o A dictator automatically has veto power. A dictator always has veto power, in any situation where a unanimous vote is required, every voter has veto power. 25) Find the Shapley-Shubik power distribution of the weighted voting system [5: 3, 2, 1, 1] 10. Here P 1 plays the role of a "spoiler"- while not having enough votes to be a dictator, the player has enough votes to prevent a motion from passing. b. Part 2: Is there a dictator? 3. (a) every player has veto power. In a weighted voting system, a voter with veto power is the same as a dictator. (d) P3 is the only player with no veto power. It is not necessary to put numbers in all of the boxes, but you should fill them in order, starting at the upper left and moving toward the lower right. B) every player has veto power. They were granted the special status of Permanent Member States at the Security Council, along with a special voting power known as the "right to veto". B) every player has veto power. 8. So my question is: In a voting system, can a dictator exist alongside players with veto powers and/or a player who is a dummy? D) For the voting system shown identify which players, if any, have veto power. A player is typically . 6) In the weighted voting system [12:11, 5, 5, A) no player has veto power. c) all voters that have veto power. Objective: Recognize the notation for weighted voting system and be able to define quota, player, dictator, dummy and veto power. In this situation, P 1 has veto power. 11. c. 12. We observed that all . This does not mean a motion is guaranteed to pass with the support of that player. C) P1 has veto power but is not a dictator. This problem has been solved! Assume the quota is the number q. See the answer See the answer See the answer done loading. Since 45/2 < 39 <45, this is a reasonable weighted voting system. systems and the second voters in the two systems and the third voters in the two systems and not change the minimal winning coalitions. If no one has veto power, and no one is a dummy., find the Banzhof power distribution. Explain why or why not. Q . Problem 2 The European Union Council (2010). With 11 votes, P 1 is called a dictator. C) P1 has veto power but is not a dictator. Exit Ticket. If there are no players that fit the description, leave the space blank. 4 This figure may differ from the sum of the percentages shown for individual countries because of . 3 These countries have accepted the obligations of Article VIII, Sections 2, 3, and 4 of the Articles of Agreement. 24) Consider the weighted voting system [8: 7, 6, 2] (a) Write down all the sequential coalitions, and in each sequential coalition underline the pivotal player. 1. 7. When the quota is 23 c. When the quota is 26 Please enter voting weights, with their multiplicities. for ordinary decisions the existing weighted voting system disproportionately favours. value of q so that no voter has veto power? When the quota is 16. 11. For each of the following weighted voting systems with 3 voters, determine if the system is equivalent to a dictatorship, unanimity, majority, clique, or chair veto (see the top of p. 432). Thus in this case no one has veto power. In weighted voting, we are most often interested in the power each voter has in influencing the outcome. d) all dummy voters . * A player cannot force a motion to pass, but can force a motion to fail Consider this weighted voting system: [12: 9, 5, 4, 2] Can P 1 make the motion pass by himself/herself? 2. An individual with one share gets the equivalent of one vote, while someone with 100 shares gets the equivalent of 100 votes. b. If no one has veto power, and no one is a dummy., find the Banzhof power distribution. Now suppose we create a new yes-no voting system by adding a clause that gives voters A veto power. Weighted voting system - individuals/political bodies can cast more bal-lots than others. c) majority rules. When the quota is 19 b. C)there are no dictators. . D) 7. b. E) none of these Refer to the weighted voting system 9:4, 3, 2, 1] and the Shapley-Shubik definition of power. Objective: Recognize the notation for weighted voting system and be able to define quota, player, dictator, dummy and veto power. (25 points) Quotas and Properties of Weighted Voting Systems Consider a weighted voting system with three players having weights 10, 5, and 2, and the quota q (assumed to be an integer, i.e., a whole number). 16) In the weighted voting system , a two-thirds majority of the votes is needed to pass a motion. 