- A defeats B if more votes prefer A over B than B prefer over A.
- A challenges B if more than or an equal number of votes prefer A over B than prefer B over A.
- A defeats B by X, where X is equal to the difference between the number of votes that prefer A over B and the number of votes that prefer B over A, if A defeats B.
- A superchalleges B, where A has a supermajority requirement of (X:Y) if the number of votes that prefer A over B multiplied by Y is greater than or equal to the number of votes that prefer B over A multiplied by X.
- A is considered if A superchallenges all options with supermajority requirements less than A.
- A is considered if A challenges B, where B has supermajority requirements greater than or equal to A.
- A has a beatpath to B of strength X, if A and B are considered and A defeats B by X, or if A, B and C are considered and A defeats C by Y and C has a beatpath to B of strength Z, where X is equal to the minimum of Y and Z.
- A has a beatpath to B of strength 0 if there is no non-zero X such that A has a beatpath to B of strength X.
- A has a beatpath win to B if the largest X such that A has a beatpath to B of X is greater than the largest Y such that B has a beatpath to A of Y.
- A is a finalist if A is considered and there is no B such that B has a beatpath win to A.
- A is a winner if A is a finalist and there is no B such that the casting vote prefers B over A.
I've pieced together an implimentation in Haskell, if anyones interested. I don't know how badly its broken though.
Anyway, heres the results of CCSSD compared to the draft, sprinkled with objectiveness then smothered in opinion.
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Raul Miller wrote:
A requires 2:1 majority; D is the default optionCCSSD: B wins.
3 ABD
1 BDA
1 DAB
D defeats A 4:3
A defeats B 4:1
B defeats D 4:1
eliminate 4:1
D defeats A 4:3
tie between B and D
______________________________________________________________________
Here, the B voters are penalised for being sincere. The B voters as a whole prefer A over B, and being sincere voters, propose A and vote sincirely for it. If the B voters were insincere, by voting B over A, they would of recieved a more preferable result.
In my opinion, if a supermajority option X does not win, then the winner should be the condorcet winner of the non-supermajority options or a supermajority option which is not X, unless supermajority option X is involved in a cycle involving at least one other supermajority option and one other non-supermajority option.
That principle seems to stop the supermajority option spoiling in this case, I'm not sure about others.
Raul Miller wrote:
A requires 2:1 majority; D is the default optionCCSSD: B Wins
60 ABD
30 BAD
10 DBA
B defeats D 90:10
A defeats D 90:20
A defeats B 60:40
A wins
______________________________________________________________________
This is more a matter of opinion on my behalf, but I think in this case, A should have to superdefeat both B and D to be declared winner. To take a hypothetical example, let
A: Change constitution (2:1 Supermajority)
B: Further discussion.
D: Do nothing (Default)
Here, change constitution only has 60:40 support verses further discussion. Not many people want to 'do nothing', but a significant 'superminority', (>= 34), would rather discuss further than change now. Using the current system, a weak default option (as in this case) will make supermajority protection have little effect, despite an other strong non supermajority option. In my opinion, a weak default option (possibly because it is obsolete), shouldn't nullify supermajority protection when there are other strong non-supermajority options.
Raul Miller wrote:
CCSSD: B winsA requires 2:1 majority; N is the default option 4 cAbN 1 cNAb 3 bcNA 3 AbcNN defeats A 8:7 c defeats N 11:0 b defeats N 10:1 A defeats b 8:3 c defeats A 8:3 b defeats c 6:5 eliminate 6:5 N defeats A 8:7 c defeats N 11:0 b defeats N 10:1 A defeats b 8:3 c defeats A 8:3 c wins ______________________________________________________________________
In this vote, the 3 AbcN voters could insincerly vote bAcN.
Then B would defeat A 6:5.
B already defeats C and N pairwise.
So B is condorcet winner.
By voting insincerely, the 3 AbcN voters now have a more favourable result, because they prefer B, the winner when they vote insincerely (bAcN), over C, the winner when they vote sincerely. That is, the 3 AbcN voters benefit by voting insincerely.
This is another example of the rough principle I said in the first example that _generally_ the condorcet winner of the non-supermajority options should win if the supermajority does not win. This seems to select the condorcet winner of non-supermajority options without requiring voters to vote insincerly to achieve that result.
Although, I'm if using a method that selects B as the winner of the original vote such as CCSSD solves the problem of insincere voting or just shifts it elsewhere.
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In conclusion, I've got a vibe that treating the default option differently to other non-supermajority options regarding supermajority defeats can reduce stability and encourage insincere voting. Though nothing hard and fast though. Point out places where CCSSD does worse than the current draft, in the above examples or others, because I've probably got a biased view of my own proposal. Anyway, hope you find these psudeo-random thoughts useful.
Clinton
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