[EM] PR-STV with approval based elimination

[Kristofer Munsterhjelm]

Raph Frank wrote:
> On Fri, May 1, 2009 at 6:53 PM, Kristofer Munsterhjelm
> <km-elmet at broadpark.no> wrote:
>> If there are two seats and the "left" and "right" factions are of equal
>> size, and both have respective centrists, the outcome should have a "left
>> centrist" (which is close to the median voter of the left faction) and a
>> "right centrist" (which is close to the median voter of the right faction).
>> That there is one member of the left group and one member of the right group
>> in the outcome is explicit proportional representation, but that each
>> representative is a centrist within his group is compromise.
> 
> However, standard PR-STV will effectively decide which left candidate
> wins using IRV, which isn't a centrist finding method.

That's true. STV's core method, IRV, is quite bad. What STV does have 
going for it is that it is Droop proportional and well known.

Other methods may be better. I've already mentioned QPQ, though I'm 
unsure of what its core method is; and also, Schulze STV seems to be 
better than STV by my simulations (and reduces to Schulze's method, 
which is Condorcet, in the single winner case).

> What about instead of making it general, voters are allowed to vote
> for more than 1 candidate as first choice.
> 
> All first choice candidates are considered approved for calculating elimination.
> 
> Otherwise, the vote gets split equally between all remaining first
> choice candidates.
> 
> Another issue is if the approval votes should also be rescaled once a
> candidate is elected.

The problem in using any other method than Plurality for counting the 
votes in an STV method is that of elimination. If someone votes for A 
with strength 1 and B with strength 0.5, and A wins, then how much do 
you downweight that voter? The A voters should be reweighted so that the 
surplus is distributed evenly, then A is eliminated, but if this causes 
score changes, then the effective voting power is no longer equal to the 
surplus.

I ran into that while trying to generalize STV to work with Borda (and 
more generally, any sort of weighted positional system). Approval 
without rescaling might dodge it (since the voting power doesn't change 
by removing a candidate), but Range with rescaling wouldn't.