Problem

Four students are running for president of the Current Events Club: Arthur (A), Brandy (B), Chandra $(C)$, and Darrell (D). The preference ballots for the candidates are shown. Construct a preference table to illustrate the results of the voting. \[ \begin{array}{l} \text { DBAC DABC DABC DBAC DABC DBAC } \\ \text { CABD DABC DAAC DABC ACBD DABC } \end{array} \] \begin{tabular}{r|llll} Numlve of votes & 6 & 4 & 1 & 1 \\ \hline Flast cholce & D & D & A & C \\ Second choice & A & B & C & A \\ Third cloice & B & A & B & B \\ Fourth choice & C & C & D & D \end{tabular} \begin{tabular}{r|llll} Number of votes & 6 & 4 & 1 & 1 \\ \hline Fint cholce & D & D & C & A \\ Second choice & A & B & A & C \\ Third choice & B & A & B & B \\ Fourth choice & C & C & D & D \end{tabular} \begin{tabular}{r|llll} Number of votes & 5 & 1 & 5 & 1 \\ \hline Fint choice & D & D & A & C \\ Second choice & B & A & C & A \\ Third choice & A & B & B & B \\ Fourth choice & C & C & D & D \end{tabular} \begin{tabular}{r|llll} Number of votes & 4 & 6 & 1 & 1 \\ \hline Fist choice & D & D & A & C \\ Second cholice & B & A & C & A \\ Thind choser & A & B & B & B \\ Fourth choice & C & C & D & D \end{tabular}

Solution

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 :\(\boxed{\text{The preference table is as follows:}}\) \[\begin{array}{l|cccc} & \text{First Choice} & \text{Second Choice} & \text{Third Choice} & \text{Fourth Choice} \\ \hline \text{Arthur (A)} & 1 & 8 & 4 & 0 \\ \text{Brandy (B)} & 0 & 3 & 8 & 0 \\ \text{Chandra (C)} & 1 & 1 & 0 & 10 \\ \text{Darrell (D)} & 10 & 0 & 0 & 2 \\ \end{array}\]

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