[EM] Tideman and GMC

[Blake Cretney]

Dear Markus,

> Dear Blake,

> Example:
> 
>     26 voters vote C > A > B > D.
>     20 voters vote B > D > A > C.
>     18 voters vote A > D > C > B.
>     14 voters vote C > B > A > D.
>     08 voters vote B > D > C > A.
>     07 voters vote D > A > C > B.
>     07 voters vote B > D > A = C.
> 
> Tideman would elect candidate C.
> But it is possible that candidate A is a SASW and candidate C is no SASW
> and it is not possible that candidate A is no SASW and candidate C is a
> SASW. Therefore rather candidate A than candidate C should be elected.

What about

25 A D B C
35 B A D C -> B
30 D C A B
4  A D C B
6  C A D B
             winning-votes
A->D 35-30   35
A->B 65-35   65
C->A 36-29   36
B->C 60-40   60
D->B 65-35   65
D->C 59-6    59

Here, A is in the SASW; D is not.  A wins in Tideman (winning-votes),
but D wins in Schulze.

> You wrote (24 Jan 2000):
> > I have made some attempts to show that Schulze (path voting) is in some
way
> > intuitive.  That is, it seems to rely on "arguments" composed of majority
> > views, where the strength of the argument is equal to its weakest link.
> >
> > So, if we have
> >
> > A>B 30
> > B>C 20
> > C>D 15
> >
> > If we view pairwise decisions as more probably correct than incorrect, we
> > have to view this as evidence that A is better than D.  But what if we
also
> > knew that
> >
> > C>E 30
> > E>B 25
> >
> > Clearly, this gives evidence contrary to one of the links in our chain of
> > argument (B>C).  It suggest that it is more likely that C is better than
B,
> > than the contrary.  The whole chain of argument falls apart.  In fact, it
is
> > Tideman that makes use of this additional information.
> 
> It is not correct to say that "Tideman makes use of additional
information."
> For every pair of election methods it is possible to create a situation
such
> that both election methods lead to the same result and such that -if this
> situation is slightly modified- election method 1 still leads to the
> same result as before and method 2 leads to a different result.
> But it is not correct to conclude that election method 2 uses more
> information. All election methods use the same information; they only
> interpret this information differently.

My point was not that Tideman makes use of more information, in
general.  My point was only that additional information is used in a
particular situation, and that in that situation the additional
information seems relevant.  Of course, this assumes an attempt to
base the method on probability, evidence, or some similar grounds.

That is, if we justify Schulze on the basis that a path of victories

A>B, B>C, C>D

should be granted as evidence that A>D, as an obvious result of
believing that each pairwise victory is evidence of the superiority of
the winner over the loser, then we must also acknowledge that a path
contradicting one of these pairwise victories (a side-path) must
contradict the entire chain of argument.  Tideman ensures that if a
path is to be "locked", each victory must not contradict a higher
"locked" path.  So, it is using the information provided by these
side-paths.

---
Blake Cretney