9 people reviewing each other in 6 categories - rig the score

[arminxo]

First of all, I apologise if this thread does not belong to this subforum because it's too basic for what you consider here.

I need help with the following. We need to review each other at work. However, the process is senseless given that we don't even all cooperate and will not be fair to everyone. For this reason, we decided to rig the review so that everyone gets the same score. The setup is:

1. 9 people review each other
2. Self review is not allowed, so each person reviews the other 8, ranking them from 1 to 8.
3. The ranking is carried out in 6 categories.

I have no idea how to approach the problem or set it up. Is there anyone who could help with the problem so that every person reviewed in the end gets the same score?

Eternally grateful.

Thanks.

 

[arminxo]

Maybe I haven't managed to make the problem clear. If I review other 8 people, I need to rank them from 1 to 8 (1 being the lowest score) for each of the 6 categories. Each of 9 people does this for the other 8. So, there are quite a number of rankings here.

 

[stapel]

Maybe I haven't managed to make the problem clear. If I review other 8 people, I need to rank them from 1 to 8 (1 being the lowest score) for each of the 6 categories. Each of 9 people does this for the other 8. So, there are quite a number of rankings here.

And the poster provided you with one such ranking. Are you saying that you need a listing of all such, or a count of all such possible, or something else other than a valid ranking?

Please be specific. When you reply, please include the full text of, and instructions for, the problem, along with a clear listing of your thoughts and efforts so far. Thank you!

 

[Ishuda]

First of all, I apologise if this thread does not belong to this subforum because it's too basic for what you consider here.

I need help with the following. We need to review each other at work. However, the process is senseless given that we don't even all cooperate and will not be fair to everyone. For this reason, we decided to rig the review so that everyone gets the same score. The setup is:

1. 9 people review each other
2. Self review is not allowed, so each person reviews the other 8, ranking them from 1 to 8.
3. The ranking is carried out in 6 categories.

I have no idea how to approach the problem or set it up. Is there anyone who could help with the problem so that every person reviewed in the end gets the same score?

Eternally grateful.

Thanks.

To make sure I understand, lets do a smaller sample [less possibilities]. Suppose there are three people: People A, B and C rank each other [but not themselves] in terms of the category speed of service
A can rank (1a) B=1, C=2 or (2a) B=2, C=1
B can rank (1b) A=1, C=2 or (2b) A=2, C=1
C can rank (1c) A=1, B=2 or (2c) A=2, B=1
The total score is to add A's, B's and C's ranking, for example
(1a), (2b), and (2c) for A=3, B=2, C=3

Now, A, B & C decide between them they want the total scores to be the same for all. Which rankings should be used by each person. Interesting problem.

The problem you have is that there are 9 people and 6 categories. BTW: Use the same rankings on all categories and it just becomes one category again. If the answers all come out the same on all categories, it will be obvious the results are cooked, so it might as well be made even more obvious.
Hint: [If I understand the problem correctly]
-1234
4-123
34-12
234-1
1234-

 

[arminxo]

To make sure I understand, lets do a smaller sample [less possibilities]. Suppose there are three people: People A, B and C rank each other [but not themselves] in terms of the category speed of service
A can rank (1a) B=1, C=2 or (2a) B=2, C=1
B can rank (1b) A=1, C=2 or (2b) A=2, C=1
C can rank (1c) A=1, B=2 or (2c) A=2, B=1
The total score is to add A's, B's and C's ranking, for example
(1a), (2b), and (2c) for A=3, B=2, C=3

Now, A, B & C decide between them they want the total scores to be the same for all. Which rankings should be used by each person. Interesting problem.

The problem you have is that there are 9 people and 6 categories. BTW: Use the same rankings on all categories and it just becomes one category again. If the answers all come out the same on all categories, it will be obvious the results are cooked, so it might as well be made even more obvious.
Hint: [If I understand the problem correctly]
-1234
4-123
34-12
234-1
1234-

Thank you very much for your time and attempt. It seems to me that you understand the problem perfectly.

1. I don't seem to be following what you mean by "use the same ranking on all categories and it just becomes one category again".

2. It's not a problem if it's made obvious. The example you give at the end of your post works perfectly (assuming that vertical sum represents one person's score). However, it seems to be effectively using a zero (the blank) in the ranking (probably assuming that one person that is out of the process). Unfortunately, it seems to me that this can't work because this person is out and the blank can't be in different places for each category (again assuming each row would represent a category, and each column a person).