On Sun, Feb 1, 2009 at 12:06 AM, Kristofer Munsterhjelm <[email protected]> wrote: > The vote splitting would go like this: Say a Droop quota votes { A B C } in > each permutation with equal probability, then a bunch of other candidates. > The other voters vote the other candidates randomly before any of A B C. > Then a method using Plurality with random elimination might end up > eliminating one of A, B, or C, before it finds out that a Droop quota > supports the set {A B C}. I don't know if this is actually possible, though.
If the coalition is solid, and A is the last candidate remaining, then all of those voters will vote A>(everyone else) as the 2 other candidates have been eliminated. A will now exceed the Droop quota and is immediately elected. The same logic applies for B and C. These eliminations don't have to happen in sequential rounds. Once then 2nd last candidate in the coalition is eliminated, the last member automatically exceeds the quota on the subsequent round. > Strictly speaking, it's not that difficult to meet the DPC. Just make a > DSC/DAC variant where you count all possible subsets. Elect the candidates > that the DPC say must win, then do whatever you want after that. Such a > method would be nearly useless in practice, since it would have a great > discontinuity - it wouldn't elect near-DPC-eligible candidates any more > often than it would elect candidates far from the DPC (unless the base > method somehow had this property). I am not sure how useless it would be. I do think there could be massive strategy issues though. A faction would have to be careful that they vote their own candidates as a bloc at the start. > For STV, I think the reweighting matters in letting the method discover the > Droop quotas. Again, I'm not sure. If elimination order doesn't matter, then > one could make a DPC version of Random Ballot: pick the candidate/s above > quota if there is/are any, then eliminate the candidate that ranks last on a > random uninspected ballot. Afterwards, mark that ballot inspected. If the > vote-splitting argument above works, elimination order *does* matter, > though. I don't think the order matters, so the above method would meet Droop. However, the candidate that actually represents the faction would be decided by random ballot. Depending on how you set up PR-STV methods, the intra faction election is different. With CPO-STV and Sculze-STV, I think the factional election ends up being a condorcet method. For example, if you were electing 2 seats and had the following votes 15: A1>A2>A3 10: A2>A1>A3 15: A3>A2>A1 30: C 15: B1>B2>B3 10: B2>B1>B3 15: B3>B2>B1 Standard PR-STV will go as Round 1 and 2 A2 eliminated B2 eliminated Round 3 and 4 A3 eliminated B3 eliminated Results A1: 35 C: 30 B1: 35 Thus B1 and A1 will win. In effect, in each faction/party, the winner was selected by IRV. However, using my suggestion to allow 2 different counting methods for election and elimination, the results change. The rule is - equal ranks allowed - election count -> vote divided equally - elimination count -> vote given at true strength to all Assume the voters decide to vote 15: A1>A2>A3 10: A2>A1>A3 15: A3=A2>A1 30: C 15: B1>B2>B3 10: B2>B1>B3 15: B3=B2>B1 (The x3 voters realise that they probably won't win anyway). Round 1: Election count A1: 15 A2: 10 + 15/2 = 17.5 A3: 7.5 C: 30 B1: 15 B2: 10 + 15/2 = 17.5 B3: 7.5 => nobody elected Elimination count A1: 15 A2: 10 + 15 = 25 A3: 15 C: 30 B1: 15 B2: 10 + 15 = 25 B3: 15 Hmm, 4 way tie :). I will eliminate A1 and B3 (so both types of elimination are considered). Round 3: Election count A1: xx A2: 10 + 15/2 + 15 = 32.5 A3: 7.5 C: 30 B1: 15 B2: 10 + 15 = 25 B3: xx => nobody elected Elimination count A1: xx A2: 10 + 15 + 15= 40 A3: 15 C: 30 B1: 15 B2: 10 + 15 = 25 B3: xx B1 eliminated Round 4: election count: A1: xx A2: 32.5 A3: 7.5 C: 30 B1: xx B2: 40 B3: xx B2 elected Round 5 A3 eliminated Round 6 A2 elected. A2 and B2 are elected. Thus the intra-faction election proceeded using approval. ---- Election-Methods mailing list - see http://electorama.com/em for list info
