[EM] Fw: IBCM, Tideman, Schulze

[Markus Schulze]

Dear Mike,

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.

***

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).

***

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"?

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de