[EM] Smith//PC , GSFC, & SDSC

[MIKE OSSIPOFF]

>Why does your 5 Oct 2000 example demonstrate that Smith//PC
>fails GSFC and SDSC?


Of course I didn't post examples--I only posted example outlines.

The outlines don't prove anything.

I'll post numerical examples next.

Because those 2 criteria mention majorities, it's necessary to
specify the number of voters, and that means that the examples will
have to show actual rankings (sometimes sincere, & sometimes voted).

The examples that are needed to show Smith//PC's failure of GSFC
& SDSC involve a cycle & a subcycle. A "2-ring circus" like that,
in which it's necessary to show the rankings that make it happen,
isn't the easiest kind of example to write. But I'll post the
numerical examples as soon as I get them written.

In the meantime, I'd like to make a few brief comments:

1. Until I post the numerical examples, you can rightly say that it'
hasn't been proven that Smith//PC fails GSFC & SDSC. That's ok. It
_is_ demonstrated that Tideman(wv) & SSD  (The 2 best Condorcet versions)
meet those 2 criteria.

Now, if, until I post the examples, you want to claim that Smith//PC
passes, and if you want to drop BeatpathWinner and replace it with
Smith//PC, that's fine with me. But don't be surprised when it's
shown that Smith//PC fails GSFC & SDSC.

Though Smith//PC isn't my favorite, and though I advocate Tideman(wv)
& SSD instead, as the best rank counts, I don't want to discourage
you from replacing BeatpathWinner with Smith//PC. That's because,
even though BeatpathWinner is better than Smith//PC, BeatpathWinner
is also much less suited to be a public proposal, due to its greater
complexity and its lack of natural & obvious motivation & justification.

2. I admit, and have alway asserted, that, though PC & Smith//PC
fail SDSC, they don't _easily_ fail that criterion. They require a
complicated & elaborate example in order to fail SDSC. I always said
that. Now I repeat it, so you'll understand that writing the failure
examples is easier said than done. But I'll write them & post them
as soon as they're written.

But if it's your point that the failure examples are complicated &
elaborate enough, difficult enough to write, that, for practical
purposes, it's almost as if Smith//PC met those criteria, then I
won't disagree with that.

3. If you aren't abandoning BeatpathWinner and replacing it with
Smith//PC, then can we say that no one is currently proposing
Smith//PC? Ordinarily it isn't considered super important to demonstrate
criterion failures of methods that aren't being proposed. IRV is
being proposed. Why don't you ask me to give you  examples of IRV
failing GSFC & SDSC, instead of Smith//PC? Because you know that
Smith//PC is more difficult, due to the elaborate subcycle examples
needed? :-)

Actually, for IRV, we'd only need to show it failing SFC & WDSC,
since anything that fails those also fails GSFC & SDSC.

[end of 3 comments]

Anyway, if you want failure examplels for Smith//PC, those will be
posted as soon as I write them.

Mike Ossipoff

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