Andy, I like the idea of iterating RRV to infinity to find the weights for a weighted voting system.
And of course,interpreted stochastically. it also gives another solution to Jobst's consensus challenge. I doubt that it is always the same as the Ultimate Lottery. Probably an example where sequential PAV differs from PAV would show that. I suspect that, unlike sequential PAV and RRV, both ordinary PAV and the Ultimate Lottery may be computationally NP-complete. Forest ----- Original Message ----- From: Andy Jennings Date: Monday, May 16, 2011 9:46 am Subject: Re: [EM] electing a variable number of seats To: [email protected] Cc: [email protected] > Forrest, > > With this profile, using RRV, Y is elected in round 1 and X is > elected in > round 2. As such, they will have equal weight. > > However, we can continue to iterate RRV, without removing these > candidates. The more times a candidate is chosen, the more > voting weight he will get. > The election continues: > Round 3: Y > Round 4: X > Round 5: Y > Round 6: Y > Round 7: X > Round 8: Y > Round 9: X > Round 10: Y > > A,B,C, and D are never elected and X and Y will get 40% and 60% > of the > voting power, respectively. > > This method of using RRV and determining the voting power as the > number of > seats goes to infinity is not equivalent to the Ultimate Lotter > multiwinnermethod you describe, is it? > > Andy > > > > On Thu, May 12, 2011 at 12:35 PM, wrote: > > > If, in addition to allowing the number of seats to vary, you > are willing to > > allow different weights for different > > seats, then there is another solution: find the best > proportional lottery L > > (e.g. by use of the Ultimate > > Lottery), and then, instead of using the lottery L to choose > one of the > > candidates, use it to give weights > > to the candidates, and then seat only the ones with positive > weights..> > > For example, if the range ballots were > > > > 20 A(100) X(90) > > 20 B(100) X(90) > > 30 C(100) Y(80) > > 30 D(100) Y(80), > > > > then L would give 40% to X and 60% to Y, > > > > so X and Y would be the only candidates seated, and their respective > > weights would be 40 and 60 > > percent. > > > > Most of the other methods proposed would seat four candidates > A, B, C, and > > D, and give them equal > > weight. > > > > Which do you think is best in this case? > > > > Andy, how would you compare these two outcomes with RRV? > > > > ---- > > Election-Methods mailing list - see http://electorama.com/em > for list info > > > ---- Election-Methods mailing list - see http://electorama.com/em for list info
