This is a drastically chopped down version of my response to the Buddha/Eudora message trilogy. I want to focus on one issue.
On Wed, Nov 29, 2000 at 06:17:13PM -0500, Buddha Buck wrote: > Option: Smith/Condorcet > > Of the n options in the Smith set, order the n*(n-1) pairwise results by > number of votes for the winning choice, strongest to weakest. (e.g., if A > beat B by 100:50, and B beat C by 76:74, order them as AB first, BC second, > because 100 is bigger than 76). > > Drop the weakest defeat iteratively until one option is unbeaten. That > unbeaten option is the winner. > > Advantages: Variants have been studied for 200+ years. > Disadvantages [I picked this mechanism because it's the first one for which you claimed "no disavantages". I believe that your "disadvantages" for these various methods are incorrect in a large number of cases, but I don't feel like tackling that issue point by point.] I'm trying to figure out how to implement the concept of "supermajority" in this voting system. I don't think it can be done in a reasonable fashion, because in this system (and many of the others), you're voting against yourself. Here's an example set of votes (for a ballot which offers "ABCDE" as options): ACBDE AD AEBD BACED BEC C CABED CADB CDA E Here's the condorcet strengths: 7:2 C:D 7:2 A:E 6:1 A:D 6:2 A:B 6:3 C:E 5:2 B:E 5:3 C:B 5:3 B:D 5:4 E:D 5:4 C:A C wins (it's unbeaten). Now, if we introduce a 3:1 supermajority which only affects C, C loses: 7 : 2 A:E 6 : 1 A:D 6 : 2 A:B 5 : 2 B:E 5 : 3 B:D 5 : 4 E:D 4 : 1 2/3 A:C 3 : 1 2/3 B:C 2 1/3: 2 C:D 2 : 3 C:E And, that makes sense, because I constructed that set of votes with a linear random number generator. But, let's try a simpler multi-option ballot, with everyone in favor. Ballot: ABC, 3:1 supermajority required for A, 10 votes, all cast as: ABC. If there was no supermajority, the ballots would look like: 10:0 A:B 10:0 B:C 10:0 A:C And you can figure out by inspection that A wins. However, with the 3:1 supermajority which affects A, you get: 10 : 0 B:C 3 1/3: 0 A:B 3 1/3: 0 A:C B wins. There is a similar flaw even without supermajority (by indicating a second or even third preference, I can tip the balance in favor of another option, causing it to win), but that's a bit more subtle to talk about. What's interesting is that most of the voting mechanisms you posted about share this characteristic about supermajority votes. [Of course, the characteristic goes away if you offer a simple 2 choice ballot, because in that circumstance they're all equivalent.] -- Raul P.S. pseudocode *is* poorly written english.
