# [EM] clone confusion

Warren Smith wds at math.temple.edu
Sat Jan 27 13:48:00 PST 2007

```>WDS: 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.

>Venzke: Hmm, does it really demand this? I think it only demands that if A=B
and you clone B, A cannot be ranked strictly above or strictly below
the entire set of clones.

That is A=B could become A=B1>B2 or B1>A=B2 or maybe even B1>A>B2, but
not A>B1>B2 or B1>B2>A.

because "iff" is a BIDIRECTIONAL
implication, i.e. a logical equivalence (<==> arrow),
and Schulze says  A>B iff  A>(all B clones)   ,
we see "A NOT-GREATER-THAN (all B clones)"   implies  A not greater than B.
And similarly for the < versus > inequality, and since A not< B and A not> B
is the the same as A=B,
we see that
A=B in an an old vote in the old election <==>
A=(all B clones) in the new one with B cloned  (under Schulze defn).

Bleah.  elementary logic, my dear Watson.

Similarly, you've got to watch out for demands probabilites "not increase."
Put a couple of those demands together and you can deduce probabilities "always stay the same."
If you aren't careful.  We need to figure out exactly what it is we want the
clone immunity defintion to say and not more.   It looks to me like that didn't happen
as yet.

PS:  I agree that approval fails clone immunity (with whatever definition of clone immunity
I would want, anyhow).  But  would want to try to define it so IRV and Schulze both
satisfy clone immunity (and range too).

Warren D. Smith
http://rangevoting.org

```