2 Voting power varies on certain matters pertaining to the General Department with use of the Fund's resources in that Department. Q. Veto Power Example (Veto Power) In the original situation [14 : 9;8;3;1], both Joe and Jim have "veto power." Definition (Veto Power) A player hasveto powerif the sum of all other votes is less than q. Identify the player who is a dictator. When major policy decisions require that the editorial Which voter(s) in the weighted voting system [9 : 5, 4, 3] have veto power? For example, if the answer is P1P1 and P2P2, enter 1,2. c. Compute the Banzhaf Power Index for this system. In a weighted voting system, is a voter with veto power the same as a dictator? (3 points) In the system [10: 4, 4, 2], nd the Banzhaf Power Index for each . Find the Banzhaf power index for a weighted voting system with 4 players where one has veto power and one is a dummy (and the other two are regular players). C) and have veto power, is a dummy. 5. 9. Ex 2 (LC): Consider the weighted voting system: [q: 6, 4, 3, 3, 2, 2]. How many distinct coalitions are there in which exactly seven members vote YES? Find the Banzhaf power distribution of the weighted voting system [33: 18, 16, 15, 2] Consider the weighted voting system [17: 13, 9, 5, 2]. Explain why or why not. A WEIGHTED SYSTEM A yes-no voting system is said to be a weighted system if it can be described by specifying real number weights for the voters and a real number quota—with no provisos or mention of veto power—such that a coalition is winning precisely when the sum of the weights of the voters in the coalition meets or exceeds the quota. Voter A is also pivotal if he or she is in position 4, where he or she brings the weight from 6 to 9. 2.7 Veto Power Consider the weighted voting system [12: 9, 5, 4, 2]. A 1. Chapter 2. D. there are no dictators. A) 5 B) 22 C) 36 D) 42 2) How many players are in this weighted voting system? How does one recognize a dictator, player with veto power, or a dummy from the weighted voting system? Veto power means you only can block any motion, not necessarily that you can pass one on your own. It was . Consider the weighted voting system [15: 8, 5, 3, 1] Identify any players who have veto power. Type of weighted voting system Veto power system CERDEÑA, Simon Christopher A. GED102-A15 . (b)There are 5 weight-2 voters, and the weight-3 voter Identify the dictators, if any. veto power of the United States is so important to decisions requiring q = 0. In such a case, no motion can pass unless that player votes for it. Weighted voting games are coalitional games in which each player has a weight (intuitively corresponding to its voting power), and a coalition is successful if the sum of its weights exceeds a given threshold. The value of the quota q is 16) _____ A) 20. A) P1 is a dictator. This is called weighted voting The quote can be a simple majority, or unanimity, or anything in between . Examples of Weighted Voting Systems Definitions Players - Weights - Quota - Dictator - Veto Power - Dummy - Coalitions - Grand Coalition - Winning Coalition - Critical Players - Critical Count - Ex 1: Looking at {101:99,98,3}, who has the power? Consider the weighted voting system [q: 15, 8, 3, 1] Find the Banzhaf power distribution of this weighted voting system, When the quota is 19. Find the Banzhaf power distribution of the weighted voting system [33: 18, 16, 15, 2] Consider the weighted voting system [17: 13, 9, 5, 2]. How many such coalitions are there? In addition, identify which player(s) is the . Group Work: Worksheet F5.1 In weighted voting, a player's weight does not always tell the full story of how much power the player holds. weighted voting system (WVS), a player's weight refers to the number of votes allotted to that player and is . A voting formula that counts votes depending on what criterion is deemed to be the most significant, such as population or wealth. Q. That is V wi < q. Chapter 11: Weighted Voting Systems For each of the following weighted voting systems, determine whether each voter (a) is a dictator, (b) is a dummy, (c) has veto power, or (d) none of these. Complete parts a. through d. below. Find the Banzhaf power index for the weighted voting system \([36: 20, 17, 16, 3]\text{. o For example: [7: 8, 4, 2, 1] A player has veto power if the combined weight of all the other players does not meet the quota. Here P 1 plays the role of a "spoiler"- while not having enough votes to be a dictator, the player has enough votes to prevent a motion from passing. TRUE: this is the de nition of \veto power." 