[EM] Tideman and GMC

[Markus Schulze]

Dear Blake,

you wrote (24 Feb 2000):
> What I consider to be more important, however, is that Tideman is more
likely
> than Schulze to honour the result of an individual pairwise victory.
That is,
> if a majority of those with a preference rank A over B, Tideman is more
likely
> to ensure that this is reflected in the final ranking, including the ranking
> for first place.
>
> To put it more precisely, Tideman over-rules a pairwise majority only if
this
> is necessary in order to honour a greater pairwise majority.  If it is
unable
> to honour it, it skips it.  This ensures that a majority that can't be
> honoured does not end up over-ruling a majority that can, as can happen in
> Schulze.

That isn't true.

Both methods (= Tideman and Schulze) guarantee that if candidate A
pairwise defeats candidate B then this is reflected in the final ranking
unless there is a beat path from candidate B to candidate A which consists
only of pairwise defeats that are stronger than the pairwise defeat A:B.

Therefore both election methods guarantee that if candidate A pairwise
defeats candidate B then this is reflected in the final ranking unless this
would contradict a stronger pairwise defeat.

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de