[EM] clone immunity definitional problems

[Markus Schulze]

Dear Warren,

you wrote (27 Jan 2007):

>  * Schulze does not say anything explicitly about equalities but some
>    facts can be deduced because he used "iff" rather than "if."  (By
>    the way, it might be better merely to use "if" because "iff" may
>    lead to insurmountable problems...).  Here are deduced facts:
>  * iff A=B in in an old vote in the old election, then A=(all B clones)
>    in the new one. That is a very strong demand by Schulze, and one I
>    feel should be avoided if we can avoid it.  In other words, I think
>    Schulze's definition is a bad definition because this demand is way
>    too strong.  However, maybe Schulze was forced to do that because
>    trying to weaken it leads to insurmountable problems.  If so I
>    retract my complaint.
>  * If A=C in in an old vote in the old election, then A=C in the new
>    one. (I have no objection to that.)

That's exactly what I wanted to say.

*********

You wrote (27 Jan 2007):

>  * I can't decode Schulze's third and last demand; too many subscripts
>    and superscripts - but perhaps he meant that cloning B leaves
>    all win probabilities unaltered for the uncloned candidates (and
>    consequently, the probability of B winning remains the same albeit
>    split among B's clones).  If that is what Schulze meant, then
>    he definitely made a bad mistake because of problems 1 and 2 up
>    top. These problems essentially would cause clone-immunity under
>    Schulze's definition to be a property that simply could never be
>    satisfied by any reasonable voting method - kind of a
>    self-contradicting property.

The third demand says that, if there is at least one voter w who
either strictly prefers candidate A to candidate B or strictly
prefers candidate B to candidate A, then cloning the candidate B
must not change the win probability of candidate A.

Markus Schulze