3. A quota, and at least one weight with multiplicity must be entered. }\) Solution The voting system tells us that the quota is 36, that Player 1 has 20 votes (or equivalently, has a weight of 20), Player 2 has 17 votes, Player 3 has 16 votes, and Player 4 has 3 votes. When the quota is 18. The procedures for voting in the Council of the European Union are described in the treaties of the European Union.The Council of the European Union (or simply "Council" or "Council of Ministers") has had its voting procedure amended by subsequent treaties and currently operates on the system set forth in the Treaty of Lisbon.The system is known as qualified majority voting Weighted Voting Weighted Voting In a corporate shareholders meeting, each shareholders' vote counts proportional to the amount of shares they own. 9. But a dictator can do . A player is said to have veto power if a motion cannot pass without the support of that player. Motion. Voting System ; Voting System . A dictator has a weight that exceeds or equals the quota. Consider the weighted voting system [13: 13, 6, 4, 2] a. Power Index ways to measure the share of power that each participant in a voting system has The Shapely-Shubik Power Index Closing Product. C 3. 11)In the weighted voting system 9 : 11, 4, 2, A)P1 has veto power but is not a dictator. For example, voting by stockholders in a corporation, more votes being held by countries with stronger economic powers . B) 40. Power Distribution in Four-Player Weighted Voting Systems JOHN TOLLE Carnegie Mellon University Pittsburgh, PA 15213-3890 tolle@qwes.math.cmu.edu The Hometown Muckraker is a small newspaper with a few writers and layout person-nel, and an editorial staff of four. (So the total number of votes is V = w 1 + w 2 + + w N:) Quota: q = number of votes necessary for a motion to pass. Exit Ticket. Of course, all 5-coalitions are winning since our voting systems have no veto power. 10. (b) A player has veto power if and only if the player is a critical player in . The weighted voting system when they formed the company was [ 60: 40, 30, 25, 5]. C) 59. The Veto Power System This is one type of weigthed voting system where each voter has a veto power meaning if one voter does not vote no resolution will be passed. {54: 45,10,1} a. Analyze two different weighted voting scenarios & identify the quota and players in proper notation. False. A voter whose vote is necessary to pass any motion has veto power. Here is the voting system: [13: 13, 6, 4, 2] It's asking me to identify the dictator which is Player 1. _____ Can P 2, P 3, and P 4 make the motion pass without P 1? Consider a weighted voting system with three players. No Player has veto power. 1. A weighted voting system has five voters. Weighted Voting Systems. Let's analyze this idea of power more closely by computing the power index. In the sequential coalition P3, P2, P1, P4 . If none of them have veto power then select none. In the weighted voting system [ 57: 23, 21, 16, 12], are any of the players a dictator or a dummy or do any have veto power. In general, if a weighted 4. (a) [30: 20, 17, 10, 5]. Third, the . D) every player has veto power. 6. B)P1 and P2 have equal power, P3 is not a dummy. B. 10. 3. The value of the quota is A. [ 15: 6, 4, 4, 2] Select all that apply. Consider the weighted voting system [13: 13, 6, 4, 2] a. This video explains how to find the Banzhaf power index in a weighted voting system.Site: http://mathispower4u E) none of these. ( . ) E)none of these 11) 12)In the weighted voting system 14 : 7, 7, 6, A)P1 and P2 have equal power, P3 is a dummy. 14. Instead, it can be desirable to recognize differences by giving voters different amounts of say (weights) concerning the outcome of an election. Recall the first example of a weighted voting system we looked at [51: 49, 40, 11]. b) unanimity. 1.1 Weighted voting systems and yes-no systems Voting procedure: "support" or "object" a given motion/bill (no "ab-stain"). Key questions in coalitional games include finding coalitions that are stable (in the sense that no member of the coalition has any . Suppose we have a four-person weighted voting system with positive weights a,b,c, and d for the voters named A,B,C, and D, respectively. Solution Since no player has a weight higher than or the same as the quota, then there is no dictator. A weighted voting system has 12 members. B) has veto power, is a dummy. Identify players with veto power, if any c. Identify dummies, if any. 9. This happens because if we remove P 1 's 9 votes the sum of the remaining votes (5 + 4 + 2 = 11) is less than the . A player has veto power if and only if the player is a member of every winning coalition. Name: CHAPTER 2 Weighted Voting For questions #1 - #8: Use 36: 18, 11, 7, 4, 2 1) What is the quota of this weighted voting system? In a weighted voting system . Ex. So each permanent member has veto power. D) no player has veto power. In a weighted voting system, is a voter with veto power the same as a dictator? In a weighted voting system with 4 voters, the minimal winning coalitions are: {A, B}, {A, C}, {B, C, D} a. (b) [38: 20, 15, 12, 5]. Returning to the weighted voting system [3: 2, 1, 1] we studied two examples ago, find the number of winning and blocking coalitions for which each voter is a critical voter. The value of the quota q is: Questions 15 and 16 refer to the weighted voting system [8 : 6,3,2] and . 