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.

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.

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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Using the preference schedule below, who would win the method of Pairwise Comparison is used? No. of voters 14 10 8. 4 1 1st choice Abby Ced Dora Ben Ced 2nd choice Ben Ben Ced Dora Dora 3rd choice Ced Dora Ben Ced Ben 4th choice Dora Abby Abby Abby Abby O a. Dora O b. Abby Ос. Ced O d. Ben
A statistics student wants to determine if a quiet room is a better study environment for students than a noisy environment. 151 students were recruited for an experiment. 75 students were randomly assigned to a quiet study environment while the other 76 were assigned to a noisy environment. Students in each group were given a short booklet from which to study and then were given a brief multiple- choice test. 52 of the students who studied in the quiet study environment passed the test, compared to 43 students who were in the noisy environment. Let Pi = the true proportion of all students like these who study in a quiet environment and pass the test and P2 = the true proportion of all students like these who study in a noisy environment and pass the test. Which of the following are correct for conducting a significance test of P1 – P2? 1. Но: Р1 — Р2 — 0 II. Ha: P1 – P2 + 0 II. Both the Random and Large Counts conditions are met.
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
3. Given the following weighted voting system [16: 12, 7, 4], is there a player that has the veto power? If so, which player and why? Write your response below:
1. Thirteen members of a dinner committee want to decide what kind of background music will be played during a meal. Their choices are easy listening, jazz, classical, and new age. Following are their preference rankings: Number of Voters Easy Listening 1 3 1 2 2 2 1 1 1 1 1 2 2 3 4 4 Jazz 3 3 1 1 3 Classical 3 2 4 4 1 1 2 New age 4 4 4 3 3 4 1 A) What option would win using the plurality method? (Show vote totals) B) top two finishers? (Show vote totals) What option would win using the plurality method with a runoff between the C) counts. (You should say if you are using Easy Borda method). Which candidate would win using the Borda method? Show the Borda
1. Thirteen members of a dinner committee want to decide what kind of background music will be played during a meal. Their choices are easy listening, jazz, classical, and new age. Following are their preference rankings: Number of Voters 1 3 1 2 2 2 1 1 Easy Listening 1 1 1 2 2 3 4 4 Jazz 2 3 3 1 1 2 2 3 Classical 3 2 4 3 4 1 1 2 New age 4 4 2 4 3 4 3 1 A) What option would win using the plurality method? (Show vote totals) B) What option would win using the plurality method with a runoff between the top two finishers? (Show vote totals) C) Which candidate would win using the Borda method? Show the Borda counts. (You should say if you are using Easy Borda method).
Consider the weighted voting system {25: 26, 11, 7, 4, 3}. Are there any players that are dictators, or players with veto power, or dummy players? If so, identify who the players are. a Dictator(s) = Player 1, Veto Power = Player 2, Dummy Player(s) = Player 2, 3, 4, 5 b Dictator(s) = Player 1, Veto Power = nobody, Dummy Player(s) = 1, 2, 3, 4, 5 Dictator(s) = Player 1, Veto Power = Player 1, Dummy Player(s) = Player 1, 2, 3, 4, 5 %3D %3D d. Dictator(s) = Player 1, Veto Power = Player 1, Dummy Player(s) = Player 2, 3, 4, 5 %3D %3D O O O O
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?