Schulze Method - Implementation

Implementation

The only difficult step in implementing the Schulze method is computing the strongest path strengths. However, this is a well-known problem in graph theory sometimes called the widest path problem. One simple way to compute the strengths therefore is a variant of the Floyd–Warshall algorithm. The following pseudocode illustrates the algorithm.

1. # Input: d, the number of voters who prefer candidate i to candidate j.
2. # Output: p, the strength of the strongest path from candidate i to candidate j.
4. for i from 1 to C
5. for j from 1 to C
6. if (i ≠ j) then
7. if (d > d) then
8. p := d
9. else
10. p := 0
12. for i from 1 to C
13. for j from 1 to C
14. if (i ≠ j) then
15. for k from 1 to C
16. if (i ≠ k and j ≠ k) then
17. p := max ( p, min ( p, p ) )

This algorithm is efficient, and has running time proportional to C3 where C is the number of candidates. (This does not account for the running time of computing the d values, which if implemented in the most straightforward way, takes time proportional to C2 times the number of voters.)