# [EM] Cloneproof Schwartz Sequential Dropping / Schulze

James Green-Armytage jarmyta at antioch-college.edu
Thu Jul 17 20:59:04 PDT 2003

A v B:	50 v 50
A v C:	40 v 30
A v D:	40 v 30
B v C:	40 v 30
B v D:	40 v 30
C v D:	60 v 40

Arrgh! Sorry. I think that my last post didn't make any sense! C is the
winner for 'Plain Condorcet' aka Sequential Dropping, but C couldn't be
the winner with Schwartz Sequential Dropping, could he?
That is, only A and B are members of the Schwartz set, as they not beaten
by C or D, but C and D are both beaten by them. Is that correct?
So am I wrong in saying that SSD would return the same result as CSSD,
i.e. the tie between A and B?

Sorry for thinking out loud here. I guess I'm still lost so far.

_________________________________________

Here are the definitions that were recommended to me:

Marcus Schulze's description of CSSD, from August 1998:

Step1: Calculate the Schwartz set among the potential winners
and eliminate all those candidates, who are not in the
Schwartz set of the potential winners!

Step2: If there is still more than one potential winner, then
replace the weakest pairwise defeat (i.e. the pairwise
defeat with the smallest absolute number of votes for
the winner of that pairwise comparison) between two
potential winners with an equality! Pairwise defeats,
that have already been replaced by an equality, stay
replaced. Go to Step1!
Otherwise, if there is only one potential winner, then
this potential winner wins the election.

***

Mike Ossipoff's description of CSSD, from January 2001:

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.

***

Mike Ossipoff's description of SSD, from January 2001:

Drop the weakest defeat that is among the current Schwartz set.
Repeat till there's an unbeaten candidate.

***

The key difference between Mike's two definitions seems to be between the
phrase "till there are no cycles," and the phrase "till there's an
unbeaten candidate".
Does the second meaning necessarily refer to one, single, exclusive
unbeaten candidate, whereas the first definition allows for two tied
candidates? This doesn't seem entirely right, but it's the only thing I've
been able to think of so far.

-- James