Consider a weighted voting system with three players. If only Player 1 has veto power, and there are no dummies, find the Banzhof power distribution.
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Consider a weighted voting system with three players. If only Player 1 has veto power, and there are no dummies, find the Banzhof power distribution.
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- The students in a class get to decide on the color of the classroom. The two choices are blue and yellow. Polling shows yellow is preferred by a small majority, 53% for yellow to 47% for blue. However, before the vote is held, a new color choice is added: red. Not a lot of people like red, but there are some yellow supporters who would actually vote for red. The results of the vote are below. Blue Yellow Red 46% 44% 10% What statement below is correct about adding a third choice to the plurality vote? O a Ob Oc d Red did not win the vote, but it draws enough support away from yellow to make blue the winner, even though a majority of students preferred yellow over blue when there were two choices. Red did not win the vote, but it had no effect on drawing enough support away from yellow to make blue the winner, even though a majority of students preferred yellow over blue when there were two choices. Red did not win the vote, so because of this, yellow should win the vote over blue.…Consider a weighted voting system with three players. If Players 1 and 2 have veto power, and Player 3 is a dummy, find the Banzhof power distribution.A committee consists of five executives, three women and two men. Their names are Maria (M),John (J), Susan (S), Will (W) and Holly (H). The committee needs to select a chairperson and a secretary. Itdecides to make the selection randomly by drawing straws. The person getting the longest straw will beappointed chairperson, and the one getting the shortest straw will be appointed as secretary. The possibleoutcomes can be represented in the following manner.MS SM HM JM WM MH SH HS JS WSMJ SJ HJ JH WH MW SW HW JW WJHere, for example, MS represents the outcome that Maria is appointed chairperson and Susan is appointed assecretary.(a) List the outcomes constitution each of the following four eventsA = Event a male is appointed chairpersonB = Event Holly is appointed chairpersonC = Event Will is appointed secretaryD = Event only females are appointed(b) Calculate P(not A)(c) Calculate P(B and D)(d) Calculate P(B or C) (maria,susan and holly are female/women and john and will are male)
- The city of Raleigh has 6,000 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 350 randomly selected registered voters was conducted. 151 said they'd vote for Brown, 191 said they'd vote for Feliz, and 8 were undecided.Use this information from the sample to complete the following statements about the population of all registered voters in Raleigh. Round your answers to the nearest person.Based on this sample, we could expect _____ of the 6,000 registered voters to vote for Brown. Based on this sample, we could expect _____ of the 6,000 registered voters to vote for Feliz. Based on this sample, _____ of the 6,000 registered voters are still undecided.A 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.A public opinion poll in Ohio wants to determine whether registered voters in the state approve of a measure to ban smoking in all public areas. They randomly select 50 voters from each county in the state and ask whether they approve or disapprove of the measure.This is an example of
- In 2012 American Idol completed its 11th season withJennifer Lopez, Steven Tyler, and Randy Jackson asjudges. Although the judges express their opinions aboutthe contestants’ performances, viewers vote to keep theirfavorites in the competition. During each episode, hostRyan Seacrest explains how viewers can vote via text,phone call, or online. Nothing prevents a viewer fromsubmitting multiple votes. Each week the contestant with the lowest number of votes is removed from the com-petition. Why are the results not a true depiction of all Americans’ musical preferences?A) Undercoverage biasB) Voluntary response biasC) The judges’ comments influence voters’ opinions.D) Since some voters may vote multiple times, one votedoes not correspond to one person.E) All of the above.The city of Raleigh has 7200 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 200 randomly selected registered voters was conducted. 119 said they'd vote for Brown, 76 said they'd vote for Feliz, and 5 were undecided. This sample statistic suggests that we might expect of the 7200 registered voters to vote for Brown.The class field trip to the zoo was a huge success! The kids especially liked the bears, the dolphins, the monkeys, and the elephants. Taking a poll, the teachers found the following: all those who liked bears also liked the monkeys. Half of those who liked dolphins also liked monkeys. There were 24 who liked dolphins. However, none of those who liked elephants also liked bears. There were 16 who liked dolphins but not elephants. All those who liked elephants also liked monkeys. Half of those who liked elephants also liked dolphins. None who liked bears also liked dolphins. There were 9 who liked only monkeys. There were 15 who liked bears. How many liked monkeys? How many liked monkeys, elephants, and dolphins – all 3?
- A group of 249 students vote for their favorite restaurant. There are many variables involved in voting and various methods to determine the winner. If 61 vote for restaurant A, 58 for restaurant B, 42 for restaurant C, 46 for restaurant D, and 42 for restaurant E, who is the obvious winner? Choose the correct answer below. OA. restaurant A B. restaurant C C. restaurant D D. restaurant B OE. restaurant E 3 3Each student has a mathematics requirement (to take at least one mathematics course) and a Science requirement (to take at least one science course). A poll of 140 students show that: 60 completed math, 45 completed science, 20 completed both. Find the number of students that neither completed the requirement.Consider a weighted voting system with three players. If only Player 1 has veto power, and there are no dummies, find the Banzhof power distribution.Player 1: Player 2: Player 3: