*To*: debian-vote@lists.debian.org*Subject*: Re: Request for comments [voting amendment]*From*: Raul Miller <moth@debian.org>*Date*: Thu, 14 Nov 2002 16:56:03 -0500*Message-id*: <[🔎] 1037310963.a37bed59@debian.org>*In-reply-to*: <[🔎] 3DD2DC8A.5060309@14850.com>*References*: <[🔎] 1037073338.72aff062@debian.org> <[🔎] 20021112094922.GU16954@apocalypse.deadbeast.net> <[🔎] 1037142234.dd78df4a@debian.org> <[🔎] 3DD2DC8A.5060309@14850.com>

On Wed, Nov 13, 2002 at 06:13:14PM -0500, Buddha Buck wrote: > Definition: A "ballot" consists of a ranking A>B>C>D>... of options > submitted by a voter. It defines a total ordering of options for a > particular voter (i.e., for any pair of options A and B, we can claim > that a particular voter feels either A>B, A<B, or A=B, and iff A>B, then > B<A). Ok. Note that A=B only happens for the case where the voter mentioned neither A nor B in their ballot. In my opinion, we should ignore the number A=B: it should have no bearing on the result. > Let |A>B| be the number of voters who voted A>B. > Similarly, for |A<B| and |A=B|. > > (Obviously, |A>B| + |A=B| + |A<B| = total number of voters, because of > the definition of a ballot.) Ok. > > 2. Options which do not defeat the default option are eliminated. > > > > Definition: Option A defeats option B if more voters prefer optio > > A over option B than prefer option B over option A. > > Let A>>B ("A defeats B") if |A>B| > |B>A| > Let A==B ("A ties B") if |A>B| = |B>A| > Let A<<B ("A is defeated by B") if |A>B| < |B>A| > (Note: A==A, for all options A) > > Eliminate all options A if Default>>A. > > Clarification: What if Default==A? Then A does not defeat the default option. > > 3. If an option has a quorum requirement, that option must defeat > > the default option by the number of votes specified in the quorum > > requirement or the option is eliminated. > > Does is mean: > > Eliminate A if |A>Default| < Quorum > > or > > Eliminate A if |A>Default| - |Default>A| < Quorum It means "Eliminate A if |A>Default| - |Default>A| < Quorum". You should have been able to determine this the text I proposed by examining the definition of "defeat". > Again, how do we deal with that |A=Default| case? See above. > > > > 4. If an option has a supermajority requirement, that option must > > defeat the default option by the ratio of votes specified in the > > quorum requirement or the option is eliminated. > > (?) Eliminate A if |A>Default| / |A<Default| < Supermajority Ratio Yes. The original language in the constitution makes that clear, I'll include some of that language in my next draft. > Again, what about the |A=Default| votes? > > > > 5. If one remaining option defeats any other remaining options, > > that option wins. > > s/any/all/ Oops, yes. > "Condorcet Winner" > > If there is a remaining option A, such that for all remaining options B, > either A=B, or A>>B. A=B is a tie -- ties are recognized in a seperate procedural step. I suppose I could add some rules to recognize ties in additional places, but in my opinion that's unnecessary complexity. > > 6. If more than one option remains after the above steps, we use > > Cloneproof Schultz Sequential Dropping to eliminate any cyclic > > ambiguities and then pick the winner. These represent a procedure > > and must be carried out in the specified order: > > > > i. All options not in the Schultz set are eliminated. > > > > Definition: An option C is in the Schultz set if there is no > > other option D such that C is in the beat path of D AND D is > > not in the beat path of C. > > Let A>>>B mean there is a possibly empty sequence C, D, ..., E, F of > remaining options such that A>>C, C>>D, ..., E>>F, F>>B > > Then B is on the beat path of A. > > The Schultz Set = { A | A>>>A } No, because the schultz set includes ties. > Note: Because A==A, it isn't the case that A>>A, so if the Schultz set > includes A, then there must be a B!=A such that A>>B>>...>>A. Since > A>>B, we then have B>>...>>A>>B, so B is also in the Schultz set. > Therefore, the Schultz Set can't be a Singleton Set. I don't agree with this reasoning. However, once we have a singleton set we have a winner, so we could almost treat your conclusion as true. > > Definition: An option F is in the beat path of option G if > > option G defeats option F or if there is some other option > > H where option H is in the beat path of G AND option F is in > > the beat path of H. > > > > ii. Unless this would eliminate all options in the Schultz set, > > the options which have the weakest defeat are eliminated. > > > > Definition: The strength of a defeat is represented by two > > numbers: the number of votes for the defeated option and the > > number of votes for the defeating option. > > > > The more votes in favor of a defeated option, the weaker > > the defeat. Where two pairs of options have the same number > > of votes in favor of the defeated option, the fewer votes in > > favor of the defeating option, the weaker the defeat. > > So if we have two defeats A>>B and C>>D, then we lexigraphically compare > (|B>A|, -|A>B|) and (|D>C|, -|C>D|) > > What do you mean by "options with the weakest defeat"? I meant |A>B| and |B>A| where (|B>A|, -|A>B|) is a weakest defeat, [I didn't phrase that very will in the draft.] > My understanding was that we were removing defeats from consideration. > If, for example, there were four options A, B, C, D in the Schultz Set, > we'd initially be looking at the following set of defeats, in strongest > to weakest order: > > A>>B > A>>D > B>>C > C>>A > D>>C > B>>D > > After eliminating the weakest defeat (in this case, B>>D, we no longer > consider it when determining the Schultz Set, as if we had declared > B==D, so that neither B>>D or D>>B held. In essence, yes. More specifically, |B>D|=|D>B|=0. > So what do we really want to eliminate here? We want to eliminate that option pair from consideration when determining the next Schwartz set. > And... > > What if we had |D>C| = |B>D|, |D=C| = |B=D|, |D<C| = |B<D|, so that > neither D>>C nor B>>D was weaker than the other? Do we eliminate both > defeats? Yes -- this is very important if there's only a small number of voters participating. Also, I used this in how I phrased the rule to recognize ties. > > iii. If eliminating the weakest defeat would eliminate all options > > in the Schultz set, a tie exists and the person with the > > casting vote picks from among these options. > > Hmmm, if we had: > > Defeats = {A>>B, B>>C, C>>A} > > then the Schultz set is {A, B, C}. Eliminating the weakest defeat > (C>>A) would break all the cycles, so !(A>>>A), !(B>>>B), !(C>>>C), so > the Schultz set is now empty. Do we want to the casting-vote-caster to > decide in this case, or do we want to say that A wins? The schultz set is not empty. A is in the schultz set, and A wins. > I think it would be better to declare a tie iff all the DEFEATS would be > eliminated, not all the options. Since all the defeats would be > eliminated only if they were all of equal strength, there shouln't be a > problem. A tie exists after all defeats have been eliminated, not before. > > iv. Otherwise, a new schultz set is found, with those weakest > > defeats eliminated, > > > > v. If this new schultz set contains only one option, that option > > wins. > > As defined, the Schultz set can't be singleton. Maybe I'm > misinterpreting teh Schultz set. Yes. Thanks, -- Raul

**References**:**this is not a draft***From:*Raul Miller <moth@debian.org>

**Re: this is not a draft***From:*Branden Robinson <branden@debian.org>

**Request for comments [voting amendment]***From:*Raul Miller <moth@debian.org>

**Re: Request for comments [voting amendment]***From:*"Buddha Buck" <bmbuck@14850.com>

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