Table 23 - 2
$\begin{array}{|l|l|l|l|}\hline&&\text { Voter Type }\
\hline &\text { Type 1 } & \text { Type 2 } & \text { Type 3 } \
\hline \% \text { of electorate }&35 & 45 & 20 \
\hline 1^{\text {st }} \text { choice }&\text { C } & \text { A } & \text { B } \
\hline 2^{\text {nd }} \text { choice }&\text { A } & \text { B } & \text { C } \
\hline 3^{\mathrm{rd}} \text { choice }&\text { B } & \text { C } & \text { A } \
\hline
\end{array}$ Suppose a town is to vote on three possible locations for a new park: A, B, or C.The preferences are in table 23-2.Suppose the mayor decides on the following Borda count voting scheme: For each option, we will give one point for last place, two points for second last, and three points for the third last etc.The outcome with the most points is the winner.
-refer to the information provided.The Borda count fails to satisfy which of Arrow's properties of a perfect voting system?
A)unanimity
B)transitivity
C)independence of irrelevant alternatives
D)no dictators

Question

Table 23 - 2
 $\begin{array}{|l|l|l|l|}\hline&&\text { Voter Type }\
\hline &\text { Type 1 } & \text { Type 2 } & \text { Type 3 } \
\hline \% \text { of electorate }&35 & 45 & 20 \
\hline 1^{\text {st }} \text { choice }&\text { C } & \text { A } & \text { B } \
\hline 2^{\text {nd }} \text { choice }&\text { A } & \text { B } & \text { C } \
\hline 3^{\mathrm{rd}} \text { choice }&\text { B } & \text { C } & \text { A } \
\hline
\end{array}$ Suppose a town is to vote on three possible locations for a new park: A, B, or C.The preferences are in table 23-2.Suppose the mayor decides on the following Borda count voting scheme: For each option, we will give one point for last place, two points for second last, and three points for the third last etc.The outcome with the most points is the winner.
-refer to the information provided.The Borda count fails to satisfy which of Arrow's properties of a perfect voting system?
A)unanimity
B)transitivity
C)independence of irrelevant alternatives
D)no dictators

Quizplus · Accepted Answer

The Borda count fails to satisfy independence of irrelevant alternatives, as the ranking of an option can be manipulated by introducing a new irrelevant option. For example, if a new option D is introduced that is similar to option B, voters may move their preference from B to D, resulting in a different outcome even though nothing has changed about A or C.

Table 23 - 2 Suppose a Town Is to Vote on Three Possible Locations