The preference table for an election is given. Use the table to answer the questions below. A. Using the Borda count method, who is the winner? B. Is the majority criterion satisfied? Why or why not? \begin{tabular}{|l|l|l|l|l|} \hline Number of Votes & 40 & 32 & 20 & 8 \\ \hline 1st Choice & B & A & A & C \\ \hline 2nd Choice & C & C & D & D \\ \hline 3rd Choice & D & D & B & B \\ \hline 4th Choice & A & B & C & A \\ \hline \end{tabular} A. Using the Borda count method, the winner is B. Is the majority criterion satisfied? Why or why not? No. The winner of the election received the majority of votes. Yes. The candidate who received the majority of first-place votes won the election. No. The candidate who received the majority of first-place votes lost the election. Yes. The candidate who received the majority of first-place votes lost the election.

Step 1 ：Given the preference table for an election, we are asked to determine the winner using the Borda count method and to check if the majority criterion is satisfied.

Step 2 ：The Borda count method assigns points to each candidate based on their ranking in each voter's preference. In this case, since there are 4 candidates, the 1st choice gets 4 points, the 2nd choice gets 3 points, the 3rd choice gets 2 points, and the 4th choice gets 1 point.

Step 3 ：We calculate the total points for each candidate: 'A' gets 256 points, 'B' gets 248 points, 'C' gets 268 points, and 'D' gets 228 points.

Step 4 ：The candidate with the highest Borda count is 'C'. Therefore, using the Borda count method, the winner is \(\boxed{C}\).

Step 5 ：The majority criterion is satisfied if the candidate who received the majority of first-place votes won the election. In this case, the candidate who received the majority of first-place votes is 'A', but the winner is 'C'.

Step 6 ：Therefore, the majority criterion is not satisfied because the candidate who received the majority of first-place votes (\(\boxed{A}\)) did not win the election.