It’s math work
Math 103:18 Post-class Assignment 6 second chancesdue March 27, 2021 There were three learning goals for the course that were associated with Post-class Assignment 5, and for which rewrite problems are available, namely 15Power-LG1: In the setting of numerical weighted voting systems, you can list winning coalitions, and determine when a player is critical. You can compute and interpret the Banzhaf power distribution. 17Power-LG3: In the setting of non-numerical weighted voting systems, you can list winning coalitions, and determine when a player is critical. You can compute and interpret the Banzhaf power distribution. 19Power-LG5: You can explain the meanings of and distinguish among dictator, dummy, and player with veto power. You can identify players in any of these categories in a specific example. When you look up your mastery scores on Post-class Assignment 5, for each of these learning goals you will find one of four possible scores, namely Mastered (M), Progressing (P), or Needs Improvement (N), or Ungradable (U). For each of the learning goals listed above, there is a “second chance problem” below, which is an opportunity to improve one of your scores. In order to show mastery level understanding, you must show your work, i.e. you must show enough steps of your thought process to make it clear that you have understood the process of obtaining your answer. 15Power-LG1: Banzhaf power in the setting of numerical weighted voting systems. Consider the weighted voting system [14: 8, 6, 6, 4], which has players A, B, C, and D respectively. (a) List all winning coalitions for this weighted voting system, and underline the critical players in each one. (b) Find the Banzhaf power distribution for this weighted voting system. (c) How many times more actual power (as measured by Banzhaf) does A have than D? 17Power-LG3: Banzhaf power in the setting of non-numerical weighted voting systems, Consider a simplified version of the UN Security Council in which there are six players (council members) A, B, C, D, E, and F. In order for a resolution to pass, a majority of council members must vote in favor of it. Moreover, A and B have veto power while the others do not. (d) List all the winning coalitions, and underline the critical players in each one. (e) Find the Banhaf power distribution for this Council. Write each player’s share of the power in fraction form. player Banzhaf power index as a fraction A B C D E F (f) How many times more power does a player with veto power have, than a player without veto power? 19Power-LG5: Dictator, dummy, and player with veto power. The weighted voting system [19: 10, 9, 5, 3] has players A, B, C, and D respectively (a) Find all players with veto power and explain how you can tell that they have veto power, or explain why there are none. (b) Find all dummies and explain how you can tell that they are dummies, or explain why there are none. (c) If we keep the weights the same but consider different values of the quota, what are all possible values of the quota which make B have veto power? Explain your answer!