[EM] Fw: IBCM, Tideman, Schulze

[MIKE OSSIPOFF]

,
>
>you wrote (23 July 2000):
> > That SSD definition has a natural & obvious motivation
> > & justification that Schulze doesn't have. Both your
> > definitions use beatpaths.
>
>But the SSD definition uses Schwartz sets. And the definition
>of Schwartz sets uses beat paths.

The Schwartz set can be defined in terms of innermost unbeaten
sets. The Schwartz set is the set of candidates who are in
innermost unbeaten sets. But my SSD definition yesterday avoided
mentioning the Schwartz set, and only spoke of innermost
unbeaten sets.


>
>***
>
>You wrote (23 July 2000):
> > Markus wrote (22 July 2000):
> > > Example:
> > >
> > >   A:B=50:50
> > >   B:C=43:48
> > >   C:A=35:44
> > >
> > >   SSD chooses candidate A decisively because candidate A is
> > >   the unique Schwartz winner.
> >
> > Correct.
>
>I mentioned that example because once many active members of this
>mailing list agreed that if there are only three candidates then
>the winner should be the PC[va] winner and because in the example
>above SSD doesn't choose the PC[va] winner (as far as I have
>understood the definition of the PC[va] winner correctly).

I admit that's true, because of a sloppy PC definition on my
part. What I _meant_ was:

1. If anyone is unbeaten, he wins.
2. If not, then drop the weakest defeat. Repeat till there's an
unbeaten candidate.

I'd previously said that unless someone beats everyone, we
elect the candidate whose greatest defeat is the least.
I thought it was implied that A's greatest defeat is effectively
zero, because he has no defeat. But that was sloppy on my part.


>
>***
>
>You wrote (23 July 2000):
> > Yes, and based on that, and on the translations that you quoted
> > below, PC is the literal interpretation of Condorcet's words.
> > SD, as you point out isn't the literal meaning, and neither is
> > SSD.
>
>To my opinion, it is problematic to talk about the "literal
>interpretation of Condorcet's words." Condorcet neither defined
>properly what the "elimination" of a pairwise comparison is
>nor did he write what a "contradiction" is. Is A > B > C = A a
>"contradiction" or is only A > B > C > A a "contradiction"?

Sure, it isn't certain exactly what Condorcet meant or how
he'd carry out his words. That's why I named several possible
interpretations. It would have been better if he'd been more
specific, but anything consistent with his words seems to qualify
as Condorcet's method.


Mike Ossipoff

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