[EM] electing a variable number of seats

[fsimmons at pcc.edu]

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: fsimmons at pcc.edu
Cc: election-methods at lists.electorama.com

> 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?
> >
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