a word document As we've learned, the weights of the players can be deceiving when it comes to determining the amount of power each individual player has. By manipulating the quota, one can make the balance of power be whatever one wants. We’re going to work with this weighted voting system: [q: 5, 4, 3] Determine what to use for the quota to get the indicated BPI values. In each case, explain how you determined your answer by either writing a sentence or two to explain your thought process, or show the work to find the BPIs to prove that your quota actually works. 1) BPI(P1) = 33.33% BPI(P2) = 33.33% BPI(P3) = 33.33% [All players have equal power] 2) BPI(P1) = 60% BPI(P2) = 20% BPI(P3) = 20% 3) BPI(P1) = 50% BPI(P2) = 50% BPI(P3) = 0% [P3 is a dummy]
First Profile # of Voters C>D>B>A A>B>D>C Second Profile Ranking #of Ranking A 22-member committee is selecting a site for its next meeting. The choices are City A, City B, City C, and City D. Voters 7 C>D>B>A A>B>D>C A>B>C>D C>A>D>8 6. 5 A>B>C>D 5 4 D>C>B>A 4 (a) The committee members decide to use the pairwise comparison method to select a site in a nonbinding decision. Prior to any discussion, the 22 members rank the choices according to the first voter profile above. Show that City C is selected by the pairwise comparison method in the preliminary nonbinding decision. Complete the table below to demonstrate this. City A. Pairwise Comparison Points O (Type integers or decimals.) (b) The 4 committee members with the bottom ranking in the table rearrange their ranking after listening to the discussions. The other 18 committee members stick with their original rankings of the cities. For the official vote, the 22 members rank the choices according to the second voter profile above.…
*Contemporary Mathematics*
15. The downtown business association is electing a new chairperson and decides to use approval voting. The tally is below, where each column shows the number of voters with the particular approval vote. Which candidate wins under approval voting? Number of voters 8 7 6 3425 Rick X X X Daryl X X X X XX Beth X Maggie
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:
This is the entire problem using the Hamilton voting method.
Given the weighted voting system [q: 5, 4, 3, 2], find all values of q that would grant all players veto power. Group of answer choices 14 14, 15 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 13, 14

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