[EM] electing a variable number of seats

[Andy Jennings]

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 multiwinner
method you describe, is it?

Andy



On Thu, May 12, 2011 at 12:35 PM, <fsimmons at pcc.edu> 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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