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

Question

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

Quizplus · Accepted Answer

In a Borda count, each position a candidate is placed in by a voter gives them a certain number of points (with lower preferences receiving fewer points). Manipulating the outcome by a single voter (in this case, the fourth voter) would not change the fact that C, initially receiving lower overall points than D (who has two first-choice votes), cannot win solely through the manipulation of one voter's preferences without knowing the specific point values assigned to each position and the preferences of all other voters. Given the initial distribution of preferences, C does not have enough first-choice support compared to D, and the manipulation by a single voter is unlikely to overcome this deficit.

Consider the Following Preference Table for Four Voters If a Borda Count Is Used, Can the Fourth Voter