[EM] Discover Magazine article

[Markus Schulze]

Dear Blake,

you wrote (29 Oct 2000):
> It is often stated that the Tideman winner beats the Schulze winner
> more often than the opposite.  I'm going to prove this.  Also, I'm
> going to discuss Markus's point about the Schulze winner being less
> defeated.
>
> Let's say we have an example where the Schulze winner (which I will
> call S) beats the Tideman winner (which I will call T).
>
> For T to win, despite being beaten by S, it must be true that the S>T
> majority was skipped.  This can only happen if there is already a
> path locked from T to S that is greater than this majority.  The
> existence of a locked path in Tideman implies the existence of a path
> in Schulze.
>
> Since S won in Schulze, and there is a path from T to S, there must
> be an even higher path from S to T.
>
> So, consider what would happen if the S>T victory was flipped, so now
> T beats S with the same margin (or winning-votes depending on your
> preference).  The answer is, that nothing would happen.  Schulze and
> Tideman both still have higher paths that they would use instead.
>
> So, my point is that every example where the Schulze winner beats the
> Tideman winner is paired with an example where the Tideman winner
> beats the Schulze.  This is constructed simply by flipping the
> victory.
>
> However, there are some examples where the Tideman winner beats the
> Schulze winner, and which do not correspond to one of these pairs. 
> For example, 
>
> A>B 10
> B>C 9
> C>A 8
> D>B 7
> D>C 6
> A>D 5
>
> Tideman winner is A.  Schulze winner is D.  Clearly if the A>D
> victory was flipped, D would win in both methods.
>
> The basic point is this.  In Tideman, it is slightly harder to
> construct a path leading between two candidates that can make the
> direction of a victory irrelevant.  As a result, the direct
> comparison is more often decisive between the two candidates. 
> Although, I do not think we can say Tideman is superior just because
> it more often beats Schulze than the other way around, I do think
> that its lower tendency to over-rule direct comparisons is an
> advantage.
>
> It's worth pointing out that in the above example the Schulze
> winner's greatest defeat is less than the Tideman winner's.  Markus
> points out that this will more often be the case than the opposite,
> and I think it is fairly easy to see that this is so, although I'm
> not going to prove it in this email.  However, I don't see this as a
> disadvantage for Tideman.
>
> I think that the argument usually goes that this means we are
> over-ruling a greater victory, and we should not do this.  But let's
> think about what that really means.  It might mean, in the above
> example that we elect D instead of A because we want to uphold C's
> majority over A.  But let's think about the people who voted C over
> A.  Are we doing them a favour?  Do they all prefer D to A?  If we
> subtracted off the people who don't like the change, would we be left
> with a majority at all?  Clearly not, since A in fact beats D on
> direct comparison.
>
> I guess my criticism is of the view that sees a majority as something
> with a will of its own, that can go around demanding changes that
> aren't supported by the people making up the majority.

When you want to justify why the Tideman winner should be elected then
of course you have to justify why _from all candidates_ the Tideman
winner should be elected. It isn't sufficient to justify why rather
the Tideman winner than the Schulze winner should be elected.

In your example above, it isn't sufficient to justify why rather
candidate A than candidate D should be elected. You rather have to
justify why candidate A rather than any other candidate should be
elected.

It makes sense to say that as the strongest pairwise defeat of
candidate D is the weakest candidate D should be elected. But
in so far as there is no reason why only candidate A or candidate D
can be elected, it doesn't make much sense to say that as candidate A
pairwise beats candidate D candidate A should be elected.

Markus Schulze