Preference Schedule (Math Club President Election) Number of voters 14 10 4 C B B D D C A A 1st 2nd 3rd 4th A B C D Using Pairwise-Comparison Method, C wins the election by how many points? a. 2 b. 3 8 D C B A 1 C D B A
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- a committe has six members there are two members that currenlty serve as the board chairman and ranking member. Each member is equally likely to serve in any of fhe position. two membed are ranomly selected and assigned to be the new chairman and ranking member what is the probaillity of randomly selecting the two month whi currenly hold the postions of chairman and ranking member and reaassining them to their currernt postionsA university system has a total of 40 new computers to distribute to each of its three campuses. After preregistration, the enrollment at each of the campuses was the value shown in second column of the table below together with the apportionment of the computers in the third column according to the Hamilton method. Final enrollment at each of the campuses is shown in the fourth column of the table with the percent increase in enrollment over the preregistration values in the fifth column. Determine whether a population paradox will occur in the reapportionment of the computers according to final enrollments. If it does, which campus loses a computer in the reapportionment? Campus PreregistrationEnrollment Apportionment of 40 Computers Based on Preregistration Enrollment Final Enrollment % Increase in Final Enrollment Over Preregistration Enrollment A 354 4 369 4.24% B 1,054 10 1080 2.47% C 2,598 26 2612 0.54% a. The paradox will occur and Campus A will lose a…An executive board consists of a president (P) and three vice-presidents (V1,V2,V3)(V1,V2,V3). For a motion to pass it must have yes votes from three of the voting members, one of which must be the president's.A weighted system that could represent this situation is:[Q:P,V1,V2,V3][Q:P,V1,V2,V3]where:QQ = PP = V1V1 = V2V2 = V3V3 =
- Two construction companies, Giant and Sky, bid for the right to build in a field. The possible bids are $ 10 Million, $ 20 Million, $ 30 Million, S 35 Million and S 40 Million. The winner is the company with the higher bid. The two companies decide that in the case of a tie (equal bids), Giant is the winner and will get the field. Giant has ordered a survey and, based on the report from the survey, 1 concludes that getting the field for more than $ 35 Million is as bad as not getting it (assume loss), except in case of a tie (assume win) Sky is not aware of this survey. (a) State reasons why/how this game can be described as a two-players zero-sum game [In a study of preferences in leafcutter ants, a researcher presented 20 randomly chosen ant colonies with leaves from the two most common tree species in the surrounding forest. The leaves were placed in piles of 100, one pile for each tree species, close to colony entrances. Leaves were cut so that each was small enough to be carried by a single ant. After 24 hours, the researcher returned and counted the number of leaves remaining of the original 100 of each species. Some of the results are show in the following table: Tree Species Number of Leaves Removed Spondius mombin 1561 Sapium thelocarpum 851 Total 2412 Can you answer question regarding to this graph pleaseEconomist Arthur Laffer suggests that beyond a certain point, high tax rates depress the economy so much that they actually reduce tax revenues. He proposed tax reductions as a means of stimulating the economy and, as a result, increase tax revenues. In the mid 1990’s Time magazine reported that 30% of the US Congress supported a tax cut as a means of stimulating the economy and increasing tax revenues. Suppose at that time 5 members of congress were randomly selected for an interview and asked whether they supported a tax cut to stimulate the economy. 1.2) Find the probability that at least three of the five members of congress who were interviewed were in favour of a tax cut (rounded off to four decimals).
- Your Question: Number of voters 21 21 10 34 38 16 1st choice C D B A C A 2nd choice B A C B A D 3rd choice A B A D B B 4th choice D C D C D C Find the winner of the election using the Pairwise Comparison method. For each comparison, enter the number of times each candidate was preferred to the other.A vs. BVotes where A is preferred to B : Votes where B is preferred to A : A vs. CVotes where A is preferred to C : Votes where C is preferred to A : A vs. DVotes where A is preferred to D : Votes where D is preferred to A : B vs. CVotes where B is preferred to C : Votes where C is preferred to B : B vs. DVotes where B is preferred to D : Votes where D is preferred to B : C vs. DVotes where C is preferred to D : Votes where D is preferred to C : Tally the results:Points for A: Points for B: Points for C: Points for D: Who is the winner? A B C D There is a tieIn 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.Number of ballots 8 6 5 1st preference A H G 2nd preference G G H 3rd preference H A A What will the board decide if it uses the pluarlity with elimination method?
- The television show CSI: Shoboygan has been successful for many years. That show recently had a share of 19, which means, that among the TV sets in use, 19% were tuned to CSI: Shoboygan. An advertiser wants to verify that 19% share value by conducting its own survey, and a pilot survey begins with 12 households have TV sets in use at the time of a CSI: Shoboygan broadcast.Many manufacturers have quality control programs that includeinspection of incoming materials for defects. Suppose a computermanufacturer receives circuit boards in batches of five. Two boards areselected from each batch for inspection. We can represent possibleoutcomes of the selection process by pairs. For example, the pair (1, 2)represents the selection of boards 1 and 2 for inspection. a. List the ten different possible outcomes.b. Suppose that boards 1 and 2 are the only defective boards in abatch. Two boards are to be chosen at random. Define X to be thenumber of defective boards observed among those inspected. Findthe probability distribution of X.c. Let F(x) denote the cdf of X. First determine F(0) = P(X≤O). F( 1).and F(2): then obtain F(x) for all other x.Researchers constructed two test sheets, each sheet including 20 photos of the faces of dog–owner pairs taken at a dog lovers' field festival. The 20 sets of dog–owner pairs on the two sheets were equivalent with respect to breed, diversity of appearance, and gender of owners. On the first sheet, the dogs were matched with their owners, while on the second sheet, the dogs and owners were deliberately mismatched. Three experiments were conducted, and in all experiments, subjects were asked to "choose the set of dog–owner pairs that resemble each other, Sheet 1 or Sheet 2," and were simply told the aim of the research was a "survey on dog–owner relationships." In the first experiment, the original sheets were shown to subjects; in the second experiment, just the "mouth region" of the owners was blacked out in all the pictures on both sheets; in the third experiment, just the "eye region" of the owners was blacked out. Subjects were assigned at random to the three experimental groups, and…