Math and Science Solutions for Businesses/Help with computation
We conduct cheerleading tryouts at our school annually. I have doubts about the way the scores are tallied and need someone who can tell me if the system we use is valid. If it is correct then I will breathe a sigh of relief and go on : )
Currently the tryout score is determined by Student Body Vote (30%), Teacher Vote (20%), and a judges evaluation score (50%).
For this example lets assume 11 girls try out. The student votes are tallied and each girl is ranked 1-11 in the order of highest votes. Whoever gets the most student votes is ranked 1, second most votes 2, etc. This rank number (1, 2, etc.)is then multiplied by 30%. Call this number A.
The teacher votes are tallied and each girl is ranked 1-11 in the order of highest votes. Whoever gets the most teacher votes is ranked 1, second most votes 2, etc. This rank number (1,2, etc.) is then multiplied by 20%. Call this number B.
The judges scores are ranked 1-11 in the order of highest score. Whoever gets the highest judge score is ranked 1, the second highest 2, etc. This rank number (1,2, etc.) is then multiplied by 50%. Call this number C.
The three numbers are then added A+B+C=Final Score. The lowest score is then the 1st elected cheerleader, the next to lowest is the 2nd elected cheerleader, all the way to 8 since we elect 8 cheerleaders.
We have been using this system for over 15 years. A former math teacher at our school said this is the only fair way to do it since student and teacher votes are different than judges scores. I always wondered why we couldn't just multiply student votes by 30%, teacher votes by 20% and the judges score by 50% and take the highest number to figure the girl's score.
So this year when tryouts were over, we figured scores the way we have been. I then took the girl's numbers and tried out my theory. 7 of the same girls would have made it. But there would have been a difference in 2 girls. One that got it would NOT have been elected and one that did not get elected WOULD have. This has been bothering me. I teach at the school and am completely unbiased in this - I like all the girls that tried out. I just want to make sure that we are doing this fairly and no one can seem to explain if we are or not.
I know in the grand scheme of things that this is a minor issue but it has been driving me crazy so I would appreciate any help you can give me.
Thank you so much in advance!
The method used by your school for selecting the cheerleaders by rank is known as the Borda method: see link
It is a widely used method for combining the rankings from different groups (eg., college sports teams).
The actual Borda method described in the link is slightly different from your current school's method in that the highest rank gets the highest score, whereas in your method, the lowest "score" (combined ranking) wins. Mathematically, they are the equivalent.
The Borda method tends to reflect broader support for a candidate in that a candidate that doesn't get the most 1st place votes but gets a lot of 2nd and 3rd may win in the final ranking. Thus a widely popular but not spectacular (to a certain group or two) candidate may end up winning. The Borda method is also susceptible to voting manipulation (purposely voting for a candidate to dilute support for another), although I doubt that would be a problem in your case.
The weighting of the 3 groups (students, teachers and judges) simply reflects an a priori assignment of importance. For instance, if there are numerically only a few judges compared with a much larger student body, then common sense says that the judges votes will need to be given more weight. The alternative that you mention retains this weighting, combining the weighted the votes before the ranking. This "weighted voting" technique is used in board rooms where the weight of the vote depends on the number of shares held by a board member. It is usually associated with situations where a certain minimum of votes is needed to pass (yay or nay) a resolution and can bring into play the "power" of a voting group.
I haven't found anything that unambiguously argues for or against the 2 methods you present. I can say that the Borda method is mathematically viable and, since many different voting systems exist, which one to use is a judgement call and that there isn't really a hands down best way.
Hope this helps. Thanks for the question.