Concept explainers
a. Verify that the weighted voting systems
b. Based on your work in (a), explain why the two proportional weighted voting systems
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Excursions In Modern Mathematics, 9th Edition
- 1. Which of the following is the critical voter for the weighted voting system below? {18: 18,7,6,4,3} a. v1,v2,v3,v4, and v5 b. v1 and v2 c. The system is not valid. d. v2,v3,v4, and v5 2. How many winning coalitions are there in the weighted voting system below? {17: 17,6,5,3,2}arrow_forwardA telecommunication company proposed construction of a cell site tower in a certain city. To determine whether this is to be constructed, a vote is to be taken among the residents of a city and the surrounding barangays. Many residents in the barangays feel that the proposal will pass because of the large proportion of city voters who favor the construction. A poll is taken to determine if there is a significant difference in the proportion of city voters and barangay voters favoring the proposal. If 250 of 400 city voters favor the proposal and 360 of 500 barangay residents favor it, would you agree that the proportion of city voters favoring the proposal is higher than the proportion of barangay voters? Use a 0.025 level of significance.arrow_forwardFind the Banzhaf power distribution of the weighted voting system [26: 16, 14, 10, 2] Give each player's power as a fraction or decimal value Player 1: Player 2: Player 3: Player 4:arrow_forward
- The customer service of a phone company is experimenting with two different systems. On Monday, they try the first system which is based on an automated menu system. On tuesday, they try the second system in which each caller is immediately connected with a live agent. A quality control manager selects a sample of seven calls each day. He records the time for each customer to have his or her question answered. The times (in minutes) are listed in the tables. A) Find the coefficient of variation for each of the two sets of data. B) Which data set is more consistent? Automated Menu Live agent 11.7 6.2 7.4 2.9 3.9 4.4 2.9 4.1 9.2 3.4 6.3 5.2 5.5 3.7arrow_forwardRefer to the weighted voting system [15: 9,8,7] and the Shapley-Shubik definition of power. A. Which member of the sequential coalition <P2, P3, P1> is pivotal? P2 None of them are pivotal players. P3 P1 B. The Shapley-Shubik power distribution of the weighted voting system is P1: 1/3 P2: 1/3 P3: 1/3 P1: 1/2 P2: 1/2 P3: 0 P1: 2/3 P2: 1/3 P3: 0 P1: 2/3 P2: 1/6 P3: 1/6arrow_forwardplease help me with this question ASAParrow_forward
- 1. How many Winning Coalitions are there for the weighted voting system below? [ 15:10, 7, 6]arrow_forward2. Three friends decides whether to go to the night club on Friday night or not every week. The data of several votings is presented in the table. Andrey Bob Constantine | Final decision 1| yes | 2 | no 3 no 4 yes 5 yes yes yes yes yes yes no no yes no no no no yes no yes There is no more information about the voting system, the results of other polls are also unknown. Is their rule: 1) anonymous, 2) neutral, 3) monotone? Explain your answer.arrow_forwardFor the weighted voting system W={q:P1, P2, P3, P4}={16:12, 6, 4, 2). What is the BPI of P2? (answer in decimal form)arrow_forward
- A vote is to be taken among the residents of a town and the surrounding county to determine whether a proposed chemical plant should be constructed. The construction site is within the town limits, and for this reason many voters in the county believe that the proposal will pass because of the large proportion of town voters who favor the construction. To determine if there is a significant difference in the proportions of town voters and county voters favoring the proposal, a poll is taken. If 120 of 200 town voters favor the proposal and 240 of 500 county residents favor it, would you agree that the proportion of town voters favoring the proposal is higher than the proportion of county voters? Use an α = 0.05 level of significance.arrow_forwardA state official wants to know which party the voters in his state feel is best qualified to lead the country over the next 10 years. He mails a questionnaire on this subject to an SRS of 1600 voters in his state. His staff reports that 325 questionnaires have been returned, of these 241 respondents feel the Democratic Party is best qualified to lead the country over the next 10 years. Question: Please tell us: a) Population b) Samplearrow_forward3. m W Electing the president To become president of the United States, a candidate does not have to receive a majority of the popular vote. The candidate does have to win a majority of teh 538 Electoral College otes. Here is a stemplot of the number of electoral votes in 2016 for each of the 50 states and the District Columbia: or bu GSAAW W N N HTOO 20 29 00 8 5 5 600 3506 000 a w B 3 6 6 1 1 a. Find the median. 8 3 6 6 1 1 74 NA 2 3 9.1.81 Electoral Votes KEY: 515-55 4 Sheen and la cause Mean would be more b. Without doing any calculations, explain how the mean and median compare. to right parameter because its 50 states c. Is the value you found in part (a) a statistic or a parameter? Justify your answer. a large sample from all Number of subjects 4 8. Do adolescent girls eat fruit? We all know that fruit is good for us. Here is a histogram of the number of servings of fruit per day claimed by 74 seventeen-year-old girls in a study in Pennsylvania: 15 8999 2.2 Median: 2…arrow_forward
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