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 documentAs 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] # Chapter Two Project**Due:** Oct 3 by 11:59pm **Points:** 10 **Submitting:** a file upload **File Types:** doc, docx, pdf, jpg, and png **Available:** until Dec 16 at 11:59pm **Instructions:**Here’s a [video explaining the instructions for this project](#).1. **Submission Guidelines:** - Write your answer on your own sheet of paper and either scan it or take a picture of it to upload. Alternatively, type your answers into a Word document.2. **Understanding the Project:** - The project's focus is on weighted voting systems, where the weights of the players can be deceiving in terms of determining the actual power each player holds. - By manipulating the quota, the balance of power can be adjusted as desired.3. **Voting System Details:** - We will use the following weighted voting system: **[q: 5, 4, 3]**.4. **Objective:** - Determine the appropriate quota to achieve the specified BPI (Banzhaf Power Index) values.5. **Tasks:** - **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]6. **Explaining Your Solution:** - In each scenario, describe how you determined your answer. You can write a sentence or two to explain your thought process or provide the calculations to demonstrate how your proposed quota achieves these BPI values.Remember to ensure clarity and precision in your submissions, adhering to the guidelines presented above. Good luck! # Meaningful Voting SystemsThere are some limitations on what the quota could be.Here are some examples that show some problems with choosing just any number for the quota.**[4: 3, 2, 1, 1, 1]**This system has 5 players. It has a total weight of 3 + 2 + 1 + 1 + 1 = 8. Four votes are required to pass a motion.Suppose that Player One (3 votes) and Player Three (1 vote) decide to vote in favor, but Player Two (2 votes), Player Four (1 vote), and Player Five (1 vote) all oppose the motion.Then it is 4 votes in favor (3 + 1) and 4 votes against (2 + 1 + 1). Nothing is decided.In order to avoid this problem of ties, we announce that the **quota must be at least a majority of the total weight.**Here’s another example where things can go wrong.**[7: 2, 2, 1]**This system has 3 players. It has a total weight 2 + 2 + 1 = 5. Seven votes are required to pass a motion.In this case, even if all three players vote “Yes,” they will only have 5 votes, and they will never pass any motions.To avoid this problem, we announce that the **quota must be less than or equal to the total weight.**Algebraically, this looks like this:\[\frac{w_1 + w_2 + w_3 + \ldots + w_n}{2} < q \leq w_1 + w_2 + w_3 + \ldots + w_n\]In a weighted voting system with N players:

The voters may not have the same authority in some elections. As a result, their authority shifts.…

Answered: Write your answer on your own sheet of…

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