Mathematics in Action

Pairwise Comparison with the MAS Election



  • A vs. B:

    Preference Schedule for the MAS Election
    Number of voters 14 10 8 4 1
    1st choice A C D B C
    2nd choice B B C D D
    3rd choice C D B C B
    4th choice D A A A A

    A ranks better than B 14 times.
    B ranks higher than A 10 + 8 + 4 + 1 = 23 times.
    So the score for A vs. B is 14 to 23.
    So B gets 1 point.


  • A vs. C:

    Preference Schedule for the MAS Election
    Number of voters 14 10 8 4 1
    1st choice A C D B C
    2nd choice B B C D D
    3rd choice C D B C B
    4th choice D A A A A
    A ranks higher than C 14 times.
    C ranks higher than A 10 + 8 + 4 + 1 = 23 times.
    So the score for A vs. C is 14 to 23.
    So C gets 1 point.


  • A vs. D:

    Preference Schedule for the MAS Election
    Number of voters 14 10 8 4 1
    1st choice A C D B C
    2nd choice B B C D D
    3rd choice C D B C B
    4th choice D A A A A
    A ranks higher than D 14 times.
    D ranks higher than A 10 + 8 + 4 + 1 = 23 times.
    So the score for A vs. D is 14 to 23.
    So D gets 1 point.


  • B vs. C:

    Preference Schedule for the MAS Election
    Number of voters 14 10 8 4 1
    1st choice A C D B C
    2nd choice B B C D D
    3rd choice C D B C B
    4th choice D A A A A
    B ranks higher than C 14 + 4 = 18 times.
    C ranks higher than B 10 + 8 + 1 = 19 times.
    So the score for B vs. C is 18 to 19.
    So C gets 1 point.


  • B vs. D:

    Preference Schedule for the MAS Election
    Number of voters 14 10 8 4 1
    1st choice A C D B C
    2nd choice B B C D D
    3rd choice C D B C B
    4th choice D A A A A
    B ranks higher than D 14 + 10 + 4 = 28 times.
    D ranks higher than B 8 + 1 = 9 times.
    So the score for B vs. D is 28 to 9.
    So B gets 1 point.


  • C vs. D:

    Preference Schedule for the MAS Election
    Number of voters 14 10 8 4 1
    1st choice A C D B C
    2nd choice B B C D D
    3rd choice C D B C B
    4th choice D A A A A
    C ranks higher than D 14 + 10 + 1 = 25 times.
    D ranks higher than C 8 + 4 = 12 times.
    So the score for C vs. D is 25 to 12.
    So C gets 1 point.

    Summary:

    MAS Election: Pairwise Comparisons
    Pair Score Points
    A vs. B 14 - 23 B : 1
    A vs. C 14 - 23 C : 1
    A vs. D 14 - 23 D : 1
    B vs. C 18 - 19 C : 1
    B vs. D 28 - 9 B : 1
    C vs. D 25 - 12 C : 1

    Total Points:
    A : 0
    B : 2
    C : 3
    D : 1
    So C is the winner!!!