Problem

Seventeen people serve on a board and are considering three alternatives: A, B, and C. Here are the choi
\[
\begin{array}{cccccc}
(\mathrm{ABC}) & (\mathrm{ACB}) & (\mathrm{BAC}) & (\mathrm{BCA}) & (\mathrm{CAB}) & (\mathrm{CBA}) \\
1 & 4 & 3 & 2 & 4 & 3
\end{array} .
\]

Determine the winner, if any, using the given voting method.
Plurality method
$A$ is the winner.
$B$ is the winner.
$C$ is the winner.
There is no winner.
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Answer

\(\boxed{\text{The winner is C}}\)

Steps

Step 1 :The problem presents a voting scenario where 17 people are voting for three alternatives: A, B, and C. The votes are distributed as follows: ABC (1 vote), ACB (4 votes), BAC (3 votes), BCA (2 votes), CAB (4 votes), and CBA (3 votes).

Step 2 :The voting method used is the Plurality method. In this method, each voter is allowed to vote for only one candidate, and the candidate who polls the most among their counterparts is elected. In this case, we need to count the number of votes for each alternative (A, B, and C) in the first position, because in the Plurality method, only the first choice is considered.

Step 3 :By counting the votes for each candidate in the first position, we find that A has 5 votes, B has 5 votes, and C has 7 votes.

Step 4 :Since C has the most votes, the winner is C.

Step 5 :\(\boxed{\text{The winner is C}}\)

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