[EM] unintended changes in pairwise preferences

[Markus Schulze]

Dear Stephen Turner,

you wrote (17 Jul 2005):
> Is it known whether there can exist a procedure in
> which a pair (P1,P2) can never be reversed in the
> social ordering by changing only the unrelated (P3,P4)
> pairwise preferences in one or more ballots?

The Simpson-Kramer MinMax method satisfies this criterion.

*********

You wrote (17 Jul 2005):
> Among the criteria we usually discuss on this
> list, we do not have one on "stability", which should
> mean something like: "a small change in the ballots
> should change the outcome as rarely as possible".
> This seems desirable.  Has it already been discussed
> somewhere?

This criterion has been discussed in 2000 under the term
"indirect strategies". I argued that the Schulze method
(a.k.a. Schwartz sequential dropping, cloneproof Schwartz
sequential dropping, beatpath method, beatpath winner,
path voting, path winner) is better than Tideman's
ranked pairs method (according to this desideratum)
because the Schulze method chooses almost always the
same candidate as the Simpson-Kramer MinMax method.
For example, I wrote (3 Feb 2000):

http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-February/003556.html

> In the Schulze Method, the strength of the pairwise defeat B:D
> has no influence on the final winner; even if we set B:D=100:0
> or B:D=0:100, candidate A stays the Schulze winner. On the other
> hand, if we set B:D=59:41 then the Tideman winner is changed from
> candidate C to candidate A.
>
> You seem to believe that the fact that the Tideman winner usually
> depends on more elements of the matrix of pairwise defeats is a
> selling point. I view this fact of Tideman to be the fatal flaw in
> this method. The reason: If the question whether candidate A or
> candidate C is elected unnecessarily depends on how many voters
> prefer candidate B to candidate D then it is possible to manipulate
> the result of the elections by ranking B respectively to
> candidate D insincerely.
>
> In other words: If an election method should be as difficult as
> possible to manipulate then it should not only meet monotonicity,
> local independence from irrelevant alternatives, complete
> independence from clones, and beat path GMC, the result of the
> election method should also depend on as few irrelevant information
> as possible.

On the other side, Steve Eppley wrote (17 May 2000):

http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-May/003998.html

> In scenarios where direct strategies exist, the existence
> of indirect strategies in addition should not be considered
> a problem.

With "direct strategies", Steve Eppley meant "compromising"
and "burying".

Markus Schulze