Consider the following preference table for four voters to answer the Questions $$\begin{array} { l l l l l }
\text { First choice } & \text { B } & \text { D } & \text { A } & \text { C } \
\text { Second choice } & \mathrm { C } & \mathrm { B } & \mathrm { C } & \mathrm { D } \
\text { Third choice } & \mathrm { A } & \mathrm { C } & \mathrm { B } & \mathrm { B } \
\text { Fourth choice } & \mathrm { D } & \mathrm { A } & \mathrm { D } & \mathrm { A } \
\text { Fifth choice } & \mathrm { E } & \mathrm { E } & \mathrm { E } & \mathrm { E }
\end{array}$$
-If a Borda count is used, can the second voter manipulate the outcome so that D wins?

Question

Consider the following preference table for four voters to answer the Questions $$\begin{array} { l l l l l } 
\text { First choice } & \text { B } & \text { D } & \text { A } & \text { C } \
\text { Second choice } & \mathrm { C } & \mathrm { B } & \mathrm { C } & \mathrm { D } \
\text { Third choice } & \mathrm { A } & \mathrm { C } & \mathrm { B } & \mathrm { B } \
\text { Fourth choice } & \mathrm { D } & \mathrm { A } & \mathrm { D } & \mathrm { A } \
\text { Fifth choice } & \mathrm { E } & \mathrm { E } & \mathrm { E } & \mathrm { E }
\end{array}$$
-If a Borda count is used, can the second voter manipulate the outcome so that D wins?

Quizplus · Accepted Answer

In Borda count, each candidate receives points according to their ranking on each voter's preference table. The points are added up and the candidate with the highest total points wins. In this case, the points received by each candidate are:

- A: 9
- B: 11
- C: 8
- D: 12
- E: 0

Even if the second voter switches their first and second choices to make D their first choice and B their second choice, D will only receive 14 points (12 from the second voter and 2 from the third voter) while B will still receive 11 points (4 from the first voter, 6 from the second voter, and 1 from the third voter). Therefore, the outcome cannot be manipulated and B will still win.

Consider the Following Preference Table for Four Voters to Answer