this is a question my teacher gave to us in class the other day.
We will consider a simplified situation, involving 5 players- A,B,C,D and E
In a round robin tournament the results were:
A beat C and D
B beat A
C beat B,D and E
D beat B
E beat A,B and D
1. produce a matrix M, and find the current ranking for these players
2. One player is not happy with the outcome, and suggests to you, as the officail ranker, that is unfair to give equal importance to first, second and thrid- order influence, and perhaps arbitrary constats could be allocated to weight these influences, that is use:
M+aM2+bM3.... and so forth
If a little money were to change hands, is it possible for you to produce a different ranking, which you can and must justify mathematically?
I have tried many, many, many arbitrary constants.
some of them are
Would anybody please be able to exaplin to me if you can make arbitrary canstants that would change to order of the results? i was thinking if the constants are arbitrary then would the order of the athelets stay the same ??
please help cheers