Answered

An employer surveys employees to see which lunch choice they should have at a work picnic. Here are the results:

\begin{tabular}{|l|l|l|l|l|}
\hline & 8 voters & 6 voters & 3 voters & 3 voters \\
\hline First choice & Tacos & Pizza & Sandwiches & Pizza \\
\hline Second choice & Pizza & Tacos & Tacos & Sandwiches \\
\hline Third choice & Sandwiches & Sandwiches & Pizza & Tacos \\
\hline
\end{tabular}

Based on these results, perform an instant runoff. Which accurately describes the process and results to find a winner using instant runoff?

A. Tacos win. They have 8 first-place votes to start. Then, they came in second twice so they should be the winner.

B. Tacos win. They have 8 first-place votes to start. Then, sandwiches are eliminated because they have the fewest first-place votes, so tacos moves up to get three more first-place votes.

C. Pizza wins. It has the first place votes in two columns.

D. Pizza wins. It has the plurality of the first-place votes (more first place votes than any other food).

E. Pizza wins. Tacos are eliminated in the first round, so pizza moves up in the first column.



Answer :

GinnyAnswer
Let's solve the problem step-by-step using the method of instant runoff voting to determine which lunch choice should win.

1. Initial vote distribution:
- Tacos: 8 votes
- Pizza: 6 votes + 3 votes = 9 votes
- Sandwiches: 3 votes

Since no choice has a majority (more than 10 votes out of a total of 20 votes), we proceed to the next step by eliminating the choice with the fewest votes.

2. Eliminate the choice with the fewest votes:
- Sandwiches have the fewest votes (3 votes). So, we eliminate Sandwiches and redistribute their votes according to their voters' second choices.

3. Redistribute Sandwiches' votes:
- All 3 voters of Sandwiches have Tacos as their second choice.

Therefore, after redistribution:
- Tacos: 8 votes + 3 redistributed votes = 11 votes
- Pizza: 9 votes

4. Compare the votes after redistribution:
- Tacos: 11 votes
- Pizza: 9 votes

Since Tacos now have the majority of the votes (11 out of 20), Tacos win the instant runoff voting.

Thus, the correct description of the process and result is:
- Tacos win. They have 8 first-place votes to start. Then, Sandwiches are eliminated because they have the fewest first-place votes, so Tacos move up to get three more first-place votes.

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