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
hundred regular votes.]
[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
> discarded.
I'm not at all clear what you're objecting to, here. Is there something
ambiguous about that phrasing?
> > 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
instead of mine.]
--
Raul
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