5. You are given the weighted voting system (q: 10,5, 3,2).(a) What is the highest possible value of the quota q?(b) Is there a value of q for which P₁ is a dictator?(c) [Bonus] For which values of the quota q are there exactly two players with veto power?

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Answered: 5. You are given the weighted voting…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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13. Copeland's rule is a voting system that, like Condorcet's method, looks at one-on-one contests. It, however, takes as the election winner the candidate with the best "win-loss record." Use the following ballots to show that Copeland's rule is manipulable: Election 1 a. Who is the winner of Election 1? Number of voters (4) first A A D second third fourth В fifth OBECA D OBA
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Adviser to 42 Member local charter of the national mathematics honor society At the end of the semester, I need to hold elections for a society President, Vice-President, Secretary, Treasurer. If only 25 of the current members are considered (some are seniors and will be graduating!), how many different slates of officers can I have?
The U.S. Census Bureau conducts annual surveys to obtain information on the percentage of the voting-age population that is registered to vote. Suppose that 713 employed persons and 613 unemployed persons are independently and randomly selected and that 338 of the employed persons and 244 of the unemployed persons have registered to vote. Can we conclude that the percentage of employed workers ( p1 ), who have registered to vote, exceeds the percentage of unemployed workers ( p2 ), who have registered to vote? Use a significance level of α=0.1 for the test. Step 1 of 6 : State the null and alternative hypotheses for the test. Step 2 of 6 : Find the values of the two sample proportions, pˆ1p^1 and pˆ2p^2. Round your answers to three decimal places. Step 3 of 6 : Compute the weighted estimate of p, p‾p‾. Round your answer to three decimal places. Step 4 of 6 : Compute the value of the test statistic. Round your answer to two decimal places.…
i) A public opinion surveyed a simple random sample of 1000 voters. Respondents were classified by gender (male or female) and by voting preference (Average, Good, or Excellent). Results are shown in the contingency Table 4 below. Voting Preferences Total Average Good Excellent Male 210 120 70 400 Female 200 350 50 600 Total 410 470 120 1000 Make a clustered bar chart to show all the possibilities of voting preferences when gender is known. NOTE: DO NOT SOLVE ON EXCEL AND CLASSIFY EACH STEPS
Suppose you have populations of 7000, 5000, 1000 in 3 states and n representatives are to be allocated using Hamilton's method. There is an Alabama paradox from n=6 to n=7. Please find a second pair (n,n+1) where a paradox is observed.
Consider the weighted voting system [q: 7, 3, 1] Which values of q result in a dictator (list all possible values) What is the smallest value for q that results in exactly one player with veto power but no dictators? What is the smallest value for q that results in exactly two players with veto power?
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5. You are given the weighted voting system (q: 10,5, 3,2). (a) What is the highest possible value of the quota q? (b) Is there a value of g for which P is a dictator? (e) [Bonus] For which values of the quota q are there exactly two players with veto power?