1. Consider set of altematives A (a,b,c,d, e) and set of voters N = (1,2,3,4,5), that havethe following preferences on set A:P, P2 P3 P. Psс dd bab bdd eebdeeeaaa) Find the majority graph and Condorcet winners.b) What should be chosen according to the Nanson rule?c) What should be chosen according to the Hare's rule (single transferable vote)? Use herealphabet order for tie-breaking.d) Find the social decision if the federation rule P (P, n P)U P, will be used. Here XPTYmeans that altemative x is less preferable than alternative y for voter i.

Given:Consider set of alternatives and set of voters , that have the following preferences on set…

Answered: 1. Consider set of alternatives A = (a,…

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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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.
5. An office manager is looking to purchase a new printer for his office. He has narrowed his choices down to four printers but cannot decide which of the four he prefers. He has decided to choose two of the four printers at random, and then to let the other members of the office decide which of the two they prefer. The speeds, in pages per minute, of the four printers are 25, 30, 27, and 32. Considering the speeds of the two printers chosen to be the sample, what are the mean and the standard deviation of the sample mean?
The profile below shows the preferences of voters in an election with 4 candidates (W, X, Y, and Z). Number of voters Preference Z>X > W>Y W> X > Y>Z 34 30 26 Y> Z>W> X 22 X >Z>W>Y 10 Y>W >Z> X а. Determine the plurality winner of this election. b. Determine if there is a Condorcet winner of this election. You must show all possible pair-wise subelections of two candidates. Does this election satisfy the Condorcet Winner Criterion (CWC)? Why or why not? с.
For an election with four candidates (A, B, C, D) consider the following preference table: NUMBER OF VOTERS 6. 1st Choice A C 2nd Choice В A C A 3rd Choice A 4th Choice C В Using the majority method, which candidate wins the election? 8 5.
For the weighted voting system [12: 8,6,5,3]: a. List all coalitions; identify which are winning coalitions. b. Determine the critical players in each winning coalition. Determine the Banzhaf power distribution for the system. C.
A team is planning a group vacation to one of the following locations: Alaska (A), Florida (F), San Antonio (S), or Hawaii (H). The employees rank the four possible sites according to the following preference table: No. of 5 7 7 5 6 8 Votes 1st A H A A H 2nd H 3rd A H A 4th F A H A H If the Borda Count Method, which location got the lowest Borda Score? (A Florida, 98 (B San Francisco, 95 Florida, 95 D San Francisco, 98 LL
1. Number of voters 11 9 14 1st choice B A C 2nd choice C B B 3rd choice A C A Find the winner of this election under the plurality method.Winner = 2. Number of voters 7 7 6 5 7 10 1st choice B B D C C A 2nd choice A C A B D C 3rd choice D A B D B D 4th choice C D C A A B Find the winner of this election under the plurality method.Winner = 3. Number of voters 4 13 14 1st choice B C A 2nd choice C B B 3rd choice A A C Find the Condorcet Candidate, if there is one. If there is not a Condorcet Candidate, enter noneCondorcet Candidate = 4. Number of voters 13 14 18 9 1st choice D B A C 2nd choice B C D D 3rd choice C A B A 4th choice A D C B Find number of points Candidate D receives under Pairwise Comparison (Copeland's Method)Points = Find the winner of this election under Pairwise Comparison (Copeland's Method)Winner = 5. Number of voters 21 15 17 14 22 31 1st choice C D A C A B 2nd choice B A D…
Answer the question about the preference schedule. How many voters preferred Candidate C to Candidate D? Preference Scheduleſfor an election. BED E First Second c E свА E A Third B E C A B C D Fourth B A Fifth Voters 12 S 9. 3. 16 a) 40 b) 37 c) 11 d) 27
6) For a certain election with 5 candidates, Sequential Pairwise found candidate D to be the winner when the agenda was: D, B, C, A, E. If the agenda was changed to: C, B, E, D, A, who would be 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.
2. A survey on a sample of 35 new cars being sold at a local auto dealer was conducted to see which of three popular options: Air-conditioning (A), Bluetooth (B), and Rear Camera (C), were already installed. The survey found: 18 had A, 13 had B, 12 had C, 5 had A and B, 8 had A and C, 6 had B and C, 4 had all three options. Find the number of cars that had (a) A and B but not C, (b) A and C but not B, (c) B and C but not A; (d) only one of the options; (e) at least one option; (f) exactly two options; (g) none of the options.
Candidates A, B, C, and D are competing to win an award. There are 5 voters in this election. The chart below shows the preference schedule. Voter 1 1st choice. A 2nd choice B 3rd choice C 4th choice D Voter 2 Voter 3 B C C B D D A A Voter 4 D B C A Voter 5 A D C B 8. Consider the following fairness criterion: If a majority of the voters have candidate X ranked last, then candidate X should not be a winner of the election. (a) Give an example to show that the plurality method violates this criterion. (b) Give an example to show that the plurality with elimination method violates this crite- rion.

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