# [EM] Rejecting the Schulze preferential voting method: a time for reform

Markus Schulze markus.schulze at alumni.tu-berlin.de
Thu Dec 18 11:24:09 PST 2003

```Dear Craig,

you wrote (18 Dec 2003):
> Let's consider the algorithm itself. Here I quote from the VM 17
> PDF file:
>
> ---
> :     Suppose that d[X,Y] is the number of voters who
> :     strictly prefer candidate X to candidate Y. Then the
> :     Smith set is the smallest non-empty set of candidates
> :     with d[A,B] > d[B,A] for each candidate B outside this
> :     set.
> ---
>
> The English text of Schulze probably seems to imply this
> interpretation:
>
> * Let there be only 3 candidates. Let the ballot papers be these:
>
> 2 (CA)
> 5 (CAB)
> 1 (CBA)
>
> What is Mr Schulze's d[A,B] ?.
>
> We could look at the computer algorithm source code but it takes
> the "d" matrix as an input. The vote counting algorithm can't actually
>
> The d[A,B] value would be:
>
>  (Interpretation 1) the number 7, or
>  (Interpretation 2) the number 5, or
>  (Interpretation 3) the number 6, or
>  (Interpretation 4) the number 4, or
>
> I suppose Interpretations 3 and 4 can be rejected.
>
> ...

In the Introduction of the quoted paper, I write: "It is presumed
that each voter casts at least a partial ranking of all candidates."

Markus Schulze

```