Consider the following preference table for three voters to answer Questions $$\begin{array} { l l l l }
\text { First choice } & \text { B } & \text { D } & \text { A } \
\text { Second choice } & \mathrm { C } & \mathrm { B } & \mathrm { C } \
\text { Third choice } & \mathrm { A } & \mathrm { C } & \mathrm { B } \
\text { Fourth choice } & \mathrm { D } & \mathrm { A } & \mathrm { D } \
\text { Fifth choice } & \mathrm { E } & \mathrm { E } & \mathrm { E }
\end{array}$$
-Is there an agenda for which A would win a sequential pairwise election?

Question

Consider the following preference table for three voters to answer Questions $$\begin{array} { l l l l } 
\text { First choice } & \text { B } & \text { D } & \text { A } \
\text { Second choice } & \mathrm { C } & \mathrm { B } & \mathrm { C } \
\text { Third choice } & \mathrm { A } & \mathrm { C } & \mathrm { B } \
\text { Fourth choice } & \mathrm { D } & \mathrm { A } & \mathrm { D } \
\text { Fifth choice } & \mathrm { E } & \mathrm { E } & \mathrm { E }
\end{array}$$
-Is there an agenda for which A would win a sequential pairwise election?

Quizplus · Accepted Answer

No matter what agenda is chosen, A cannot win a sequential pairwise election. In any pair-wise comparison involving A, at least two voters have A ranked below the other option. Hence, A will never have a majority in any sequential pairwise election.

Consider the Following Preference Table for Three Voters to Answer