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Basic Math/Contest Voting

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QUESTION: Hi,

Some friends and I are going to have a competition and each of us will vote on all contestants except ourselves. How can the votes most accurately be tallied to determine who gets 1st, 2nd, etc. place?

There are 7 contestants. Each will vote on the other 6 contestants.

We'd like to have each contestant rank the other 6 as they see fit from 1st, 2nd, etc. place.

Thanks!

ANSWER: John,
One of the easiest way is to weight each rank with some number. Let us say, for the first rank, we assign weight of 6 (considering that there are 6 contestants for everyone). So the weightage will be as below:

Rank          Weight
1          6
2          5
3          4
4          3
5          2
6          1

Now, for each individual, sum up the weights for all 6 votes. e.g. let us take your case. Assume that you get following ranks from other 6 voters: 3, 4, 1, 2, 1, 6
Weights for these ranks are 4, 3, 6, 5, 6, 1 respectively. Sum of these weights is 25. Likewise calculate sum of weights for all contestants. The one with the maximum sum will be the winner (because we have assigned higher weights for higher ranks).

I hope that this is clear. All the best!

Regards,
Pawan

---------- FOLLOW-UP ----------

QUESTION: Thank you for your response.

It's interesting that you mentioned those numbers for rank and weight. I experimented with those making up some examples of votes, and I ended up with some ties.

I'd like to use a system that avoids ties.

I tried this:

Rank Weight
1    100
2    70
3    45
4    25
5    10
6    0

That seems to reduce the likelihood of receiving ties, although some still occurred after making up some example votes.

Do you know of an approach that will definitely prevent having any ties at all?

Maybe some kind of wild card voting component? Or perhaps a way to break ties while tallying votes?

Thanks!

Answer
Hi John
This is interesting!
Here is the fact. You need to assign weights depending on the importance of the rank. e.g. If rank 1 is the most important for you and rank 2 is not very important, then you may assign weights of 100 and 20 respectively. On the other hand, if rank 1 and rank 2 are equally important for you with little difference, then you may assign weights of 100 and 90 respectively. So ultimately it ends up in what do you want to achieve and how important ranks are for you. Weighting method itself means the same.

If you get ties, then for those particular candidates, you may figure out which one has been voted for higher ranks (ignoring weights at this time).
e.g. say A and B have got the same score. Then if A has received rank 1 three times and B has received rank 1 2 times, then A is the winner.

Please feel free to let me know if you have any more questions on this.

Regards,
Pawan

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Pawan Musale

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I can answer Basic Mathematics questions like: Natural Numbers, Integers, Real Numbers, Complex Numbers, Number Theory, Geometry, Trigonometry, Graph Theory, Square Roots, Basic Integration, Profit-Loss problems, Work-Time problems, Equations etc I can try to answer questions of probability and set theory

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Tutoring on allexperts.com since long time

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I am Bachelor of Engineering (Instrumentation) from the reputed institute in India.

Awards and Honors
I was 18th in High School Scholarship examination in Maharashtra State of India. I was second in Mathematics in Maharashtra State in Secondary School Certificate examination.

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