[EM] Fixing IRV
rmoore4 at home.com
Fri Aug 10 19:00:15 PDT 2001
Markus Schulze wrote:
> Granted, but RP _is_ as an example of the negation. And as I said,
> proving the negation _does_ disprove the original statement.
RP *is not* an example of the negation. RP does not
eliminate candidates in the process of finding the winner.
> Suppose, that Tideman didn't propose RP but RP-elimination
> and that it didn't occurred to him that RP-elimination = RP.
Whether it occurs to him or not isn't relevant. It is the
existence of the equivalence that matters, not whether we
are capable of perceiving it.
> How do you want to check whether a given elimination method can
> also be defined as a method that doesn't "eliminate alternatives
> prior to selecting a winner"?
It is not reasonable to ask for a way to check this in
general. As Godel showed, there are true statements in
mathematics for which no proof can be found. So we may have
to live with the possibility that there may be methods out
there for which we cannot determine (with the certainty of
mathematical proof) if there is an equivalent
non-elimination method. If so, the proposition that the
equivalent exists (or not) for such a method will remain a
conjecture. Maybe it's true that no such problematic methods
exist (meta-statement). Maybe someone can even prove (or
disprove) this meta-statement. Then again, maybe the
meta-statement is true but cannot be proven.
In other words, "don't go there".
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