[EM] Cloneproof SSD

[MIKE OSSIPOFF]

Markus wrote:

>you wrote (21 Jan 2001):
> > When we randomly choose a tiebreaking
> > ballot, the members of the C clone set, no matter how many of them
> > there are, are no more likely to be at the top of that ballot than
> > A & B are. A, B, and the C clone set are equally likely to be at the
> > top of that tiebreaking ballot, as they should be. Adding those C
> > clones hasn't increased the probability of the winner being a C clone.
>
>It isn't clear to me how you use random ballot to decide which
>pairwise defeat you drop.
>Markus Schulze

Cloneproof SSD, as I define it, doesn't use Random Ballot to decide
which defeat to drop. If there are 2 or more equally weakest defeats
in the Schwartz set, it drops them all simultaneously.

However, I probably misread your example. I assumed that all the
defeats among then C clone set were equal, but you hadn't said that.
So what happens is that the defeats among the clone set, which are
all weaker than the other defeats in the Schwartz set, are dropped
1-by-1. While that's happening, the Schwartz set isn't changed,
because each clone retains a beatpath to all the other clone, via
A & B (The beatpath definition of the Schwartz set is sometimes
convenient. It's equivalent to the unbeaten-set definition).
Likewise, each clone retains a beatpath to & from each of the
nonclones, A & B.

So then, after all the defeats among the clone set have been dropped
1 by 1, the reamaining defeats are all equal, and so they'r dropped
simultaneously. _Then_ we use Random Ballot to choose which candidate
wins. That's all we use Random Ballot for. We don't use it to determine
which defeat to drop.

Mike Ossipoff


_________________________________________________________________
Get your FREE download of MSN Explorer at http://explorer.msn.com