Step 1 :Given the preference ballots for the candidates, we are asked to construct a preference table to illustrate the results of the voting.
Step 2 :The preference table should show the number of votes each candidate received for each rank (first choice, second choice, etc.).
Step 3 :We first create a dictionary to store the votes for each candidate.
Step 4 :We then iterate through the ballots and update the dictionary accordingly.
Step 5 :The ballots are as follows: ['DBAC', 'DABC', 'DABC', 'DBAC', 'DABC', 'DBAC', 'CABD', 'DABC', 'DAAC', 'DABC', 'ACBD', 'DABC'].
Step 6 :After counting the votes, we find that the votes for each candidate are as follows: Arthur (A): [1, 8, 4, 0], Brandy (B): [0, 3, 8, 0], Chandra (C): [1, 1, 0, 10], Darrell (D): [10, 0, 0, 2].
Step 7 :Finally, we construct the preference table based on the votes each candidate received for each rank.
Step 8 :The preference table is as follows: \[\begin{array}{l|cccc} & \text{First Choice} & \text{Second Choice} & \text{Third Choice} & \text{Fourth Choice} \\ \hline \text{Arthur (A)} & 1 & 8 & 4 & 0 \\ \text{Brandy (B)} & 0 & 3 & 8 & 0 \\ \text{Chandra (C)} & 1 & 1 & 0 & 10 \\ \text{Darrell (D)} & 10 & 0 & 0 & 2 \\ \end{array}\]
Step 9 :\(\boxed{\text{The preference table is as follows:}}\) \[\begin{array}{l|cccc} & \text{First Choice} & \text{Second Choice} & \text{Third Choice} & \text{Fourth Choice} \\ \hline \text{Arthur (A)} & 1 & 8 & 4 & 0 \\ \text{Brandy (B)} & 0 & 3 & 8 & 0 \\ \text{Chandra (C)} & 1 & 1 & 0 & 10 \\ \text{Darrell (D)} & 10 & 0 & 0 & 2 \\ \end{array}\]