There was some difficulty copying Norm's letter from disk, and so
I'll do that later. For now, let me make just a few comments.
When I first defined Cloneproof SSD, here & elsewhere, the first thing
I said was, "SSD can be made cloneproof by changing its stopping rule."
That should have been clue #1 that Cloneproof SSD is just SSD with
a different stopping rule.
Then, I stated the definition of Cloneproof SSD. It was identical
to SSD's definition, except that the stopping rule was different.
That should have been clue #2 that Cloneproof SSD is just SSD with
a different stopping rule.
Somehow Norm missed both clues.
Norm apparently does understand the definition of SSD, because he
agrees that, when there are no pairwise ties, it's equivalent to
Schulze's method. But if he understands SSD's wording, how come he
gets so all confused by Cloneproof SSD's definition, which is identical
except for a different stopping rule? Even after I spelled it out that
Cloneproof SSD is SSD with a different stopping rule?
But Norm invented a wildly different method which he calls Cloneproof
SSD. Norm, I encourage you to invent whatever you want to, but please
use an original name for your inventions. And would you be so kind as
to let me be the one who decides what is my definition of a method
that I propose?
As I said, Markus Schulze, the proponent of Schulze's method, says
that Cloneproof SSD and Schulze are equivalent, always producing the
same winner(s), or the same win-probabilities.
Norm, you said you were going to test for that equivalence with your
simulations. I take it that you've done that testing for your very
own "Cloneproof SSD", which isn't mine. Now, why don't you start over,
and, this time, test for Cloneproof SSD, as I define it, to test for
that equivalence. Yes or No: Can you find an example where Cloneproof
SSD fails a criterion that Schulze passes, or is less decisive than
Schulze? Yes or No: Can you find an example where the 2 methods produce
different winner-sets, or different win-probabilities?
I've written a demonstration that the Cloneproof SSD & Schulze are
equivalent. I'll post it later. But there's nothing un-obvious about
the demonstration. Assume that a certain candidate is a Schulze winner
(not necessarily the only one), and ask whether that candidate can
fail to be undefeated after Cloneproof SSD has gotten a current Schwartz
set containing no cycles. Then assume that a candidate is not a Schulze
winner, and ask whether that candidate can be undefeated at that time.
But I'll send my demonstration of that later.
Can we dispense with wasting people's time by defining & discussing
Reverse Tideman, DCD, IBCM, & Peyton Young's method? I don't want to
waste the letter kilobytes needed to demonstrate that none of those
, iterated or otherwise, is Cloneproof SSD. When talking about Cloneproof
SSD & its properties, I'm going to have to insist that we only use
my own definition, by my own wording.
So then Norm shows that his method, which he calls "Cloneproof SSD",
but which I'll call Petry's method, fails Monotonicity.
If you want to show that Cloneproof SSD fails a Criterion, Norm,
show that by using _my_ definition of Cloneproof SSD.
Applying Cloneproof SSD to Norm's Monotonicity example, it doesn't
fail Monotonicity. In the 1st election, it chooses C. In the 2nd
election, when some voters have changed their ballots by voting A
over C, that changes the winner from C to A.
Now, since Cloneproof SSD's definition is so brief, and since it's
been misunderstood, can I repeat it?
Cloneproof SSD is SSD with a new stopping rule: We don't stop until
there are no cycles in the current Schwartz set. Otherwise it's the
same as SSD. I'll restate it here:
Drop the weakest defeat that's among the current Schwartz set. Repeat
till there are no cycles in the current Schwartz set.
(The current Schwartz set is the Schwartz set based only on undropped
defeats).
[end of definition]
Now Norm, is that clear? That definition is not complicated.
Mike Ossipoff
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