[EM] calculating the N matrix in Schulze STV

[Markus Schulze]

Hallo,

N[{a,b,c},d] = 169 or Ñ[{a,b,c}, {a,b,d}] = 169 means
that W=169 is the largest value such that the electorate
can be divided into 4 disjoint parts T1,T2,T3,T4 such that

(1) Every voter in T1 prefers candidate a to candidate d;
and T1 consists of at least W voters.

(2) Every voter in T2 prefers candidate b to candidate d;
and T2 consists of at least W voters.

(3) Every voter in T3 prefers candidate c to candidate d;
and T3 consists of at least W voters.

Here is the example of page 38:

Group 1: 60 voters a > b > c > d > e
Group 2: 45 voters a > c > e > b > d
Group 3: 30 voters a > d > b > e > c
Group 4: 15 voters a > e > d > c > b
Group 5: 12 voters b > a > e > d > c
Group 6: 48 voters b > c > d > e > a
Group 7: 39 voters b > d > a > c > e
Group 8: 21 voters b > e > c > a > d
Group 9: 27 voters c > a > d > b > e
Group 10: 9 voters c > b > a > e > d
Group 11: 51 voters c > d > e > a > b
Group 12: 33 voters c > e > b > d > a
Group 13: 42 voters d > a > c > e > b
Group 14: 18 voters d > b > e > c > a
Group 15: 6 voters d > c > b > a > e
Group 16: 54 voters d > e > a > b > c
Group 17: 57 voters e > a > b > c > d
Group 18: 36 voters e > b > d > a > c
Group 19: 24 voters e > c > a > d > b
Group 20: 3 voters e > d > c > b > a

T1, T2, and T3 can be chosen as follows:

T1
Group 1: 60 voters a > b > c > d > e
Group 2: 1 voter a > c > e > b > d (one of the 45 voters of group 2)
Group 3: 30 voters a > d > b > e > c
Group 4: 15 voters a > e > d > c > b
Group 5: 12 voters b > a > e > d > c
Group 9: 27 voters c > a > d > b > e
Group 19: 24 voters e > c > a > d > b

T2
Group 2: 44 voters a > c > e > b > d (44 of the 45 voters of group 2)
Group 7: 39 voters b > d > a > c > e
Group 8: 17 voters b > e > c > a > d (17 of the 21 voters of group 8)
Group 12: 33 voters c > e > b > d > a
Group 18: 36 voters e > b > d > a > c

T3
Group 6: 48 voters b > c > d > e > a
Group 8: 4 voters b > e > c > a > d (4 of the 21 voters of group 8)
Group 10: 9 voters c > b > a > e > d
Group 11: 51 voters c > d > e > a > b
Group 17: 57 voters e > a > b > c > d

Markus Schulze