3. Find all the winning coalitions. 21) In the weighted voting system [13 : 12, 7, 2], A) no player has veto power. (A weight's multiplicity is the number of voters that have that weight.) An object's change in position relative to a reference point. Player 1, with 6 votes When the . This tye of voting system will occur when quota is equal to the sum of all the votes. Question: Which voter(s) in the weighted voting system [9 : 5, 4, 3] have veto power? Review I Weighted voting is any voting system where di erent voters' votes matter di erently I Examples: electoral colleges, shareholders' meetings, U.N. Security Council, parliaments I Voter P i's vote has weight w i I Total number of votes is V = w 1 + w 2 + :::+ w N I There is a quota q I Number of votes needed to pass a motion I Notation for a weighted voting system is [q : w The video provided an introduction to weighted voting. In each of the following weighted voting systems, determine which players, if any, have veto power. Beginnings We'll begin with some basic vocabulary for weighted voting systems. Let us illustrate the bottom-up construction of this set of winning coalitions: {P 1P 2P 3} ⇒ {P 1P 2P 3P 4} S {P 1P 2P 3P 4P 5} {P 1P 2P 3P 5} {P . Consider the weighted voting system $[\mathrm{q}: 15,8,3,1]$ Find the Banzhaf power distribution of this weighted voting system, a. This happens because if we remove P 1 's 9 votes the sum of the remaining votes (5 + 4 + 2 = 11) is less than the . 9. If so, select all the players that have veto power. Analyze two different weighted voting scenarios & identify the quota and players in proper notation. Short hand notation is discusses as well as the definitions of a dictactor, veto power, and dummy pla. Identify players with veto power, if any c. Identify dummies, if any. a motion. Part 1: What is the quota? Find the Banzhaf power distribution of the weighted voting system [29: 17, 12, 11, 5] Give each player's power as a fraction or decimal value. Recall that a dictator is a member that is part of every winning coalition and is not a member of any losing ones. _____ A player with weight w has veto power if . Veto Power When one person has the power to defeat or block a measure by himself. Veto Power Veto power: - must not be a dictator _____ _____. Chapter 11: Weighted Voting Systems For each of the following weighted voting systems, determine whether each voter (a) is a dictator, (b) is a dummy, (c) has veto power, or (d) none of these. to win is called the quota For example, in the US Congress, a 2/3 majority in each house is required to override a Presidential veto There are 435 votes in the House of Representatives, so 290 votes would be the quota It is not necessary to put numbers in all of the boxes, but you should fill them in order, starting at the upper left and moving toward the lower right. In the following weighted voting systems, say which voters (if any) have veto power. It's also asking me to identity the player with the veto player (if any) and/or dummy (if any). players. Describe this weighted voting system using the standard notation $\left[q: w_{1}, w_{2}, \ldots, w_{N}\right]$ Check back soon! In the weighted voting system [q : 10, 8, 6] a strict majority of the votes is needed to pass a motion. That means everybody has equal power (with any interpretation of power). Consider the weighted voting system [q: 15, 8, 3, 1] Find the Banzhaf power distribution of this weighted voting system, When the quota is 15. d. Compute the Banzhaf Power Index for this system. Find all the winning coalitions c. Find the critical voters d. Compute the Banzhaf Power Index for each of the voters e. Identify any dictator or dummies in the system 1. Weighted Voting Systems Weighted voting system: A voting system with N players, P 1;P 2;:::;P N. Weights: w i = number of votes controlled by player P i. Given the weighted voting system [5: 3, 2, 1, 1, 1], find which voters of the coalition {A, C, D, E} are critical? A weighted voting system has four voters, A, B, C, and D. List all possible coalitions of these voters. weighted voting system. B. PI has veto power but is not a dictator. Please enter voting weights, with their multiplicities. D) no player has veto power. FALSE: In this system a unanimous vote is required to reach the quota. The weighted voting system that Americans are most familiar with is the Electoral College system used to elect the President. (b) Find the Shapley-Shubik power distribution of this weighted voting system. 