2. Consider the following preference schedule for an election:Number of voters1st choice2nd choice3rd choice4th choice(a) How many people voted in this election?(b) How many votes are needed for majority?i. vote-for-twoii. plurality votingiii. Borda count4 52C AA BD C A сBA D DC D B B60(c) Use the following methods to find the winner. If there is a tie, suggest a reasonabletie-breaking rule and find the winner.iv. plurality-with-eliminationv. Is there a Condorcet candidate in this election?vi. In this election, does plurality vote violate Condorcet fairness criterion?vii. Suppose that the preference schedule above refers to a straw poll. Now we hold anofficial election - and everyone votes the same except for the two voters in the lastcolumn: they switch their votes and move C ahead of A in their ballots. Useplurality-with-elimination to find the winner of the official poll.viii. the results of (iv) and (vii) imply violation of which fairness criterion.

To find the approximate percentages using the empirical rule (also known as the 68-95-99.7 rule),…

Answered: 2. Consider the following preference…

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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Refer to the following preference schedule to answer parts (a) – (i). a. How many votes were cast? _________ b. How many votes are needed to receive a majority? ________ c. Find the plurality winner: _________Show work to support the selection process. d. Did the plurality winner also receive a majority? _________. e. Find the winner by a single runoff of the top two candidates: ________Show work to support the selection process below. f. Find the winner by a sequential runoff: ________Show work to support the selection process. g. Find the winner by a Borda count: ________Show work to support the selection process. h. Find the winner, if any, by the method of pairwise comparisons: ________Show work to support the selection process i. From the results of (a)-(h) is there a clear winner? Explain.
10
hree-Way Race Preference Schedule. Consider a three-way race between candidates called A, B, C. Make a preference schedule for the following results: 22 voters rank the candidates in the order (first choice to last choice) A, B, C. 20 voters rank the candidates in the order C, B, A. 16 voters rank the candidates in the order B, C, A. 8 voters rank the candidates in the order C, A, B. The answers are in the attached table.
Suppose a six-member committee needs to select a chair from among three candidates named Li, Condie, and Kargbo. Their preference rankings are as follows: Number of Voters 1 1 2 2 Li 1 1 2 3 Condie 2 3 1 2 Kargbo 3 2 3 1 Who is the winner using Borda’s method? A) Li B) Condie C) Kargbo D) none of these
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.)
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).
Question2. A periodic function of period 27 is defined for 0 ≤ x ≤ 2π by (0 ≤ x ≤ 1/n) 글자 ( n < x≤n) == π (π< x < ²/n) |x − 2π (²n≤ x ≤ 2n) f(x) = X Sketch f(x) for (-2π < t < 4n) and find the Fourier series in expanded form. Also express the Fourier series in general form.
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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