# Re: RFD: Reviving Constitutional amendment: Smith/Condorcet vote tallying

```On Thu, Oct 17, 2002 at 01:47:35PM +1000, Anthony Towns wrote:
> YM "Schwartz set" here? [0] There might be a "Schulze set" of some sort?

http://www.barnsdle.demon.co.uk/vote/condor2.html says:

"1. An "unbeaten set" is a set of candidates none of whom is beaten by
anyone outside that set. 2. An innermost unbeaten set is an unbeaten
set that doesn't contain a smaller unbeaten set. 3. The "Schwartz set"
is the set of candidates who are in innermost unbeaten sets."

I can't find any meaningful references to "schulze set" using google,
but if I recall correctly, "schulze set" has a different definition.

Remember that "innermost unbeaten set" is an ambiguous term if there
are any pairwise ties in an innermost unbeaten set.

> If so, it's defined as: "The Schwartz set is the smallest non-empty set
> of options such that no option within the set is beaten by any option
> outside of the set." It's probably easier to say it that way (since you
> don't need to discuss "beat path" at all then).

In my original draft, I used the term "Candidate" in place of "Schwartz
set" (and the grammar was a bit different).  Personally, I'm not
particularly attached to the terminology, as long as it's unambiguous
and understandable.

> It'd probably be more intuitive to say "A dominates B if A beats B,
> or there is some other option C, where C dominates B and A beats C" or
> something similar, so it's clear which direction the beat path goes in.
> That rephrases the above as: "An option A is said to be in the Schultz
> set if there is no option B where both B dominates A, but A does not
> dominate B".

"Dominates" invites non-technical comparisons between the proposed
mechanism and the existing mechanism.  I'd like to avoid that term
if possible.

> >     5. All options which do not beat the default option by their
> >        supermajority ratio are discarded, and references to them
> >        in ballot papers will be ignored.
> >     6. If a quorum is required, there must be at least that many votes
> >        which prefer the winning option to the default option. If there
> >        are not then the default option wins after all. For votes
> >        requiring a supermajority, the actual number of Yes votes is used
> >        when checking whether the quorum has been reached.
>
> Shouldn't the quorom be counted at the same time the supermajority is?

The quorum mechanism is structurally different from the supermajority
requirement.

This does raise the question: should the supermajority ratio be applied
to quorum requirements?  If you're happy applying the ratio in that
fashion, it would seem reasonable to combine these into one.  However,
that's a different proposal.

> >     7. If no option beats the default option, the default option wins.
>
> Why this special case? The Perl program I wrote for this uses the
> following system:

To deal with the case of no votes and on a ballot with no quorum
requirement.

> #     1. Calculate Schwartz set according to uneliminated defeats.
> #     2. If there are no defeats amongst the Schwartz set:
> #           2a. If there is only one member in the Schwartz set, it wins.
> #           2b. Otherwise, there is a tie amongst the Schwatz set.
> #           2c. End
> #     3. If there are defeats amongst the Schwartz set:
> #           3a. Eliminate the weakest defeat/s.
> #           3b. Repeat, beginning at 1.
>
> It might make sense to say:
>
> 	2a. If there is only one member in the Schwartz set, it wins.
> 	2b. If the default option is in the Schwartz set, it wins.
> 	2c. Otherwise, the voter with a casting vote may choose a
> 	    winner from the remaining options, or may choose to let the
> 	    vote be retaken.

In other words, don't bother dropping weakest defeats?

[1] This is a different proposal.
[2] This makes the casting vote much more powerful than the the current
draft.  [In some cases, the casting vote becomes more powerful than a
[3] If you want to discuss this further I'd like to lay out a theoretical
basis for the discussion -- do you care enough to make that worthwhile?

I think I'm ok with your other rephrasings, but I think it's important
to draw a line between "expressing the concept better" and "expressing
a different concept".

> that is, only do special cases when you really don't have a choice.
>
> >     8. If only one option remains in the schultz set, that option is
> >        the winner.
> >     9. If all options in the schultz set are tied with each other,
> >        the elector with the casting vote picks the winner from the
> >        schultz set.
>
> "tied with each other" doesn't seem particularly well defined, IMO.
> Every single pairwise comparison has to be exactly balanced, or already

I'm not at all clear what you're objecting to, here.  Is there something

> >    10. Otherwise, there are multiple options in the schultz set and
> >        they are not defeated equally:
> >           a. The weakest defeat is identified.  The weakest defeat
> >              is the fewest votes against any option in the schultz
> >              set, and (for that many votes against) the most votes
> >              for the corresponding option in the schultz set.
> >           b. If more than one option has the exact same number of
> >              votes in favor and the exact same number of votes opposed,
> >              and if those numbers are the same as for the weakest defeat,
> >              all these option pairs are considered to be examples
> >              of the weakest defeat.
> >           c. The schultz set is then refigured with the Beats of the
> >              weakest defeats eliminated.
> >           d. We resume at step 8 with the new schultz set to determine
> >              the winner.
>
> "refigured" isn't well defined.

I'm having trouble understanding this objection as well.

Hmm.. can you propose some alternate interpretations of "refigured"?
[That way I can pick the one that I intended and we can use your phrasing