[EM] Reply to Norm's misdefinition

[MIKE OSSIPOFF]

>On January 30, 2001 Mike Ossipoff wrote:
>
> >
> >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?
> >
>
>etc.
>
>Mike seems to be implying that I was attempting to redefine his proposed
>method in order to level false criticisms against it.

I didn't say it was intentional, and I didn't say that it wasn't
intentional. I merely said that you've written a wildly different
definition of my proposal.


>When I began looking at Cloneproof SSD, I referred to the definition that
>Mike had supplied, which was:
>
>"Drop the weakest defeat that's among the Schwartz set. Repeat till there
>are no cycles in the Schwartz set. Whoever is unbeaten at that time wins."
>
>The way I interpreted this was:
>
>1. Calculate the Schwartz set, S.
>2. Drop the weakest defeat in S (if there is more than 1 equal, drop them
>all)
>3. Repeat (2), until there are no cycles among candidates in S.
>
>Mike's intended method was:
>
>1. Calculate the Schwartz set, S.
>2. Drop the weakest defeat in S (if there is more than 1 equal, drop them
>all)
>3. Repeat (1), until there are no cycles among candidates in S.

Excuse me, but what you say I intended is the same as what you say
is your interpretation. Instead of coming up with all these theories
about what I indended, it would be more practical to just address
the problems that you have with my wording, as I try to do below.


>I believe that the definition that Mike supplied was unclear, and that the
>my (admittedly incorrect) interpretation of Cloneproof SSD is also 
>described
>by the definition he supplied.  The problem is that it is not obvious what
>exactly is being repeated -- is it the dropping of weakest defeats, or the
>calculation of Schwartz sets?  Even with Mike's clarified definition, I
>don't think it is obvious.  Others may disagree, of course.

Ok, do you know what this means:

IRV:

Eliminate the candidate who, among the uneliminated candidates, has
fewest votes. Repeat till a candidate has a majority of the votes.

[end of definition]

Presumably, you'd ask: Exactly what is being repeated here? Is it the
elimination of candidates, or is it the looking-up of which
candidates are undefeated?

Nonsense. The 1st sentence refers to the uneliminated candidates,
and so when we execute that sentence, we must look up which candidates
are uneliminated.

Cloneproof SSD:

Drop the weakest defeat that's among the Schwartz set based only
on undropped defeats. Repeat till there are no cycles in the
Schwartz set based only on undropped defeats.

[end of definition]

The 1st sentence refers to the Schwartz set based only on undropped
defeats. Executing the 1st sentence requires looking up which
defeats are undropped, and determining the Schwartz set based on
that.

If Norm is unable to understand that, then he must also be unable
to understand the IRV definition.

In fact, Norm understood my definition of ordinary SSD. And yet,
in Cloneproof SSD's definition, wording that is identical to wording
in ordinary SSD has suddenly become unclear to Norm.

>
> >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.
> >
>
>After receiving your reply on Sunday ("Possible misunderstanding of
>definition"), I did precisely this.  I applied both the Schulze method and
>my revised implementation of Cloneproof SSD to a series of 'Smith 
>Matrices',
>and could not discover *any* difference in results over a great many trials
>with a large number of candidates (25,000 trials, 15 candidates).
>Therefore, I think it is safe to say that Cloneproof SSD is equivalent to
>Schulze, and therefore has the same properties as that method (Clone
>Independence, Monotonicity, etc.)
>
>A *proof* that the methods are equivalent would be better, of course,

That will be along tonight or tomorrow. I meant to send it tonight,
but I replied to Norm's letter instead. I'd better send the
demonstration of equivalence tomorrow.


but I
>have no doubt that Cloneproof SSD is the same as the Schulze beatpath 
>method
>(at least, as I had always understood it -- more on this later).
>
> >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?
>
>No.  The methods are equivalent, provided that the 'beatpaths' used in
>Schulze's method are constructed using pairwins only>

> >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.
> >
>
>I agree it's not complicated (presupposing one understands the Schwartz-set
>concept), but no, it still isn't very clear, for reasons explained above.

I hope that I've answered your unclarity claim, earlier in this
letter.

Mike Ossipoff

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