In the following voter profile, use the Borda Method to determine the winner. If candidate d drops out, and a second election is held, who is the winner if the Borda Method is again used? Does the Borda Method violate the Independence of Irrelevant Alternatives Criterion in this election
Process?
$\begin{array}{c|l}
\text { Number of Voters } & \text { Ranking } \
\hline 3 & acbd \
7 & bacd \
5 & abcd \
8 & acdb \
7 & cdab \
4 & bdac \
6 & dbac \
6 & cbda \
4 & cadb
\end{array}$
A) a; a, no
B) a; b, yes
C) $b ; b$, no
D) $b$; $a$, yes

Question

In the following voter profile, use the Borda Method to determine the winner. If candidate d drops out, and a second election is held, who is the winner if the Borda Method is again used? Does the Borda Method violate the Independence of Irrelevant Alternatives Criterion in this election
Process? 
$\begin{array}{c|l}
\text { Number of Voters } & \text { Ranking } \
\hline 3 & a>c>b>d \
7 & b>a>c>d \
5 & a>b>c>d \
8 & a>c>d>b \
7 & c>d>a>b \
4 & b>d>a>c \
6 & d>b>a>c \
6 & c>b>d>a \
4 & c>a>d>b
\end{array}$
A) a; a, no
B) a; b, yes
C) $b ; b$, no
D) $b$; $a$, yes

Quizplus · Accepted Answer

The Borda Method assigns 3 points to a first-place vote, 2 points to a second-place vote, 1 point to a third-place vote, and 0 points to a fourth-place vote. Using this method, the total number of points for each candidate is as follows:a: 3(3) + 2(7) + 3(5) + 3(8) + 1(7) + 2(4) + 1(6) + 1(6) + 2(4) = 60b: 3(7) + 2(3) + 2(5) + 1(8) + 4(7) + 3(4) + 2(6) + 3(6) + 1(4) = 56c: 2(3) + 3(7) + 1(5) + 2(8) + 4(7) + 1(4) + 1(6) + 3(6) + 3(4) = 46d: 1(3) + 1(7) + 1(5) + 1(8) + 2(7) + 4(4) + 3(6) + 2(6) + 1(4) = 30Therefore, candidate a is the winner using the Borda Method.If candidate d drops out, the total number of points for each candidate is as follows:a: 3(3) + 2(7) + 3(5) + 3(8) + 1(7) + 2(4) + 1(6) + 1(6) = 54b: 3(7) + 2(3) + 2(5) + 1(8) + 4(7) + 3(4) + 2(6) + 3(6) = 52c: 2(3) + 3(7) + 1(5) + 2(8) + 4(7) + 1(4) + 1(6) + 3(6) = 44Therefore, candidate a is still the winner using the Borda Method.The Independence of Irrelevant Alternatives Criterion states that the winner of an election should not change if the set of candidates is changed, as long as the relative rankings of the remaining candidates do not change. In this election, the winner is a both before and after candidate d drops out. Therefore, the Borda Method does not violate the Independence of Irrelevant Alternatives Criterion in this election.

In the Following Voter Profile, Use the Borda Method to Determine