Math Homework week 101. In voting among three candidates, the outcomes are reported as following table.(ABC) (ACB) (BAC) (BCA) (CAB) (CBA XXXXXXXXXXa) If a person ranks B as their first choice, A as...

Math Homework week 10
1.
In voting among three candidates, the outcomes are reported as following table.
(ABC) (ACB) (BAC) (BCA) (CAB) (CBA)
9 4 3 0 2 4
(a) If a person ranks B as their first choice, A as their second choice and C last, how would this
be written?
(
BAC
)
(b) How many voters have this preference?
3
2.
(a) If there are 40 voters and 5 candidates, how many total points would there be in a Borda
count?
600
(b) If there are 70 voters and 4 candidates, how many total points would there be in a Borda
count?
700
(c) If there are 600 voters and 3 candidates, how many total points would there be in a Borda
count?
3600
3.
Use following formula to determine how many total points there would be in a Borda count with
n voters and m candidates.
= (1 + 2+ 3+…..+ m)*n =


.
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=4299303
4. Twelve board members are voting on after-meeting activities, and they are asked to check any
that they might like. The outcome of their choices is shown as following table. What is the
outcome using approval voting?

Drinks



1 2 3 4 5 6 7 8 9 10 11 12
Snacks

X X X X X

X X X X

Drinks X

X X X

X

X X

Travel talk

X

X X

Speaker

X

X X

X X X

X X
5.
Twelve people serve on a board and are considering three alternatives: A, B, and C. The choices
followed by vote is shown in following table. Determine the winner, if any, using a Borda count.
The winner is
A

(ABC) (ACB) (BAC) (BCA) (CAB) (CBA)
2 4 2 1 2 1
6.
The South Davis Faculty Association is using the Hare method to vote for their collective
bargaining representative. Their choices are the All Faculty Association (A), American
Federation of Teachers (B), and California Teachers Association (C). The results of the
preferences are shown in the following table.
(ABC) (ACB) (BAC) (BCA) (CAB) (CBA)
13 1 3 7 3 20
(a) Which organization is selected for collective bargaining using the Hare method?
A B C
(b) Does the choice in part a violate the majority criterion?
Yes No
7. The Adobe School District is hiring a vice principal and has interviewed four candidates:
Andrew (A), Bailey (B), Clark (C), and Davy (D). The results of the hiring are shown in the
following table.
(ACDB) (CBAD) (BCDA) (DBCA)
7 5 3 2
(a) Who is the winner using the plurality method?
A B B
(b) Suppose that Clark drops out of the running before the vote is taken. Who is the winner using
the plurality method?
A B ...