2.13: Approval Voting

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Up until now, we’ve been considering voting methods that require ranking of candidates on a preference ballot. There is another method of voting that can be more appropriate in some decision making scenarios. With Approval Voting, the ballot asks you to mark all choices that you find acceptable. The results are tallied, and the option with the most approval is the winner.

Example 12

A group of friends is trying to decide upon a movie to watch. Three choices are provided, and each person is asked to mark with an “X” which movies they are willing to watch. The results are:

\(\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline & \text { Bob } & \text { Ann } & \text { Marv } & \text { Alice } & \text { Eve } & \text { Omar } & \text { Lupe } & \text { Dave } & \text { Tish } & \text { Jim } \\
\hline \text { Titanic } & & \mathrm{X} & \mathrm{X} & & & \mathrm{X} & & \mathrm{X} & & \mathrm{X} \\
\hline \text { Scream } & \mathrm{X} & & \mathrm{X} & \mathrm{X} & & \mathrm{X} & \mathrm{X} & & \mathrm{X} & \\
\hline \text { The Matrix } & \mathrm{X} & \mathrm{X} & \mathrm{X} & \mathrm{X} & \mathrm{X} & & \mathrm{X} & & & \mathrm{X} \\
\hline
\end{array}\)

Solution

Totaling the results, we find

Titanic received 5 approvals

Scream received 6 approvals

The Matrix received 7 approvals.

In this vote, The Matrix would be the winner.

Try it Now 6

Our mathematicians deciding on a conference location from earlier decide to use Approval voting. Their votes are tallied below. Find the winner using Approval voting.

\(\begin{array}{|l|l|l|l|l|l|l|l|}
\hline & 30 & 10 & 15 & 20 & 15 & 5 & 5 \\
\hline \text { Seattle } & \mathrm{X} & \mathrm{X} & \mathrm{X} & & & \mathrm{X} & \\
\hline \text { Tacoma } & \mathrm{X} & & \mathrm{X} & \mathrm{X} & \mathrm{X} & \mathrm{X} & \\
\hline \text { Puyallup } & & \mathrm{X} & & \mathrm{X} & \mathrm{X} & \mathrm{X} & \\
\hline \text { Olympia } & & & \mathrm{X} & & \mathrm{X} & & \mathrm{X} \\
\hline
\end{array}\)

Answer

Using Approval voting:

Seattle has \(30+10+15+5 = 60\) approval votes

Tacoma has \(30+15+20+15+5 = 85\) approval votes

Puyallup has \(10+20+25+5 = 50\) approval votes

Olympia has \(15+15+5 = 35\) approval votes