2. Suppose that an employer decides to hire a new CEO using the Borda count. A panel of 35 managers, board members, an 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 rac 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?

2. Suppose that an employer decides to hire a new CEO using the Borda count. A panel of 35 managers, board members, an 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 rac 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?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

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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