Math Saves ASB Election

Last spring, I was walking through the front office of school when I was pulled into the ASB office. The director and his secretary appeared fearfully perplexed. They had the results of the election for ASB President, but could not determine a winner, so they needed the help of a math teacher. The winner was scheduled to be announced in less than an hour. Here was there quandry:

They advertised that the election would be based 20% on the Interview, 20% on Teacher Evaluations and 60% on Student Voting. Those results stared at them from a white board on the wall.

   Interview              Evaluations           Voting
Candidate #1       Candidate #1       Candidate #3

However, they could not determine from this data who won the election. I asked if they they had all standings in all three categories.They affirmed that they did and added those results to the whiteboard.

   Interview             Evaluations           Voting
Candidate #1       Candidate #1       Candidate #3
Candidate #2       Candidate #2       Candidate #1
Candidate #3       Candidate #3       Candidate #2

With this information, I posed to weight the election categories much the same way that I do my gradebook. Each candidate’s score was the sum of the three products of the Candidate’s place in the category (3 being highest score, 1 being lowest) and the percentage given that category. Thus,

#1 = 3(0.2) + 3(0.2) + 2(0.6) = 2.4
#2 = 2(0.2) + 2(0.2) + 1(0.6) = 1.4
#3 = 1(0.2) + 1(0.2) + 3(0.6) = 2.2

Candidate #1 wins!

I know there are several other mathematical methods to determine the winner. I invite those solutions in the comments below. My purpose for sharing this antecdote is to pose the question. “Why did it take a math teacher to figure this out?” These were intelligent, educated people struggling with this problem, “Why did they need a mathematician to resolve it?” The math involved is not high level, nor is this type of problem in any math curriculum that I experienced, so “How was I more adept at solving it than they were?”

I am going to surmise (inviting rebuttal), that it is my experience in solving math problems, not my content knowledge of math, that led me to the solution. I definitely have taken more math courses than the Activities Director, yet I did not need Trigonometry or Calculus to crown a champion. I needed simple problem solving skils in a mathematical context. So The Election Problem spurs me to pose more “problems” and fewer “notes and exercises” to my students.

You?

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