100分求数学题答案及过程和大概思路

1个回答

  • 记各系统元素依次为a、b、c、d...

    记极小赢家联盟为W,极大输家联盟为L,极小否决权联盟为D,明手为N.

    所有包含W的都为赢家联盟,所有L的子集都为输家联盟,所有包含D的联盟都为否决权联盟.

    a[51:52,48]

    W=[a]

    L=[b]

    D=[a]

    N没有

    b[2:1,1,1]

    W=[ab] [bc] [ac]

    L=[a] [b] [c]

    D=W

    N没有

    c[3:2,1,1]

    W=[ab] [ac]

    L=[bc]

    D=W [a] [bc]

    N没有

    d[8:5,4,3,3]

    W=[ab] [ac] [ad] [bcd]

    L=[bc] [cd] [bd]

    D=W

    N没有

    e[51:45,43,8,4]

    W=[ab] [ac] [bc]

    L=[ad] [bd] [cd]

    D=W

    N=d

    f[51:28,27,26,19]

    W=[ab] [ac] [bc]

    L=[ad] [bd] [cd]

    D=W

    N=d

    g[16:10,10,10,1]

    W=[ab] [ac] [bc]

    L=[ad] [bd] [cd]

    D=W

    N=d

    h[21:10,10,10,10,1]

    W=[abc] [abd] [abe] [acd] [ace] [ade] [bcd] [bce][bde] [cde]

    L=[ab][ac][ad][ae][bc][bd][be][cd][ce][de]

    D=W

    N没有

    i[51:28,24,24,24]

    W=[ab] [ac] [ad] [bcd]

    L=[bc] [cd] [bd]

    D=W

    N没有

    j[6:4,3,2,1]

    W=[ab] [ac] [bcd]

    L=[bc] [cd] [bd]

    D=W [bc] [ad]

    N=d

    k[4:3,1,1,1,1]

    W=[ab] [ac] [ad] [ae] [bcde]

    L=[a] [bcd] [bce][bde] [cde]

    D=W

    N=b c d e

    参考资料:《运筹与管理》1999年6月 《公平性与数学化》