How can we fairly distribute points in a peer evaluation with 6 classmates?

[egcasco]

Dear All,
I'm going through a project with my university classmates but we are asked to evaluate each other's contribution by assessing our effort in a peer evaluation form. In particular, we are asked to:

rate our collegues' contributions by assigning:

. maximum 100 points per person
. each one has to assign exactly 300 points
. not to assign any points to ourself
. differences between any score we assign to our mates has to be equal or superior to 5
. it can't be the case in which everyone has the same total score (but may be slightly different!)

we will receive a final note based on the note we receive as a group and, individually, by correcting it for a coefficient calculated as:

group final note * average score received by X / whole group's average score


The points is that we want to equally distribute our individual notes. we are 6 mates, and seems it is really difficult to go through it!


I tried solving with excel the problem and worked out for a 5 people group bu no for 6 people one! any idea?

thank you !

 

[AUMathTutor]

	a	b	c	d	e	f

a	--	30	45	60	75	90

b	90	--	30	45	60	75

c	75	90	--	30	45	60

d	60	75	90	--	30	45

e	45	60	75	90	--	30

f	30	45	60	75	90	--

 

[AUMathTutor]

This should be interpreted as: person "a" gives person "b" 30 points, person "e" gives person "c" 75 points, etc.

You'll see that each person gives out exactly 300 points, no person gives another more than 100, and the differences are greater than 5.

The method generalizes to arbitrary numbers of people. Of course, it is not guaranteed that there is a way to divide the points into integer amounts... anyway. This should about do it.

 

[egcasco]

dear aumathtutor,
it seems like we have to assign in total not 300 but 400...how does the matrix change? Thank you so much,egcasco

 

[Hurkyl]

I hope everyone in your group really does deserve the same score.