Challenging Matrix Question

• Mar 23rd 2013, 03:37 PM
Zashmar
Challenging Matrix Question
G'day
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

M= (5x5)
00110
10000
01011
01000
11010

M2 =
02011
00110
22010
10000
11110
RANKKING
M+M2=
02121=6=
Third
10110=3=
Fourth
23021=8=
First
11000=2=
Fifth
22120=7=
Second

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
M+.75M2+.5625M3....
M+.5M2+.25M3....
M+1/3M2+1/9M3....

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 ??