QUESTION 6.The 75 teachers on the faculty of Democracy College have filled out ballots in the form ofpreference lists. They are electing someone to represent themselves as Faculty Representative to theBoard of Trustees. If no candidate gets a majority (at least 38 votes), they will resolve the election usingthe Instant Runoff Voting method. The candidates are Mike the Mathematician, Beverly the Biologist,Helen the Historian, Sophia the Sociologist, and Edward the English teacher. The 75 preference lists fallinto 7 distinct groups.15MikeBeverlyHelenEdwardSophia14BeverlySophiaEdwardMikeHelen11HelenSophiaBeverlyEdwardMike10SophiaMikeHelenBeverlyEdward10EdwardSophiaMikeBeverlyHelenShow the counts, round by round, until a winner is determined.8BeverlyEdwardSophiaMikeHelen7EdwardSophiaHelenBeverlyMike

The candidates are Mike the mathematician, Beverly the Biologist, Helen the Historian, Sophia the…

Answered: QUESTION 6. The 75 teachers on the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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You are on trial for financial fraud, and there are 8 prospective judges, including Donald and Hillary, both of whom you have bribed. A three judge panel will be selected from the 8 to decide the verdict. How many such possible panels include Donald or Hillary?
A campus club needs to elect four officers: a president, a vice president, a secretary, and a treasurer. The club has five volunteers. Rather than vote individually for each position, the club members will rank the candidates in order of preference. The votes will then be tallied using the Borda Count method. The candidate receiving the highest number of points will be president, the candidate receiving the next highest number of points is vice president, the candidate receiving the next highest number of points is secretary, and the candidate receiving the next highest number of points will be treasurer. Rankings Cynthia 4 2 5 2 3 Andrew 2 3 1 4 5 Jen 5 1 2 3 2 Hector 1 5 4 1 4 Medin 3 4 3 5 1 Number of votes: 9 12 25 24 23 For the preference schedule shown, determine who wins each position in the club. president vice president secretary treasurer
Six college sorority sisters-Summer, Autumn, Wynter, June, April, and January-got together for their twentieth reunion. Since college they had moved to six different states. Two lived out west (Oregon and Washington), two lived back east (New York and New Hampshire), and two lived down south (Oklahoma and Texas). They all sat around a round table. 1. The Texan sat between Autumn and the woman who lives in New Hampshire. 2. Wynter sat across from April. 3. January sat between Summer and the Washingtonian. 4. June and the woman to her left both live out west. 5. April sat between two easterners. Where does Summer live? Where does January live? Where does Autumn live?
If you and another person are using the divide-and-choose procedure to divide something between you, would you rather be the divider or the chooser? (Assume that neither of you knows anything about the preferences of the other.)
Use the Condorcet method to determine the winner of the election. Four students are running for president of the school: • Ariana (A), • Brett (B), • • DeeDee (D). The 5 clubs and their members were asked to rank all candidates. Number of Voters 19 15 Carlos (C), and σ O O O O n d A B с D 11 7 2 Preference Order 1st to last с D B с с D A A A A C D D A с D B olmalı B B B
2. Suppose that an employer decides to hire a new CEO using the Borda count. A panel of 35 managers, board members, and other executives rank the candidates using a preference ballot. Here is the preference schedule. 1st Place Chen Ashford Ashford 2nd Place Ashford Borge Chen 3rd Place Borge Chen Borge Voters 18 16 1 (a) Find the Borda count for each of the candidates to determine who will be hired. (b) Now forget the Borda counts and look at the number of first place votes. (c) Does any candidate have a majority of the votes? Which one? (d) Does Criterion 1 apply? Has Criterion 1 been satisfied? (e) Again, forget the Borda counts and look at the number of first place votes in pairwise comparisons. Who wins in a race between Chen and Ashford? between Chen and Borge? (f) Is there a Condorcet winner? Did the Condorcet winner win the election? (g) Does Criterion 2 apply? Has Criterion 2 been satisfied?
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