3. Identify any dictators, dummies, or members with veto power. 7. Give an example of a weighted voting system with 4 voters that can be described by: a) dictatorship. Now let us look at the weighted voting system [10: 11, 6, 3]. Clearly the permanent members of the UNSC have much more power than the nonpermanent members (it was after all designed this way), but how can we measure . D 2. a formal voting arrangement where each player controls a given number of votes. 2. Show that this is also a weighted voting system. . If so, who? Consider the weighted voting system [q: 8, 4, 1]. Weighted voting systems are voting systems based on the idea that not all voters are equal. Each permanent member can thus block any motion. None, Player 1 (40), Player 2 (30), Player 3 (25 . 3. 2. 85. . Answer. Why or why not? (a)Voter A is pivotal if he or she is in position 3, where he or she brings the weight to 7. 10. Q. C. every player is a dictator. Weighted voting is applicable in corporate settings, as well as decision making in parliamentary governments and voting in the United Nations Security Council. In the weighted voting system [q 8;5;4;1], if every voter has veto power what is q? In addition, identify which player(s) is the . D)P1 is a dictator. 4. 17) In the weighted voting system , the smallest possible value that the quota q can . Part 3: Do any players have veto power? In the weighted voting system [9 : 11, 4, 2] A. PI is a dictator. (b) some player has veto power. Player 1: Player 2: Player 3: Give each value as a fraction or decimal. D. 13. This weighted voting system can be written as [] = [7 :3, 2, 2, 2, 2, 2]. Consider the weighted voting system [6: 5, 2, 1] What is the weight of the coalition formed by P1 and P3? Consider a weighted voting system with three players. (The will be called P1, P2, P3, and P4.) Given the weighted voting system [51: 45, 43, 7, 5], list all blocking coalitions. the USA. 2.7 Veto Power Consider the weighted voting system [12: 9, 5, 4, 2]. If players one and two join together, they can't pass a motion without player three, so player three has veto power. 14. 4. In the weighted voting system [q:10,9,8,1,1] a two-thirds majority of the votes is needed to pass a motion. In a weighted voting system, is a voter with veto power the same as a dictator? A voter has veto power exactly when the sum of the weights of the other voters is less than the quota. B)every player is a dictator. 2. Closing Product. In the weighted voting system [30 : 12, 8, 4, 2], the minimum percentage of votes needed to pass a motion is SO A 5920/0 600/0 Questions 5 — 7 refer to the weighted voting system [35 : 32, 15, 10, 3] and the Banzhaf definition of power. Banzhaf Power Index Number of players: Two Three Four Five Six Player's weigths: P 1 : P 2 : P 3 : P 4 : Quota: There are 15 coalitions for a 4 player voting system Weighted Voting Systems The number of votes necessary for a motion (bill, amendment, etc.) Ex. . Weighted Voting Systems. B) P1 is a dictator. Chapter 2. A WEIGHTED SYSTEM A yes-no voting system is said to be a weighted system if it can be described by specifying real number weights for the voters and a real number quota—with no provisos or mention of veto power—such that a coalition is winning precisely when the sum of the weights of the voters in the coalition meets or exceeds the quota. In the system [5: 2, 2, 1], Player 1 has twice as much power as Player 3. (c) P1 is a dictator. Given the weighted voting system [30: 20, 17, 10, 5], list all minimal winning coalitions. Identify the dictators, if any. 11. C) P1 has veto power but is not a dictator. (A weight's multiplicity is the number of voters that have that weight.) If one permanent member votes no on a motion, then even with all the other members voting for the motion, the total weight of the coalition is only 4*7 + 10 = 38, and the motion fails. In 1958, the Treaty of Rome established the European Economic Community (EEC) and instituted a weighted voting system for the EEC's governance. P1P1 = P2P2 = P3P3 = P4P4 = 8. A weighted voting system has 12 members. Consider the weighted voting system [9: 9, 5, 2, 1] Identify which players: Are dictators: Have veto power, but are not dictators: Are dummies: Identify players by their number only. A quota, and at least one weight with multiplicity must be entered. Identify the type of weighted voting system it represents b. This can be thought of as the weighted voting system [39:7,7,7,7,7,1,1,1,1,1,1,1,1,1,1] Each of the permanent members by definition have veto power, and each of the nonpermanent members. The members at that time were France, Ger- Consider the weighted voting system [18: 16, 8, 4, 1] Identify any players who have veto power.
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