[EM] Fixing IRV

[Richard Moore]

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".

Richard