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- The mathematics department is hiring a new faculty member and the five person hiring committee has interviewed our candidates Adam, Carol and On They decided to send the five ballots (reproduced in the following table). Who gets the offer?a recent survey of registered voters in city X found that 1/3 of the respondents support the District Chief Executive's property tax strategy, 1/8 indicated that they would not vote to re-elect the DCE if the strategy were implemented. of all the respondents, what fraction indicated that they would not vote the DCE if the strategy were enacted?Suppose that the plurality with elimination method is used on the following preference table. If the 5 voters who voted A, C, B, in that order, change their votes to C, A, B, determine if the monotonicity criterion satisfied. Number of Votes 2 4 5 11 First A B A C Second B C C A Third C A B B Is the monotonicity criterion satisfied?
- Suppose that three candidates for office were ranked by voters as shown in the table below. Use the Borda count method to determine the winner and then show that this method violates the majority criterion. Candidate Rankings Ahmad 2 1 2 1 3 Bennett 3 3 1 2 1 Oelker 1 2 3 3 2 Number of ballots 17 16 32 11 11Consider an election with three candidates with the following results: (ACB) 2, (BAC) 5, (CBA) 4, (CAB) 2. a) Is there a Majority winner? If not who is the Plurality winner. b) who wins using the Borda count method? c) Who wins if he or she first eliminates the one with the most Las place votes and then has a runoff between the other two?The fraternity is electing a national president and there are four candidates: Alberto (A), Bate (B), Carl (C), and Dave (D). The voter preferences are: (CADB) 93 (CABD) 113 (DABC) 123 (BADC) 143 Who wins the election using the Hare method? Does this violate the Condorcet criterion?
- Consider an election with three candidates with the results: (CBA) (ACB) (BAC) (BCA) 2 ,8, 7, 2 Who wins the election using the Borda count method?Answer the following: 1) Six hundred thirty people responded to their preferences of four dance groups in a dance contests, using 1 for their favorite and 4 for their least favorite. Results of the text votes were tallied below. Who would win the contest using the a) plurality voting system? b) plurality with elimination method of voting? c) Borda count method of voting? d) pairwise comparison voting method?The UCLA Graduate Student Association can use an instant runoff or a Bordacount method (but not both) when there are three or more candidates for office. The currentElection Board has up to 16 voters. Suppose three candidates are up for the Office of OfficialAwesomeness (Hey, give me a break - this is the last question!) Iris (I), Orchid (O), and Violet(V).(a) How many different preferences are possible?
- 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.We are in the middle of the election season with some states still having their state elections and voting for the Democratic nominee. However, since Bernie Sanders dropped out of the race, Joe Biden has become the presumptive Democratic nominee who will run against Donald Trump for the presidency in November. A recent poll from a national university was conducted by telephone with 754 registered voters from March 18 to 22, 2020. One of the questions they asked was: If the election for President was today, would you vote for … Donald Trump the Republican or Joe Biden the Democrat? [NAMES WERE ROTATED] [If UNDECIDED: If you had to vote for one of the following candidates at this moment, who do you lean toward – Donald Trump or Joe Biden?] Create confidence intervals for the percentage of registered voters who will vote for Biden and for Trump, respectively. You should have two separate confidence intervals, one for each of them. A news report citing this poll…A campus club has money left over in its budget and must spend it beforethe school year ends. The members arrive at five different possibilities, and each memberranks them in order of preference. The results are shown in the table below. 1. Using the Plurality method, how should they spend the money? 2. Use Plurality with elimination. to know how the money should be spent? 3. Using Pairwise Comparison, how should they spend the money? 4. Using the Borda count method of voting, how should the money be spent?5. In your opinion, which of the previous three methods seems most appropriate in thissituation? Why?