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I have a set of eight principles and have been tasked with working out what the top five preferred principles are. In a series of interviews, participants were asked to rank their top five, with 1 being the most preferred, and 5 being the least preferred.

We had asked participants to leave the remaining three principles blank, however, several participants misread the instructions, and ranked all of the principles, (i.e., gave all eight principles a score between 1-5). This is an example of the kind of data I am working with:

This is an example of the kind of data I am working with

I want to work out what the top five principles are, giving more weight to where participants have ranked the principle as 1, and less to principles of 5. How would I do this? Is there a way I can do this in excel?

Henry
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atem634
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  • Couldn't you just set all values more than 5 to blank? – Nimish Oct 11 '23 at 22:38
  • Hi, no, the problem is that participants have given multiple rankings out (see Participant E as an example in the image I included) – atem634 Oct 11 '23 at 22:40
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    This is fairly vague. Even if there were only three options and three voters, there's no absolute way to do it. Say the voters ranked the options as $(A,B,C), (B, C, A), (C,A,B)$. Given that, how can you say which option was preferred by the group? It's notoriously difficult to convert individual preferences into group preferences. – lulu Oct 11 '23 at 22:43
  • A specious solution might be to compare the sum of the numbers in each row, to find the principle whose sum is minimum as the preferential candidate. However, a tricky thing is that each row has different number of empty slots in the data. A possible solution is to compare the average value (AV) of available numbers in each row. For instance, the $AV_1$ for the first row is $(3+5)/2=4$, $AV_2=(1+1+2+2)/4=1.5$ for the second row, and so on. The $5$ principles with lowest AV's are selected as the preferential candidates. – user295357 Oct 12 '23 at 00:13

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