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Question 9, 11.3.11 HW Seore: 403, 14 or 35 ponts Rancis Pointreact In the weighted voting system below, the weights represent voters \( A, B, C \), and so on, in that order. Anower parts (a) trough (d) \[ [54: 20,20,20,10,10] \] Dhas \( \square \) 10 vole(s) Ehas \( \square \) \( \pi \) vote(s). c. Are there any đictators? No Yes d. Which voter(s), \% any, have veto power? A. Dand Ehaviplopower. B. Al voters have veto power. C. No voter has veto power. D. A, B, and C have veto power.

Ask by Vargas Powell. in the United States
Feb 13,2025

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- (c) No - (d) C. No voter has veto power.

Solución

To solve the problem regarding the weighted voting system represented by the notation \([54: 20, 20, 20, 10, 10]\), we need to analyze the voting weights and determine the answers to parts (c) and (d). ### Known Conditions: - The quota for passing a motion is 54 votes. - The weights of the voters are as follows: - Voter A: 20 votes - Voter B: 20 votes - Voter C: 20 votes - Voter D: 10 votes - Voter E: 10 votes ### Step-by-Step Analysis: #### Part (c): Are there any dictators? A dictator in a voting system is a voter whose vote alone can determine the outcome of a vote. This means that if the dictator votes in favor, the motion passes regardless of how the other voters vote. 1. **Calculate the total votes available:** \[ \text{Total votes} = 20 + 20 + 20 + 10 + 10 = 90 \] 2. **Determine the minimum votes needed to pass a motion:** The quota is 54 votes. 3. **Check if any voter can single-handedly reach the quota:** - Voter A: 20 votes (cannot reach 54) - Voter B: 20 votes (cannot reach 54) - Voter C: 20 votes (cannot reach 54) - Voter D: 10 votes (cannot reach 54) - Voter E: 10 votes (cannot reach 54) Since no single voter can reach the quota of 54 votes alone, there are **no dictators** in this voting system. **Answer for part (c):** No #### Part (d): Which voter(s), if any, have veto power? A voter has veto power if their vote is necessary to reach the quota. This means that if the voter votes against a motion, the motion cannot pass. 1. **Identify the combinations of votes that can reach the quota without each voter:** - **Without A (20 votes):** Remaining votes = 20 + 20 + 10 + 10 = 60 (can reach 54) - **Without B (20 votes):** Remaining votes = 20 + 20 + 10 + 10 = 60 (can reach 54) - **Without C (20 votes):** Remaining votes = 20 + 20 + 10 + 10 = 60 (can reach 54) - **Without D (10 votes):** Remaining votes = 20 + 20 + 20 + 10 = 70 (can reach 54) - **Without E (10 votes):** Remaining votes = 20 + 20 + 20 + 10 = 70 (can reach 54) From this analysis, we see that removing any of the voters A, B, C, D, or E does not prevent the remaining voters from reaching the quota of 54 votes. Therefore, no voter has veto power. **Answer for part (d):** C. No voter has veto power. ### Summary of Answers: - (c) No - (d) C. No voter has veto power.

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Beyond the Answer

In the world of weighted voting systems, historical context reveals that they often reflect real-life decision-making processes in organizations and governments. The voting structure you see above mirrors how influence is distributed among voters, which can be seen in many historical assemblies, like the United Nations General Assembly, where each member has weighted votes depending on their contribution or significance. To tackle your question about dictators and veto power: a dictator is a voter whose vote alone can sway a decision regardless of the others. In your scenario, since no single voter holds enough weight to pass a motion without the help of others, it implies that there are no dictators—everyone has a stake in the decision! Veto power, on the other hand, refers to the ability of a voter to block a motion. Here, only Voter A has enough weight to prevent a motion from passing if they oppose it, making them the one to watch!

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