Consider the following preference table for three voters to answer Questions $$\begin{array} { l l l l }
\text { First choice } & \mathrm { C } & \mathrm { D } & \mathrm { A } \
\text { Second choice } & \mathrm { B } & \mathrm { A } & \mathrm { B } \
\text { Third choice } & \mathrm { D } & \mathrm { B } & \mathrm { D } \
\text { Fourth choice } & \mathrm { A } & \mathrm { C } & \mathrm { C }
\end{array}$$
-If a Borda count is used, can the voter on the left manipulate the outcome to his or her benefit?

Question

Consider the following preference table for three voters to answer Questions $$\begin{array} { l l l l } 
\text { First choice } & \mathrm { C } & \mathrm { D } & \mathrm { A } \
\text { Second choice } & \mathrm { B } & \mathrm { A } & \mathrm { B } \
\text { Third choice } & \mathrm { D } & \mathrm { B } & \mathrm { D } \
\text { Fourth choice } & \mathrm { A } & \mathrm { C } & \mathrm { C }
\end{array}$$
-If a Borda count is used, can the voter on the left manipulate the outcome to his or her benefit?

Quizplus · Accepted Answer

The Borda count assigns points to each choice based on its rank, with the first choice receiving the most points and the last choice receiving the least points. In this case, each first choice receives 3 points, each second choice receives 2 points, each third choice receives 1 point, and each fourth choice receives 0 points. If the voter on the left convinces the other two voters to swap their first and second choices, the resulting preference table would be:

$$\begin{array} { l l l l } 
\text { First choice } & \mathrm { B } & \mathrm { A } & \mathrm { B } \
\text { Second choice } & \mathrm { C } & \mathrm { D } & \mathrm { A } \
\text { Third choice } & \mathrm { D } & \mathrm { B } & \mathrm { D } \
\text { Fourth choice } & \mathrm { A } & \mathrm { C } & \mathrm { C }
\end{array}$$

Under this new preference table, choice B would receive a total of 8 points (3 from the voter on the left, 2 from the second voter, and 3 from the third voter), while choice A would only receive a total of 6 points (3 from the third voter as a first choice and 3 from the first voter as a second choice). Therefore, the voter on the left could manipulate the outcome to benefit their first choice, B.

Consider the Following Preference Table for Three Voters to Answer