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Math Help - Challenging Matrix Question

  1. #1
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    Exclamation 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 ??

    please help cheers
    Last edited by Zashmar; March 23rd 2013 at 08:33 PM.
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  2. #2
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    Re: Challenging Matrix Question

    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?
    This made me laugh

    If you look at the sum of the rows in M, M2, M3, M4; when put in order of highest to lowest they always have the same order so unless the constants are negative which would make no sense.
    I only checked up to M4, I didn't prove that in the general case their sums always have the same order but there is certainly a trend.
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