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 ---- Election-Methods mailing list - see http://electorama.com/em for list info