*To*: debian-vote@lists.debian.org*Subject*: Hybrid Theory*From*: Raul Miller <moth@debian.org>*Date*: Sun, 8 Dec 2002 11:13:23 -0500*Message-id*: <1039364003.e4cc4b30@debian.org>*In-reply-to*: <1039280464.8937c974@debian.org>*References*: <1038167671.7a204f7a@debian.org> <1039280464.8937c974@debian.org>

Focusing on just A.6 again, in this draft: (*) Weakest defeats can now be eliminated: before a defeat of the default option is eliminated, all options which fail to meet their supermajority requirements are deleted. (*) When artificial supermajority defeats are eliminated the corresponding option is also deleted. (*) Terms expressed using mathematical shorthand have been named. (*) Other minor fixes ______________________________________________________________________ A.6 Vote Counting 1. Each voter's ballot ranks the options being voted on. Not all options need be ranked. Ranked options are considered preferred to all unranked options. Voters may rank options equally. Options left unranked by the voter are considered to be ranked equally with one another and below any ranked options. The other details of how ballots may be filled out will be included in the Call For Votes. 2. We construct the Schwartz set based on undropped options and defeats: a. An option A is in the Schwartz set if A has not been dropped and if for all options B, either A transitively defeats B, or B does not transitively defeat A. b. An option A transitively defeats an option C if A defeats C or if there is some other option B, where A defeats B AND B transitively defeats C. c. An option A defeats an option B, if the strength N(A,B)*V(A,B) is larger than N(B,A)*V(B,A), and if the (A,B) defeat has not been dropped. d. Given two options A and B, the votes V(A,B) is the number of voters who prefer option A over option B. e. If a majority of n:1 is required for A, and if B is the default option, majority requirement N(B,A) is n. In all other cases, N(B,A) is 1. 3. If any options involved in the weakest defeats between options in the Schwartz set are options in superdefeats, we drop the corresponding superdefeated options then return to step 2. a. A defeat (A,X) is weaker than a defeat (B,Y) if V(A,X) is less than V(B,Y). Also, (A,X) is weaker than (B,Y) if V(A,X) is equal to V(B,Y) AND V(X,A) is larger than V(Y,B). b. A weakest defeat is a defeat that has no other defeat weaker than it. There may be more than one such defeat. c. An option B is superdefeated by an option A if A defeats B, and if V(A,B) is not larger than V(B,A). c. Given a defeat (A,B) the options A and B are involved in this defeat. d. An option A is dropped by dropping all defeats which involve A and also stipulating that option A is not a member of the Schwartz set. 4. If there are defeats between members of the Schwartz set, we drop the weakest defeats then return to step 2. 5. If there are no defeats within the Schwartz set, then the winner is chosen from the undropped options in the Schwartz set where at least Q voters ranked that option above default option, where Q is the quorum requirement for the ballot. If there is only one such option, it is the winner. If there are multiple options, the elector with a casting vote chooses which of those options wins. "RATIONALE": Options which voters rank above the default option are options they find acceptable. Options ranked below the default option are unacceptable options. Supermajority options require some approximation of unanimity before they can be accepted. ______________________________________________________________________ This changes a few of the outcomes for tests posted in http://lists.debian.org/debian-vote/2002/debian-vote-200211/msg00321.html Here's the test cases which have changed: A requires 2:1 majority; D is the default option 3 ABD 1 BDA 1 DAB A defeats B 4:1 B defeats D 4:1 D superdefeats A 4:3 eliminate A B defeats D 4:1 B wins in previous draft, this was a tie between B and D the requirement was that D did not win Z is the default option 40 A 25 B 35 ZBA B defeats A 60:40 A defeats Z 40:35 Z defeats B 35:25 eliminate 35:25 B defeats A 60:40 A defeats Z 40:35 B wins in previous draft, Z won the requirement was that A not win Quorum of n, no supermajorities, D is the default option: 25 DAB 30 BDA 35 ABD B defeats D 65:25 A defeats B 60:30 D defeats A 55:35 eliminate 55:35 B defeats D 65:25 A defeats B 60:30 A wins unless quorum is not met in which case D wins. In the previous draft B won unless quorum was not met in which case D wins. Additionally, here's the result of the test proposed by Clinton Mead in http://lists.debian.org/debian-vote/2002/debian-vote-200212/msg00020.html A requires 3:1 majority; D is the default option 4 ABD 1 ADB 1 BDA 1 DAB A defeats B 6:1 D superdefeats A 6:5 B defeats D 5:2 eliminate A B defeats D 5:2 B wins in the previous draft, D won the requirement is that B wins ______________________________________________________________________ If there's any ambiguities or problems with this, please let me know. [And please bear with me if I seem to be asking inane questions in the course of understanding a possible problem.] Thanks, -- Raul

**Follow-Ups**:**Re: Hybrid Theory***From:*Anthony Towns <aj@azure.humbug.org.au>

**References**:**Dec 7 voting amendment draft***From:*Raul Miller <moth@debian.org>

- Prev by Date:
**Re: current A.6 draft [examples]** - Next by Date:
**Re: current A.6 draft [examples]** - Previous by thread:
**Re: Dec 7 voting amendment draft** - Next by thread:
**Re: Hybrid Theory** - Index(es):