QuestionThree directors (Fred, Steve, Eddie) are voted for. Using pairwise comparison, determine who is the selected speaker.
Studdy Solution
STEP 1
Assumptions1. The votes are summarized in the given preference table.
. The pairwise comparison method will be used to determine the speaker.
3. The pairwise comparison method involves comparing each pair of candidates and counting the number of voters who prefer one over the other.
STEP 2
First, we need to compare each pair of candidates. There are three candidates, so there will be three comparisons Fred () vs Steve (), Fred () vs Eddie (), and Steve () vs Eddie ().
STEP 3
Let's start with the comparison between Fred () and Steve (). We need to count the number of voters who prefer Fred over Steve and vice versa.
STEP 4
From the table,10 voters prefer Eddie () as their first choice, Steve () as their second, and Fred () as their third. Therefore, these10 voters prefer Steve over Fred.
STEP 5
7 voters prefer Fred () as their first choice, Steve () as their second, and Eddie () as their third. Therefore, these7 voters prefer Fred over Steve.
STEP 6
5 voters prefer Steve () as their first choice, Fred () as their second, and Eddie () as their third. Therefore, these5 voters prefer Steve over Fred.
STEP 7
Summing up the preferences, we have15 voters preferring Steve over Fred and7 voters preferring Fred over Steve.
STEP 8
Now, let's compare Fred () and Eddie (). We need to count the number of voters who prefer Fred over Eddie and vice versa.
STEP 9
From the table, voters prefer Eddie () over Fred (),7 voters prefer Fred () over Eddie (), and5 voters prefer Steve () over both. Therefore, voters prefer Eddie over Fred and7 voters prefer Fred over Eddie.
STEP 10
Finally, let's compare Steve () and Eddie (). We need to count the number of voters who prefer Steve over Eddie and vice versa.
STEP 11
From the table,10 voters prefer Eddie () over Steve (),7 voters prefer Steve () over Eddie (), and5 voters prefer Steve () over Eddie (). Therefore,10 voters prefer Eddie over Steve and voters prefer Steve over Eddie.
STEP 12
In summary, for the pairwise comparisons we have- Fred () vs Steve ():15 prefer,7 prefer F- Fred () vs Eddie ():10 prefer,7 prefer F- Steve () vs Eddie ():12 prefer,10 preferAccording to the pairwise comparison method, the candidate who is preferred in the most comparisons is selected as the speaker. In this case, Steve () is preferred in2 out of comparisons, so Steve is selected as the speaker.
The speaker selected using the pairwise comparison method is Steve.
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