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