3. Below is the preference schedule for some election where the winner is determined by single runoff. First C А В Second B C A A Third А В B Voters 9 13 11 (a) Which candidates will go to the runoff? Who wins the runoff? (b) Suppose that the 5 voters in the next to last column move A up to first place. (Just switch A and C there.) Which candidates go to the runoff now? Who wins now? (Bonus) Has Criterion 3 been met? Explain.
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- One of the voting methods requires voters to rank all candidates from the most favorable to the least favorable. Each last-place vote receives 1 point, each next-to-last place vote 2 points, and so on. This voting method is called the _________ method. The candidate with the ______ is the winner.brandon conducted a research to determine the preference of students during online classes. From the 250 students who participated in the study, 85 wanted to have synchronous classes, 90 wanted to have asynchronous classes, and 100 wanted to have blended learning. From the respondents, it was seen that 35 preferred either synchronous and asynchronous, 10 preferred synchronous and blended learning, 25 preferred blended learning and asynchronous, and exactly 55 liked two of the mode of learning. 1. How many students liked synchronous, asynchronous, and blended learning? 2. How many students liked synchronous learning, but did not preferred asynchronous or blended learning? 3. How many students did not like either of the three modes of learning? 4. Draw the initial and final Venn diagram.A weighted voting system is given by [q : 5, 2, 2], where the voters are A, B, and C. List all the possible values of q satisfying the quota restriction. For each of these values of q, determine the voters that have veto power.
- Here is the preference schedule for a recent election among four candidates: Number of voters 1 4 7 23 11 5 10 1st choice X X F F B F K 2nd choice K F X B K K X 3rd choice B K B X F X B 4th choice F B K K X B F How many voters voted in this election? How many first place votes are needed for a majority? Which candidate/choice had the most first-place votes? Which candidate/choice has the least first-place votes? Which candidate/choice had the most last-place votes? Which candidate/choice has the least last-place votes? Question 6 : 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…The Science club is selecting its representative for a competition. The members rank the 4 candidates given in the preference table below: Using the agenda ABCD, who is the pairwise sequential winner?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 [
- 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?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?2. A fraternity votes to choose a service project--visiting nursing homes, reading with children in elementary schools, or cleaning up a stretch of highway. Their preference rankings are as follows: Number of Voters 3 1 4 8 2 Visiting nursing homes 1 1 2 3 2 Reading with children 2 3 1 1 3 Cleaning highway 3 2 3 2 1 Is there a Condorcet winner? If there is no Condorcet winner, is there a Weak Condorcet winner? Show the work you do in deciding, including vote totals, and state your conclusion.
- Troye teaches two undergraduate Accounting courses at UST. The class for Income Taxationconsists of 6 sophomores and 4 juniors. The more advanced course, Business Taxation, has 7sophomores and 2 juniors. As an example of a business sampling technique, Professor Shanerandomly selects, from the stack of Income Taxation registration cards, the class card of onestudent and then replaces the card in the stack. If that student was a sophomore, Shane drawsanother card from the Income Taxation stack; if not, she randomly draws a card from the BusinessTaxation group. What is the probability of: Interpret your answers. a. A junior’s name on both draws?b. A junior’s name on the first draw?c. A sophomore’s name on both draws?d. A junior’s name on the second draw, given that a sophomore’s name was drawn on first? 2. P(ace or jack)?3. P(club or non-club)?4. P(club or black)?5. P(heart or red card)?6. P(club or spade)?Consider an election with 301 voters cast for 3 candidates. What is the smallest number of first-place votes that a candidate can receive to win by the Plurality method?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) 110 (CABD) 130 (DABC) 140 (BADC) 160 Who wins the election using the Hare method? Does this violate Condorcet criterion?