On Mon, Oct 21, 2002 at 11:30:46PM -0400, Raul Miller wrote: > > *shrug* Then how about "An option A is said to master an option, B, > > if A beats B, or if there is some other option, C, where A beats C and > > C masters B." ? Or "transitively beats" ? > In my first draft, I used "Option j is PREFERRED over option k if ...", > but that has the disadvantage of not being tied to the technical > nomenclature which has in the past been used to discuss this kind of > mechanism. Well, you just said a message ago that you didn't like using terms that'd been used before either, so that's a bit contradictory. It's weird to think that x can be "preferred" over y while y is also "preferred" over x, but probably not much more so than "masters" or "dominates" etc. > > ATM the quorum is done last ("check the winner meets quorum, if not, > > the default option wins"). > In this proposal, I'm not concerned with precisely matching the sequence > of events in the current mechanism. When I said "atm" I meant with the current draft -- the quoted phrase was from that draft. > > > > > 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. > > In which case every option will be listed as tied, and the tie-breaking > > rules can come into play. > If any of the options presented were good ideas, why would nobody vote > for them? Huh? *You* just said you were concerned with the case where no one votes. > I disagree with your assertion: > It's reasonable to consider all the options in the Scwartz set > to be "tied with each other" Well, that's nice, but unless you think I'm a raving lunatic, you're going to just have to accept my word on this one. > Tied has a specific meaning (same number of votes or as against). Any English word has many meanings, if you want to fix a specific one then you need to define it, which is my point. > Perhaps step 9 should be phrased: > 9. If all options in the schultz set, in each pairwise comparison, ^^^^^^^ Schwartz? > have both the same number of votes for the option as against the > option, a tie exists and the elector with the casting vote picks > the winner from the options in the schultz set. > That seems to eliminate the ambiguity you've described. I would still be inclined to require the default option to win if it's part of the tie. But yes, it clears up the ambiguity nicely, afaics. > > I'd suggest we be completely clear about what's going on. Something like: > > We define the "Current Schwartz Set" initially as the Schwartz > > Set calculated from the defeats of all options that have not been > > eliminated (This set is non-empty, since the default option is > > never eliminated by supermajority or quorum requirements) > > At this point we: > > 1. Eliminate all options not in the Current Schwartz Set > > from consideration. > > 2. If there are any pairwise defeats amongst members of > > the Current Schwartz Set, we: > > 2a. Choose the weakest such defeat(s) [define] > > 2b. Eliminate them from consideration [define] > > 2c. Recalculate the Current Schwartz Set, ignoring > > any options that have been eliminated, and > > ignoring any pairwise comparisons that have > > been eliminated, and return to step 1. > > 3. If there were no pairwise defeats, then: > > 3a. If there was only a single option in the Current > > Schwartz Set, it is the winner. > > 3b. If the default option is in the Current Schwartz > > Set, it is the winner. > > 3c. Otherwise, the vote is considered a tie, > > and the elector with a casting vote may choose > > to declare any of the tied options the winner, > > or may declare the default option the winner. > > Apart from the two lines marked [define], I think that's fairly > > unambiguous. (3b) replaces "7" in the draft, (3c) might be being too > > generous to whoever gets a casting vote? > Overall, I think I like this. However, I think we also need to define > "defeat". > > Here's my definitions: > > DEFEAT: > Option A is defeated by option B if option B beats option A. "A `defeat' exists between option A and option B (and A is said to defeat B) if A beats B, and the pairwise comparison between A and B has not already been eliminated from consideration." > WEAKEST DEFEAT: > Given a set of candidates and a vote, the weakest defeat is the defeat > which has the fewest opposing vote. If there's more than one pair > of options which has this many opposing votes, the weakest defeat is > the one where the defeated option also has the most votes in favor. > If there's more than one pair of options which has the fewest opposing > votes and (for that many opposing votes) the most options in favor, > then all of these defeats are considered instances of the weakest defeat. "A defeat, D, is said to be weaker than another defeat, E, (and thus E is said to be stronger than D) if it has fewer opposing votes, or it has the same number of opposing votes and more supporting votes. Two defeats, D and E, are said to be equal if the number of opposing votes are equal, and the number of supporting votes are equal. The weakest defeats of a set are the ones which are equal to each other, and weaker than all others." It might be better to recast the calculation of the "Schwartz set" in terms of "defeats" rather than "beats". Cheers, aj -- Anthony Towns <email@example.com> <http://azure.humbug.org.au/~aj/> I don't speak for anyone save myself. GPG signed mail preferred. ``If you don't do it now, you'll be one year older when you do.''
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